TY - JOUR
T1 - An optimal estimating equation based on the first three cumulants
AU - Li, Bing
N1 - Funding Information:
I am grateful to Professor Bruce Lindsay for valuable discussions throughout this work. I am also grateful to a referee and an associate editor for their constructive comments, and especially for a suggestion by the associate editor that has helped to make Theorem 1 substantially more concise and comprehensible. The research was supported by National Science Foundation Grants.
PY - 1998
Y1 - 1998
N2 - For improving on quasilikelihood estimation two types of quadratic estimating equations have been proposed, one based on the Edgeworth expansion, the other on the generalisation of the quasi-score. The first requires that the skewness of observations has a small departure from the exponential family; the second requires the knowledge of both skewness and kurtosis. We introduce an optimal quadratic estimating equation applicable when the skewness is not small and the kurtosis is unknown. Apart from optimality, the manner in which skewness is incorporated ensures that its misspecification does not affect √n-consistency, and that the estimator enjoys an invariance property akin to that of the bias-corrected maximum likelihood estimate. Simulations indicate a solid improvement in accuracy.
AB - For improving on quasilikelihood estimation two types of quadratic estimating equations have been proposed, one based on the Edgeworth expansion, the other on the generalisation of the quasi-score. The first requires that the skewness of observations has a small departure from the exponential family; the second requires the knowledge of both skewness and kurtosis. We introduce an optimal quadratic estimating equation applicable when the skewness is not small and the kurtosis is unknown. Apart from optimality, the manner in which skewness is incorporated ensures that its misspecification does not affect √n-consistency, and that the estimator enjoys an invariance property akin to that of the bias-corrected maximum likelihood estimate. Simulations indicate a solid improvement in accuracy.
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U2 - 10.1093/biomet/85.1.103
DO - 10.1093/biomet/85.1.103
M3 - Article
AN - SCOPUS:28244481800
SN - 0006-3444
VL - 85
SP - 103
EP - 114
JO - Biometrika
JF - Biometrika
IS - 1
ER -