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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, bounded and fixed p × q regressors Zi and general link function, under the most general assumption on the minimum eigenvalue of\(\sum\nolimits_{i = 1}^n {Z_i Z'_i } \) the moment condition on responses as weak as possible and other mild regular conditions, we prove that with probability one, the quasi-likelihood equation has a solution\(\hat \beta \) n for all large sample size n, which converges to the true regression parameter β0. This result is an essential improvement over the relevant results in literature.

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Authors and Affiliations

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

    Changming Yin & Lincheng Zhao

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  1. Changming Yin
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  2. Lincheng Zhao
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Correspondence to Lincheng Zhao.

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Yin, C., Zhao, L. Strong consistency of maximum quasi-likelihood estimates in generalized linear models. Sci. China Ser. A-Math. 48, 1009–1014 (2005). https://doi.org/10.1360/04ys0060

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  • DOI: https://doi.org/10.1360/04ys0060

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