TY - JOUR
T1 - Maximization by parts in likelihood inference
AU - Song, Peter X.K.
AU - Fan, Yanqin
AU - Kalbfleisch, John D.
AU - Jiang, Jiming
AU - Louis, Thomas A.
AU - Liao, J. G.
AU - Qaqish, Bahjat F.
AU - Ruppert, David
N1 - Funding Information:
Peter X.-K. Song is Associate Professor, Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada (E-mail: [email protected]). Yanqin Fan is Professor, Department of Economics, Vanderbilt University, Nashville, TN 37235 (E-mail: [email protected]). John D. Kalbfleisch is Professor and Chair, Department of Biostatistics, University of Michigan School of Public Health, Ann Arbor, MI 48109 (E-mail: [email protected]). The first author’s research was supported by an NSERC operating grant. The research was done while Song was visiting the Department of Biostatistics, University of Michigan; Song acknowledges computing support from the university. The authors would thank the editor, the associate editor, and three anonymous referees whose insightful comments and suggestions were very helpful in improving this manuscript.
PY - 2005/12
Y1 - 2005/12
N2 - This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log-likelihood from a simply analyzed model, and the second part is used to update estimates from the first part. Convergence properties of this iterative (fixed-point) algorithm are examined, and asymptotics are derived for estimators obtained using only a finite number of iterations. Illustrative examples considered in the article include multivariate Gaussian copula models, nonnormal random-effects models, generalized linear mixed models, and state-space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linear random-effects model.
AB - This article presents and examines a new algorithm for solving a score equation for the maximum likelihood estimate in certain problems of practical interest. The method circumvents the need to compute second-order derivatives of the full likelihood function. It exploits the structure of certain models that yield a natural decomposition of a very complicated likelihood function. In this decomposition, the first part is a log-likelihood from a simply analyzed model, and the second part is used to update estimates from the first part. Convergence properties of this iterative (fixed-point) algorithm are examined, and asymptotics are derived for estimators obtained using only a finite number of iterations. Illustrative examples considered in the article include multivariate Gaussian copula models, nonnormal random-effects models, generalized linear mixed models, and state-space models. Properties of the algorithm and of estimators are evaluated in simulation studies on a bivariate copula model and a nonnormal linear random-effects model.
KW - Copula model
KW - Fixed-point algorithm
KW - Generalized linear mixed model
KW - Information dominance
KW - Iterative algorithm
KW - Non-normal random effects
KW - Score equation
KW - State-space model
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U2 - 10.1198/016214505000000204
DO - 10.1198/016214505000000204
M3 - Article
AN - SCOPUS:29144456020
SN - 0162-1459
VL - 100
SP - 1145
EP - 1158
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 472
ER -