The factoring likelihood method for non-monotone missing data

Jae Kwang Kim; Dong Wan Shin

doi:10.1016/j.jkss.2011.12.003

The factoring likelihood method for non-monotone missing data

Jae Kwang Kim, Dong Wan Shin

Department of Statistics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We address the problem of parameter estimation in multivariate distributions under ignorable non-monotone missing data. The factoring likelihood method for monotone missing data, termed by Rubin (1974), is applied to a more general case of non-monotone missing data. The proposed method is asymptotically equivalent to the Fisher scoring method from the observed likelihood, but avoids the burden of computing the first and second partial derivatives of the observed likelihood. Instead, the maximum likelihood estimates and their information matrices for each partition of the data set are computed separately and combined naturally using the generalized least squares method. A numerical example is presented to illustrate the method.

Original language	English
Pages (from-to)	375-386
Number of pages	12
Journal	Journal of the Korean Statistical Society
Volume	41
Issue number	3
DOIs	https://doi.org/10.1016/j.jkss.2011.12.003
State	Published - Sep 2012

Bibliographical note

Funding Information:
The authors are grateful for helpful comments of two referees. The research was supported by National Research Foundation of Korea ( NRF-2009-0084772 , NRF-2009-0070618 ).

Keywords

EM algorithm
Gauss-Newton method
Generalized least squares
Maximum likelihood estimator
Missing at random

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10.1016/j.jkss.2011.12.003

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abstract = "We address the problem of parameter estimation in multivariate distributions under ignorable non-monotone missing data. The factoring likelihood method for monotone missing data, termed by Rubin (1974), is applied to a more general case of non-monotone missing data. The proposed method is asymptotically equivalent to the Fisher scoring method from the observed likelihood, but avoids the burden of computing the first and second partial derivatives of the observed likelihood. Instead, the maximum likelihood estimates and their information matrices for each partition of the data set are computed separately and combined naturally using the generalized least squares method. A numerical example is presented to illustrate the method.",

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AB - We address the problem of parameter estimation in multivariate distributions under ignorable non-monotone missing data. The factoring likelihood method for monotone missing data, termed by Rubin (1974), is applied to a more general case of non-monotone missing data. The proposed method is asymptotically equivalent to the Fisher scoring method from the observed likelihood, but avoids the burden of computing the first and second partial derivatives of the observed likelihood. Instead, the maximum likelihood estimates and their information matrices for each partition of the data set are computed separately and combined naturally using the generalized least squares method. A numerical example is presented to illustrate the method.

KW - EM algorithm

KW - Gauss-Newton method

KW - Generalized least squares

KW - Maximum likelihood estimator

KW - Missing at random

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The factoring likelihood method for non-monotone missing data

Abstract

Bibliographical note

Keywords

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