Application of EM algorithm on missing categorical data analysis

Expectation- Maximization algorithm, or in short, EM algorithm is one of the methodologies for solving incomplete data problems sequentially based on a complete framework. The EM algorithm is a parametric approach to find the Maximum Likelihood, ML parameter estimates for incomplete data. The algori...

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Main Author:	Hasan, Noraini
Format:	Thesis
Language:	English
Published:	2009
Subjects:	QA Mathematics
Online Access:	http://eprints.utm.my/id/eprint/12403/6/NorainiHasanMFS2009.pdf
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id	my-utm-ep.12403
record_format	uketd_dc
institution	Universiti Teknologi Malaysia
collection	UTM Institutional Repository
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Hasan, Noraini Application of EM algorithm on missing categorical data analysis
description	Expectation- Maximization algorithm, or in short, EM algorithm is one of the methodologies for solving incomplete data problems sequentially based on a complete framework. The EM algorithm is a parametric approach to find the Maximum Likelihood, ML parameter estimates for incomplete data. The algorithm consists of two steps. The first step is the Expectation step, better known as E-step, finds the expectation of the loglikelihood, conditional on the observed data and the current parameter estimates; say . The second step is the Maximization step, or Mstep, which maximize the loglikelihood to find new estimates of the parameters. The procedure alternates between the two steps until the parameter estimates converge to some fixed values.
format	Thesis
qualification_level	Master's degree
author	Hasan, Noraini
author_facet	Hasan, Noraini
author_sort	Hasan, Noraini
title	Application of EM algorithm on missing categorical data analysis
title_short	Application of EM algorithm on missing categorical data analysis
title_full	Application of EM algorithm on missing categorical data analysis
title_fullStr	Application of EM algorithm on missing categorical data analysis
title_full_unstemmed	Application of EM algorithm on missing categorical data analysis
title_sort	application of em algorithm on missing categorical data analysis
granting_institution	Universiti Teknologi Malaysia, Faculty of Science
granting_department	Faculty of Science
publishDate	2009
url	http://eprints.utm.my/id/eprint/12403/6/NorainiHasanMFS2009.pdf
_version_	1747814933711552512
spelling	my-utm-ep.124032017-09-13T08:18:32Z Application of EM algorithm on missing categorical data analysis 2009-12 Hasan, Noraini QA Mathematics Expectation- Maximization algorithm, or in short, EM algorithm is one of the methodologies for solving incomplete data problems sequentially based on a complete framework. The EM algorithm is a parametric approach to find the Maximum Likelihood, ML parameter estimates for incomplete data. The algorithm consists of two steps. The first step is the Expectation step, better known as E-step, finds the expectation of the loglikelihood, conditional on the observed data and the current parameter estimates; say . The second step is the Maximization step, or Mstep, which maximize the loglikelihood to find new estimates of the parameters. The procedure alternates between the two steps until the parameter estimates converge to some fixed values. 2009-12 Thesis http://eprints.utm.my/id/eprint/12403/ http://eprints.utm.my/id/eprint/12403/6/NorainiHasanMFS2009.pdf application/pdf en public masters Universiti Teknologi Malaysia, Faculty of Science Faculty of Science Aitken, A. P. (1974). Assessing Systematic Errors in Rainfall-Runoff Models.Journal of Hydrology. 20, 131-136. Arifah Bahar, Ismail Mohamad, Muhammad Hisyam Lee, Noraslinda Mohamed Ismail, Norazlina Ismail, Norhaiza Ahmad, Zarina Mohd Khalid.(2008). Engineering Statistics. Desktop Publisher. Beal, E. M., Little, R. J. A. (1975). Missing Values in Multivariate Analysis. J. R. Stat. Soc. B, 37, 129-145. Rindskopf. D. A (1992). General Approach To Categorical Data Analysis With Missing Data, Using Generalized Linear Models With Composite Links. Psycometrika. 57, 1, 29-42. Dempster, A. P., Laird, N. M., Rubin, D. B. (1977). Maximum Likelihood for incomplete data via the EM algorithm (with discussion). J. R. Stat. Soc. B, 39, 1- 38. Diggle, P. and Kenward, M. G. (1994). Informative Drop-out In Longitudinal Data Analysis. Applied Statistics. 43, 1, 49-93. Erling B. Anderson (1997). Introduction to the Statistical Analysis of Categorical Data. Springer-Verlag Berlin Heidelberg New York. Fienberg, S. E. (1980). The Analysis of Cross-Classified Categorical Data. Cambridge Mass.: The MIT press. Hartly, H. O., Hocking, R. R. (1971). The Analysis of Incomplete Data. Biometrics.27, 783-808. Hoo Ling Ping and Safian Uda (2006). Methods Analyzing Incomplete Categorical Data. Proceedings of the 2nd IMT-GT Regional Conferrence on Mathematics, Statistics and Applications, USM, Penang. Ismail Mohamad (2003). Data Analysis in the Presence of Missing Data. Lancaster University. Doctor of Philosophy Dissertation. Kim, J. O., and Curry, J. (1977). The Treatment of Missing Data In Multivariate Analysis. Sosiological Methods and Research. 6, 215-241. Little, R. J. A(1988). A Test of Missing Completely At Random for Multivariate Data With Missing Values. Journal of American Statistical Association. 83, 404, 1198- 202. Little, R. J. A., Rubin, D. B. (2002). Statistical Analysis With Missing Data, 2nd Edition. New Jersey.:John Wiley Madow, W. G., Nisselson, H., Olkin, I. and Rubin, D.B. (eds)(1983). Incomplete Data In Sample Surveys (Vols. 1-3). New York: Academic Press. Michiko Watanabe and Kazunori Yamaguchi (2004). The EM Algorithm and Related Statistical Models. Marcel Decker. McKendrick, A. G. (1926). Applications of Mathematics to Medical Problems. Proc.Edinburgh Math. Soc. 44, 98-130. Mood, M. A., Graybill, F. A., and Boes, D. C. (1974). Introduction to the Theory of Statistics, Third Edition.McGraw-Hill Book Company. Orchard, T., Woodburry, M. A. (1972). A Missing Information Principle: Theory and Applications. Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability. 1, 697-715. Paul G. Hoel (1984). Introduction to Mathematical Statistics, Fifth Edition. John Wiley and Sons. Rao, C. R. (1972). Linear Statistical Inference and Its Applications. New York Wiley. Roth, P. L. (1994). Missing Data: A Conceptual Review For Applied Psychologists. Personnel Psychology. 47, 537-560. Rubin, D. B. (1976). Inference and Missing Data. Biometrika. 63, 538-543. Rubin, D. B. (1991). EM and Beyond. Psychometrika. 56, 241-254.

Application of EM algorithm on missing categorical data analysis

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