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Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models

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Abstract

In a generalized linear model with q × 1 responses, the bounded and fixed (or adaptive) p × q regressors Z i and the general link function, under the most general assumption on the minimum eigenvalue of Σ n e=1 Z i Z′ i , the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangxi University, Nanning, 530004, China

    Yin Changming

  2. Department of Statistics and Finance, University of Science and Technology of China, Hefei, 230026, China

    Yin Changming & Zhao Lincheng

  3. Department of Mathematics, Guangxi Teacher College, Nanning, 530001, China

    Wei Chengdong

Authors
  1. Yin Changming
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  2. Zhao Lincheng
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  3. Wei Chengdong
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Correspondence to Yin Changming.

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Yin, C., Zhao, L. & Wei, C. Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models. SCI CHINA SER A 49, 145–157 (2006). https://doi.org/10.1007/s11425-004-5169-x

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  • DOI: https://doi.org/10.1007/s11425-004-5169-x

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