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Maximum-Likelihood-Schätzung in Modellen für kategoriale Querschnitts- und Zeitreihendaten mit fehlenden Beobachtungen. (Maximum likelihood estimation in models for categorical cross sectional and time series data with missing observations). (German) Zbl 0699.62002

Weiden: Schuch-Verlag; Zugl.: Regensburg, Univ., Diss. 1989. 110 S. (1990).
The book under review provides a systematic treatment of the problem of parameter estimation for categorical data with missing values. It can be recommended for statisticians which are confronted with this problem. Many references deal with special problems. This book simultaneously is the dissertation of the author.
The material is covered in nine chapters. Chapter I gives the formulation of the problem. Observations may be missing nonrandomly or randomly following a missing data mechanism. Chapter II deals with numerical methods of iterative maximum likelihood estimation in connection with the expectation-maximization (EM) algorithm.
The chapters III-VII are devoted to the case of independent categorical data. They deal with the inference from contingency tables. Chapter III gives statements for a general structure of data and treats the special case of two-dimensional tables, and Chapter IV shows an example which may be solved noniteratively. Chapter V describes the treatment of the problems by using loglinear models. Chapter VI deals with not exactly categorized data. Chapter VII discusses the estimation problem for a linear Poisson model.
The Chapters VIII and IX are devoted to the case of categorical time series with missing observations. A modified EM-algorithm is presented for an autoregressive logit model. The author shows that the generalized linear Kalman filter may be used for time series with missing observations. The state space method is also combined with the EM- algorithm.
Reviewer: G.Wittwer

MSC:

62-02 Research exposition (monographs, survey articles) pertaining to statistics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62H17 Contingency tables
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