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1989 · Biometrika

Regression and time series model selection in small samples

Clifford M. Hurvich, Chih‐Ling Tsai

A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called AICC, is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, AICC is found to provide better model order choices than any other asymptotically efficient method. Applications to nonstationary autoregressive and mixed autoregressive moving average time series models are also discussed.

6,433 citations0 views
DOI: 10.1093/biomet/76.2.297
1986 · Biometrika

Longitudinal data analysis using generalized linear models

Kung‐Yee Liang, Scott L. Zeger

This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for niultivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m-dependence and exchangeable correlation structures from each subject are discussed. Efficiency of the pioposecl estimators in two simple situations is considered. The approach is closely related to quasi-likelihood.

18,243 citations3 viewsFull text
DOI: 10.1093/biomet/73.1.13
1978 · Biometrika

On a measure of lack of fit in time series models

Greta M. Ljung, George E. P. Box

The overall test for lack of fit in autoregressive-moving average models proposed by Box & Pierce (1970) is considered. It is shown that a substantially improved approximation results from a simple modification of this test. Some consideration is given to the power of such tests and their robustness when the innovations are nonnormal. Similar modifications in the overall tests used for transfer function-noise models are proposed

6,091 citations0 views
DOI: 10.1093/biomet/65.2.297