FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM FACULTY OF MATHEMATICS AND NATURAL SCIENCE

FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM FACULTY OF MATHEMATICS AND NATURAL SCIENCE STATISTIKA Statistics

DOKTOR Doctoral

x

Menghasilkan lulusan pascasarjana Statistika yang memiliki integritas moral tinggi, kemampuan pengembangan dan penerapan statistika.

x

Menghasilkan penelitian pengembangan dan penerapan statistika yang bertaraf internasional.

x

Menghasilkan penerapan statistika yang berkontribusi pada penyelesaian masalah riil di masyarakat.

Kompetensi Lulusan

Graduate Competence

x

To produce statistical postgraduate students which have high morality, integrity and ability in improvement and implementation of statistics

x

To produce development research implementation at international levels

x

To produce statistical implementations which contribute to real problem solving

and

statistical

Kurikulum/Curriculum ITS : 2009-2014

Program Studi Department Jenjang Pendidikan Programme

1

STRUKTUR KURIKULUM/COURSE STRUCTURE No.

Kode MK Code SEMESTER I 1 SS09 3301 2

SS09 3302

3

SS09 3303

SEMESTER II 1 SS09 3303 2 3

Nama Mata Kuliah (MK) Course Title

sks Credits

Matematika Statistika Statistical Mathematics Model Linier yang Diperluas Generalized Linear Models Disertasi 1 Dissertation 1 Jumlah sks/Total of credits

3

Disertasi 2 Dissertation 2 Mata Kuliah Pilihan 1 Optional Subjects/Course 1 Mata Kuliah Pilihan 2 Optional Subjects/Course 2 Jumlah sks/Total of credits

2

3 2 8

3 3 8

MATA KULIAH PILIHAN SEMESTER II/ Optional Subjects/Course Semester II SS09 3201

2

SS09 3202

3

SS09 3203

4

SS09 3204

5

SS09 3205

5

SS09 3206

SEMESTER III 1 SS09 3303

Analisis Multivariate Multivariate Analysis Metode Permukaan Respon Response Surface Methods Regresi Parametrik dan Semi Parametrik Parametric and Semiparameteric Regressions Analisis Bayesian Bayesian Analysis Analisis Deret Waktu Multivariat dan Nonlinier Non Linear and Multivariate Time Series Analysis Statistika Spasial Spatial Statistics

3

Disertasi 3 Dissertation 3

6 Jumlah sks/Total of credits

SEMESTER IV 1 SS09 3303



3 3 3

6

6 6

Jumlah sks/Total of credits SEMESTER VI 1 SS09 3303

3

6 Jumlah sks/Total of credits

SEMESTER V 1 SS09 3303

3


6 6

Jumlah sks/Total of credits

6


1

2

SILABUS KURIKULUM/COURSE SYLLABUS

TUJUAN PEMBELAJARAN/ LEARNING OBJECTIVES

Credits: Tiga/Three Semester: I Memahami konsep percobaan random, variabel random, ruang probabilitas, fungsi distribusi, ekspektasi, konvergensi variabel random, model-model probabilitas, hukum bilangan besar dan teorema limit pusat dan fungsi variabel random. Mampu memahami konsep penaksiran, metode penentuan penaksir, sifat-sifat penaksir, fungsi kerugian dan resiko, statistik kecukupan. Keluarga eksponensial, ketidakbiasan, equivariance, uniformly most powerfull test, ketidakbiasan untuk uji hipotesis, hipotesis linier dan hipotesis multivariate linier. Understanding concepts of random experiments, random variables, probability measures, distribution functions, expectations, random variables convergence, probability models, Low of Large Number, Central Limit Theorem and functions of random variable. Able to understand estimation concepts, estimation methods, estimator characteristics, risk functions and sufficient statistics. Exponential family, unbiased, equivariance, uniformly most powerfull test, unbiased for hypothesis test, linear hypothesis and linear multivariate hypothesis. x

KOMPETENSI/ COMPETENCY

x x

x

Memahami konsep percobaan random, variabel random, ruang probabilitas, fungsi distribusi, ekspektasi, konvergensi variabel random, model-model probabilitas, hukum bilangan besar dan teorema limit pusat dan fungsi variabel random. Mampu memahami konsep penaksiran, metode penentuan penaksir, sifat-sifat penaksir, fungsi kerugian dan resiko, statistik kecukupan. Mampu memahami konsep Keluarga eksponensial, ketidakbiasan, equivariance, uniformly most powerfull test, ketidakbiasan untuk uji hipotesis, hipotesis linier dan hipotesis multivariate linier. Understanding

concepts

of

random

experiments,

random


MATA KULIAH/ COURSE TITLE

SS09 3301: Matematika Statistika SS09 3301: Statistical Mathematics

3

x x

x

x x x x

PUSTAKA UTAMA/ REFERENCES

Variabel random, ruang probabilitas, fungsi distribusi, ekspektasi dan momen, konvergensi variabel random, fungsi krakteristik, distribusi bersyarat dan kebebasan stokastik, hukum bilangan besar, distribusi khusus, distribusi fungsi variabel random, distribusi limit Pengantar teori peluang Transformasi variabel random dan statistik berurut Fungsi pembangkit momen Distribusi sampling, Penaksiran; penaksiran titik, penaksiran interval; statistik kecukupan, ketakbiasan, penaksir efisien, penguji hipotesis; UMPT; uji hipotesis pada sampling distribusi normal; uji khi-kuadrat, hipotesis linier pada berbagai model Anova dan Regresi; hipotesis multivariate linier dan hipotesis pada model non linier

x

Random variables, probability spaces, distribution functions, expectation and moment, random variable convergence, characteristic functions, bayes distributions and stochastic independency, Low of Large Number, particular distributions, distributions of random variable function, limit distributions x Introduction to probability theory x Random variable transformation and order statistics x Moment generating functions. Sampling distributions, inference; point estimations, interval estimations, sufficient statistic, unbiased statistic, efficient statistic and hypothesis test; Unbiased Most Powerful Test ; hypothesis test for normal distribution sample, Chi-square test, linear hypothesis for ANOVA and regression models; linear multivariate hypothesis and non linear model hypothesis x Bartoszynski, R.and Magdalena, N.B, Probability and Statistical Inference; New York : John Wiley & Sons, ,1996. x Bhat, B.R, Modern Probability Theory, New York : John Wiley & Sons,1981. x Hogg, R.V. and Tanis, E.A., Probability and Statistical Inference ,New York : Macmillan Publishing Co., 1993.


POKOK BAHASAN/ SUBJECTS

variables, probability measures, distribution functions, expectations, random variables convergence, probability models, Low of Large Number, Central Limit Theorem and functions of random variable. Able to understand estimation concepts, estimation methods, estimator characteristics, risk functions and sufficient statistics. Able to understand Exponential family, unbiased, equivariance, uniformly most powerfull test, unbiased for hypothesis test, linear hypothesis and linear multivariate hypothesis.

4

x x x


SS09 3302: Model Linier yang Diperluas SS09 3302: Generalized Linear Models Credits: Tiga/Three Semester: I Memahami dan mampu menganalisis model linier yang diperluas serta menerapkan dengan variabel respon berdistribusi normal dan distribusi lainnya. Mengerti dan memahami model dasar, penggolongan silang, dwi arah, komponen ragam, mampu mengembangkan model-model linier untuk regresi baik dengan rank penuh ataupun tidak baik untuk satu respon atau multirespon. Understanding and able to analyze generalized linear models as well as its implementation to response variables which normally and non normally distributed. Understanding methods of basic models, two way models and cross clustering models, variance components, able to make improvement in regression linear models with full rank and non full rank for single response or multiresponse. x x

KOMPETENSI/ COMPETENCY x x

Memahami dan mampu menganalisis model linier yang diperluas serta menerapkan dengan variabel respon berdistribusi normal dan distribusi lainnya. Mengerti dan memahami model dasar, penggolongan silang, dwi arah, komponen ragam, mampu mengembangkan model-model linier untuk regresi baik dengan rank penuh ataupun tidak baik untuk satu respon atau multirespon. Understanding and able to analyze generalized linear models as well as its implementation to response variables which normally and non normally distributed. Understanding methods of basic models, two way models and cross clustering models, variance components, able to make improvement in regression linear models with full rank and non full rank for single response or multiresponse.



Lehman, E.L., Theory of Point Estimation, New York : John Wiley & Sons, 1983. Lehmann, E.L., Testing Statistical Hypothesis, New York : John Wiley & Sons,1986. Shorack, G.R, Probability for Statisticians, New York : Springer, 2000.

5

x

x


x

x

x

x x


x x x x x

Regresi Linier, penaksir parameter dengan metode OLS, WLS, Maksimum Like lihood, pengujian parameter model, analisis sisaan (asumsi klasik), mendeteksi pencilan dan identifikasi pengamatan berpengaruh. Model-model regresi meliputi: non linear semu, dummy variabel dan polinomial. Seleksi variabel bebas yang meliputi: pemilihan model terbaik, ridge regresi dan regresi komponen utama. Kuadrat terkecil parsial dan estimasi Robust, Bootstrap dan Jacknife. Pendugaan dan pengujian hipotesis beberapa model linear. Model klasifikasi satu-arah dan dwi-arah. Perluasan model-model sel rataan. Model dengan peubah penyerta. Model pengaruhpengaruh campuran dan pendugaan komponen ragam, fungsi estimabel, model linier dengan rank penuh ataupun tidak baik untuk satu respon atau multirespon juga untuk model non linier. Linear regression, parameter estimation by using Ordinary Least Square, Weighted Least Square and Maximum Likelihood Methods, testing for model parameters, residual analysis (classic assumptions), outlier detections and identification for dominant observations. Regression models: quasi non linear, dummy variables and polynomial. Independent variable selections: the best model selection, Ridge regression and principal component regressions. Partial Least Square and robust estimations, Bootstrap and Jackknife. Inference and hypothesis test for linear models. One way and two ways classification models. Extended mean cell models. Models with covariates. Mixed models. Variance Component estimation, Estimable functions, full rank and non full rank linear model for single response or multi responses. Drapper, N.R. and Smith, H., Applied Regression Analysis, New York : John Wiley & Sons, 1981. Hocking, R.R., Methods and Applications of Linear Models Regression and analysis of Variance, New York : John Willey & Sons Inc., 1996. Kleimbaum, Applied Regression and Multivariate Analysis and Other Multivariate Method; New York : John Wiley & Sons, 1988. McCullagh. P and Nelder, J.A, Generalized Linear Models, New York: Chapman and Hall, 1990 Myers, R.H. and Milton, J.S., A First Course in the Theory of Linear Statistical Models, Boston : PWS-KENT Publ. Co., 1991. Rao, C.R., Linear Statistical Inference and Its Applications; 2 ed., New Delhi : Eastern Private Limited, 1973. Searle, S.R., Linear Models for Unbalanced data, New York : John nd


x

6

x x x




SS09 3303: Disertasi SS09 3303: Dissertation Credits: Duapuluh delapan/Twenty eight Semester: I-VI Mampu mengintegrasikan secara terpadu dan komprehensif mata kuliah yang didapat untuk mengembangkan teori. Able to comprehensively integrate the given subjects for further theoretical improvement. x

Mampu mengintegrasikan secara terpadu dan komprehensif mata kuliah yang didapat untuk mengembangkan teori.

x

Able to comprehensively integrate the given subjects for further theoretical improvement.

x

Kegiatan penelitian mandiri dimulai dari pembuatan proposal penelitian, seminar proposal, dan pelaksanaan penelitian. Hasil penelitian harus diseminarkan dan dipertanggung jawabkan dihadapan penguji dalam ujian Disertasi.

x x x


Self research which cover designing research proposal, seminar, and carrying out the research. The result of research should be presented and will be examined.



Wiley & Sons Inc., 1987. Seber, A.F. and Lee,A.J, Linear Regression Analysis, New York : John Willey & Sons, 2003. Sen, A. and Srivastawa, M., Regression Analysis : Theory, Method and Application, New York : Springer Verlag, 1990. Weisberg, S, Applied Linear Regression; New York : John Wiley & Sons, 1986.

7



Credits: Tiga/Three Semester: II Mampu membedakan dan menginterpretasikan data univariat, analisis eksplorasi dan pereduksi dimensi, pengujian hipotesis data multivariat, metode multisampel dan analisis diskriminan, model linier multivariate. Able to distinguish and interpret the univariate data, explorative analysis and dimensional reduction, hypothesis test for multivariate data, multisampling methods, discriminant analysis, and multivariate linear models. x

Mampu membedakan dan menginterpretasikan data univariat, analisis eksplorasi dan pereduksi dimensi, pengujian hipotesis data multivariat, metode multisampel dan analisis diskriminan, model linier multivariate.

x

Able to distinguish and interpret the univariate data, explorative analysis and dimensional reduction, hypothesis test for multivariate data, multisampling methods, discriminant analysis, and multivariate linear models.

x

Review Aljabar linier, fungsi distribusi multivariat : Multinormal, 2

x POKOK BAHASAN/ SUBJECTS

x

x

Wishart, T Hotelling. Analisis eksplorasi : Biplot, analisis korespondensi, PCA, analisis faktor, analisis cluster, multidimensional scaling dan analisis konjoint. Analisis konfirmasi : pengujian satu mean dan CI; pengujian dua mean dan CI; disain eksperimen (MANOVA) : one-way, two-way; faktorial diskriminan linier, model linier multivariate. Review of Linear algebra, multivariates distribution functions such 2

x

as Multinomal, Wishart, T Hotelling. Exploration analysis by using Biplot, Correspondence analysis, Principal Component Analysis, Factor Analysis, Cluster Analysis, Multidimensional scaling and Conjoint analysis.



SS09 3201: Analisis Multivariat SS09 3201: Multivariate Analysis

8

x

x x x x x x




SS09 3202: Metode Permukaan Respon SS09 3202: Response Surface Methods Credits: Tiga/Three Semester: II Mahasiswa mengerti, memahami dan menguasai teori rancangan percobaan , penaksiran parameter , uji hipotesis dan penentuan kondisi optimum pada beberapa model respon surface untuk satu respon dan multirespon baik linier atau non linier. Knowing and deep understanding experimental design theory, parameter estimation, hypothesis test and determining the optimum condition of surface response models for single response and multiresponse ( linear or non linear). x

mengerti, memahami dan menguasai teori rancangan percobaan , penaksiran parameter , uji hipotesis dan penentuan kondisi optimum pada beberapa model respon surface untuk satu respon dan multirespon baik linier atau non linier.

x

Knowing and deep understanding experimental design theory, parameter estimation, hypothesis test and determining the optimum condition of surface response models for single response and multiresponse ( linear or non linear).



Confirmatory analysis which cover hypothesis test for one mean and its confidence interval, hypothesis test for two mean and its confidence interval; experimental design (MANOVA) for one-way, two-ways; Linear factorial discriminant, multivariate linier models. Cristensen, R, Models for Multivariate , Time series and Spatial Data, New York : Springer, 1991. Dillon, W.K. and Matthew, G., Multivariate Analysis, Methods and Application, New York : John Wiley & Sons, 1984. Fahremeir, L. and Tutz, G., Multivariate Statistical modeling Based on generalized Linear Models, New York : Springer, 1994. Jonhson, R., Applied Multivariate Statisticals Analysis, New Jersey : Prentice-Hall Inc., 1982. Lebart, L., Morineau A. and Warwick, K.M, Multivariate Descriptive Statistical Analysis, New York : John Wiley & Sons, 1984. Timm, N.H., Multivariate Analysis with Applications in Education and Psychology, California : Wadsworth Publishing Co Inc., 1975.

9


x

x x x


x x x x


Konsep dasar permukaan respon, rancangan percobaan dan metode penaksiran parameter, penentuan kondisi optimum pada model orde 1, orde 2. Analisis permukaan multirespon linier , Analisis permukaan multirespon linier dengan blok dan Analisis permukaan respon non linier. Basic concept of response surface, experimental design and parameter estimation methods, determination of optimum conditions for 1st order models, 2nd order models. linear multiresponse surface analysis, blocking linear multiresponse surface analysis and non linear multiresponse surface analysis. Box, G P. et al., Statistics for Eksperiments, New York : John Willey & Sons, 1978. Cristensen, R, Models for Multivariate , Time series and Spatial Data, New York : Springer, 1991. Kempthorne, O, Design and Analysis of Experiments, New York : John Willey, 1980. Khuri,A.I and Cornell, J.A, Response Surface Methodology, New York : Marcel Dekker, Mc., 1996. Myers, R. H, Response Surface Methodology, Boston : Allyn and Bacon, inc, 1971.

SS09 3203: Regresi Nonparametrik dan Semiparametrik SS09 3203: Nonparametric and Semiparametric Regression Credits: Tiga/Three Semester: II


KOMPETENSI/

Mengetahui beberapa model regresi nonparametrik dan semiparametrik dan berserta sifat-sifatnya, dan mampu memodelkan perilaku data berdasarkan pendekatan regresi nonparametrik dan semiparametrik. Knowing and understanding nonparametric and semi parametric regression models as well as its characteristics. Able to model data by using nonparametric and semi parametric regressions approach based on data behavior. x

Mengetahui

beberapa

model

regresi

nonparametrik

dan


x

10

semiparametrik dan berserta sifat-sifatnya, dan mampu memodelkan perilaku data berdasarkan pendekatan regresi nonparametrik dan semiparametrik. x

Knowing and understanding nonparametric and semi parametric regression models as well as its characteristics. Able to model data by using nonparametric and semi parametric regressions approach based on data behavior.

x

Konsep dasar regresi nonparametrik dan semiparametrik, serta perbedaan dengan regresi parametrik. Estimasi kurva regresi nonparametrik dan semiparametrik dengan pendekatan Kernel, Deret Ortogonal, Spline, k-NN, Deret Fourier dan Wavelets, beserta sifat-sifatnya.


x x x x x x


x x x x x x x

Basic concepts of nonparametric and semi parametric regressions and its difference to parameteric models. Estimation of nonparametric and semi parametric regression curve by using Kernel, Orthogonal sequence, Spline, K-NN, Fourier sequence and Wavelets approach as well as its characteristics. Chui,C.K., An Introduction to Wavelets, New York : Academic Press, Inc., 1992. Enbank, R.L., Spline Smoothing and Nonparametric Regression, New York : Marcel Dekker Ins, 1988. Green, P.J. and Silverman, B.W., Nonparametric Regression and Generalized Linear Models, London : Chapman and Hall, 1994. Hardle, W., Applied Nonparametric Regression, New York : Cambridge University Press, 1990. Hardle, W., Smoothing Techniques With Implementation in S, New York : Spinger Verlag, 1991. Luenberger, D.G., Optimation by Vector Space Methods, New York : John Wiley and sons, 1969. Prenter, P.M., Spline and Variational Methods, New York : John Wiley and Sons, 1975. Rao, B.L.SP., Nonparametric Functional Estimation, New York : Academic Press, Inc, 1983. Schumaker, L.L, Spline Functions: Basic Theory, New York : John Wiley and sons, 1981. Thompson, J.R., and Tapia, R.A., Nonparametric Function Estimation, Modelling and Simulations, Philadelpia : SIAM, 1990. Wahba, G., Spline Models for Observational Data, Pensylvania : SIAM, 1990.


COMPETENCY

11


Credits: Tiga/Three Semester: II Mahasiswa mengerti, memahami dan menguasai teori Bayesian dan Empirical Bayes serta mampu mengaplikasikannya ke dalam permasalahan real. Understanding and able to implement Bayesian theory and empirical bayes to the real cases. x

Mengerti, memahami dan menguasai teori Bayesian dan Empirical Bayes serta mampu mengaplikasikannya ke dalam permasalahan real.

x

Understanding and able to implement Bayesian theory and empirical bayes to the real cases.

x

Teorema Bayes, Bayesian inference, Data augmentation, Singleparameter model, Multi-parameter model, Hirarchical model dan multi-level model, Jenis prior, prior odds, posterior, posterior odds, Bayes faktor, Bayesian non-Normal dan neo-Normal model, Bayesian Reliability, Mixture densitas, mixture regresi, mixture of mixture. Pemilihan model terbaik dengan Bayesian, Struktur Perkalian Distribusi, MCMC. Simulasi stokastik.




x x

Bayes theorem, inference Bayesian, augmentation data, models for single parameter, models for multi parameters, hierarchical models and multilevel models. Types of prior, odds prior, posterior, odds posterior, bayes factors, non normal Bayesian and neo normal models, Bayesian Reliability, density mixture, mixture regressions, mixture of mixture. x The best model selection by using Bayesian, distribution cross structure, MCMC and stochastic simulations. x Box, G. E. P. and Tiao, G. C., Bayesian Inference in Statistical Analysis, Addison-Wesley : Reading, MA, 1973. x Carlin, B. P. and Louis, T. A., Bayes and Empirical Bayes Methods for Data Analysis, London : Chapman &Hall, 1996. x Casella, G. dan Berger, R. L., Statistical Inference, California:



SS09 3204: Analisis Bayesian SS09 3204: Bayessian Analysis

12

x x x x x x x


Duxbury, 2002. Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B., Bayesian Data Analysis, London : Chapman & Hall, 1995. Martz, H.F. and Waller, R. A., Bayesian Reliability Analysis, New York : John Wiley & Sons, 1982. McLachlan G. and Basford K., Mixture models: inference and application to clustering. Marcel and Decker Inc, 1988. Tanner, M. A., Tools for Statistical Inference : Methods for the Exploration of Posterior Distributions and Likelihood Functions, 3 rd edn, New York : Springer-Verlag, 1996. Titterington M., Makov G., and Smith A.F.M., Statistical analysis of finite mixtures. UK : Willey, 1985. Zellner, A., An Introduction to Bayesian Inference in Econometrics, New York : Wiley, 1971. Software : WinBUGS 1.4, Weibull++6, MixS.

SS09 3205: Analisis Deret Waktu Multivariate dan Non linier SS09 3205: Non Linear and Multivariate Time Series Analysis


Memahami konsep-konsep statistika dalam model time series multivariat (ARIMAX, Model Intervensi, Fungsi Transfer, VARIMA, State-Space, dan VARIMAX), model-model time series nonlinier (TAR, STAR, ASTAR, dan AR-NN), model time series nonparametrik, model time series long memory (ARFIMA), dan model time series untuk varians tidak homogen (ARCH, GARCH, dan MGARCH). Dapat memodelkan time series yang multivariat, nonlinier, dan mengandung pola long memory, serta tidak homogen variansnya. Understanding statistical concept in multivariate time series models (ARIMAX, interventional models, transfered functions, VARIMA, StateSpace and VARIMAX), non linear time series models (TAR, STAR, ASTAR and AR-NN), nonparametric time series models, long memory time series models (ARFIMA) and time series models for non homogenous variance (ARCH, GARCH and MGARCH). Able to modelled time series data of multivariate case, non linear data, long memory data and non


Credits: Tiga/Three Semester: II

13

homogenous varians data.

x KOMPETENSI/ COMPETENCY

x

x x x x x POKOK BAHASAN/ SUBJECTS

x x x x x

Memahami konsep-konsep statistika dalam model time series multivariat (ARIMAX, Model Intervensi, Fungsi Transfer, VARIMA, State-Space, dan VARIMAX), model-model time series nonlinier (TAR, STAR, ASTAR, dan AR-NN), model time series nonparametrik, model time series long memory (ARFIMA), dan model time series untuk varians tidak homogen (ARCH, GARCH, dan MGARCH). Dapat memodelkan time series yang multivariat, nonlinier, dan mengandung pola long memory, serta tidak homogen variansnya. Understanding statistical concept in multivariate time series models (ARIMAX, interventional models, transfered functions, VARIMA, State-Space and VARIMAX), non linear time series models (TAR, STAR, ASTAR and AR-NN), nonparametric time series models, long memory time series models (ARFIMA) and time series models for non homogenous variance (ARCH, GARCH and MGARCH). Able to modelled time series data of multivariate case, non linear data, long memory data and non homogenous varians data. Konsep proses stasioner univariat dan multivariat, koefisien korelasi silang (CCF), matrik autokorelasi silang (MACF) dan matrik autokorelasi parsial (MPACF). Model Intervensi Fungsi Pulse, Fungsi Step, dan Model Intervensi Multi Input Fungsi Pulse dan/atau Step. Model Fungsi Transfer Multi Input. Model VARIMA, State-Space, dan VARIMAX. Uji deteksi nonlinearitas dalam time series: Uji Reset, Uji White, dan Uji Terasvirta. Model Threshold Autoregressive (TAR), Smooth Transition Autoregressive (STAR), Adaptive Smooth Transition Autoregressive (ASTAR), dan Auto-regressive Neural Network (AR-NN). MARS untuk analisis time series. Difference fraksional dan Model ARFIMA. Model ARCH, GARCH, dan MGARCH. Studi kasus untuk model time series multivariate dan nonlinier. Concept of univariate and multivariate stationer process, Cross Corrrelation Coeficients (CCC), Matrix of Autocorrelation Functions (MACF) and Matrix of Partial Autocorrelation Functions (MPACF). Intervention models of Pulse functions, Step functions, and Multi Input Intervention Models of Pulse and/or Step Functions. Models of Multi Input Transfer Functions, VARIMA models, StateSpace, dan VARIMAX. Non linearity detection test in time series : Reset Test, White Test and Terasvirta Test. Threshold Autoregressive Models (TAR), Smooth Transition Autoregressive (STAR), Adaptive Smooth Transition Autoregressive


x

14

x x x x x x x x x



SS09 3206: Statistika Spasial SS09 3206: Spatial Statistics Credits: Tiga/Three Semester: II Mengerti dan memahami pendugaan dan pemodelan korelasi spasial, prediksi dan interpolasi, mapping pola, regresi spasial, model spatial survival, Analisis spatial Bayesian dan pemodelan spatio-temporal. Understanding and able to implement spatial correlation models and estimations, forecasting and interpolation, pattern mapping, spatial regressions, survival spatial models, Bayesian spatial analysis and spatio temporal models. x


Mengerti dan memahami pendugaan dan pemodelan korelasi spasial, prediksi dan interpolasi, mapping pola, regresi spasial, model spatial survival, Analisis spatial Bayesian dan pemodelan spatio-temporal.



(ASTAR), dan Auto-regressive Neural Network (AR-NN). MARS for time series analysis. Fractional difference and ARFIMA models. ARCH, GARCH, and MGARCH Models. . Case study in multivariate time series and non linear models. Brockwell, P.J. and Davis, R.A., Time Series: Theory and Methods, 2nd Edition, New York: Springer-Verlag,1991. Box, G.E.P., Jenkins, G.M., and Reinsel, D., Time Series Analysis: Forecasting and Control; 2nd Edition, San Fransisco: Holden Day, 1994. Wei, W.W.S., Time Series Analysis: Univariate and Multivariate Methods. Second edition, USA: Addison-Wesley Publishing Co.,2006. Shumway, R.H. and Stoffer, D.S., Time Series Analysis and Its Applications with R Examples. 2nd edition, New York: Springer, 2006. Christensen, R., Linear Models for Multivariate, Time Series and Spatial Data, New York : Springer-Verlag, 1991. Priestley, M.B., Spectral Analysis and Time Series, London : Academic Press, 1981. Tong, H., Nonlinear Time Series. John Wiley & Sons, 1994. Ripley, B.D., Pattern Recognition and Neural Networks. Cambridge, 1996.

15

Understanding and able to implement spatial correlation models and estimations, forecasting and interpolation, pattern mapping, spatial regressions, survival spatial models, Bayesian spatial analysis and spatio temporal models.

x

Pendugaan dan pemodelan korelasi spasial (estimasi variogram, MLE, fitting parametric models), Bayesian spatial statistics (Bayesian estimation, Bayesian kriging, Bayesian priors for covariance parameters, Hierarchical Bayesian methods). Prediksi dan interpolasi (ordinary kriging, cokriging), Mapping pola titik, Regresi spasial dan neighborhood analysis, model spatial survival, Pemodelan spatio-temporal.


x

x x x x PUSTAKA UTAMA/ REFERENCES

x x x x

Spatial correlation models and estimations (variogram estimation, MLE, parametric models fitting), Bayesian spatial statistics (Bayesian estimation, Bayesian kriging, Bayesian priors for covariance parameters, Hierarchical Bayesian methods). Forecasting and interpolation (ordinary kriging, cokriging), mapping of points pattern, spatial regression and neighborhood analysis, survival spatial models, spatio-temporal models. Cressie, Noel, Statistics for Spatial Data, Wiley & Sons.1983. Wackernagel. H, Multivariate Geostatistics, An Introduction with Applications, H Springer-Verlag, 1995. Practical handbook of Spatial Statistics, Editor Sandra LA, USA : CRC Press.Inc., 1996. Isaaks EH, Srivastava RH, Applied Geostatistics. Oxford University Press,1989. Banerjee, Carlin and Gelfand. Hierarchical Modeling and Analysis for Spatial Data, 2004. Schabenberger and Gotway. Statistical Methods for Spatial Data Analysis, Chapman & Hall, 2004. Haining, Spatial Data Analysis: theory and practice, Univerity Press, Cambridge, 2003.


x

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FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM FACULTY OF MATHEMATICS AND NATURAL SCIENCE

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