CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2012, 28(5) 520-534 DOI:      ISSN: 1001-4268 CN: 31-1256

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A Note on Random Effects Growth Curve Models

Luo Youxi, Tian Maozai, Li Hanfang

School of Science, Hubei University of Technology, School of Statistics, Renmin University of China

Abstract��

The robustness of regression coefficient
estimator is a hot topic in regression analysis all the while. Since
the response observations are not independent, it is extraordinarily
difficult to study this problem for random effects growth curve
models, especially when the design matrix is non-full of rank. The
paper not only gives the necessary and sufficient conditions under
which the generalized least square estimate is identical to the the
best linear unbiased estimate when error covariance matrix is an
arbitrary positive definite matrix, but also obtains a concise
condition under which the generalized least square estimate is
identical to the maximum likelihood estimate when the design matrix
is full or non-full of rank respectively. In addition, by using of
the obtained results, we get some corollaries for the the
generalized least square estimate be equal to the maximum likelihood
estimate under several common error covariance matrix assumptions.
Illustrative examples for the case that the design matrix is full or
non-full of rank are also given.

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