Asymptotic Normality of Maximum Quasi-Likelihood Estimators in Generalized Linear Models with Fixed Design*期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Asymptotic Normality of Maximum Quasi-Likelihood Estimators in Generalized Linear Models with Fixed Design*

Authors:	Qibing Gao Yaohua Wu Chunhua Zhu Zhanfeng Wang

Institution:	(1) School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, 210097, China;(2) Department of Statistics and Finance, University of Science and Technology of China, Hefei, 230026, China;(3) School of Mathematics Science, Anhui University, Hefei, 230039, China

Abstract:	In generalized linear models with fixed design, under the assumption $\underline \lambda _n \to \infty$ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator $\hat \beta _n$ , which is the root of the quasi-likelihood equation with natural link function $\sum\nolimits_{i = 1}^n {X_i \left( {y_i - \mu \left( {X_i^\prime \beta } \right)} \right) = 0}$ , is obtained, where $\underline \lambda _n$ denotes the minimum eigenvalue of $\sum\nolimits_{i = 1}^n {X_i X_i^\prime }$ , X _i are bounded p × q regressors, and y _i are q × 1 responses. *This research is supported by the National Natural Science Foundation of China under Grant Nos. 10171094, 10571001, and 30572285, the Foundation of Nanjing Normal University under Grant No. 2005101XGQ2B84, the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No. 07KJD110093, and the Foundation of Anhui University under Grant No. 02203105.

Keywords:	Asymptotic normality fixed design generalized linear models maximum quasi-likelihood estimator
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