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Strong consistency of maximum quasi-likelihood estimate in generalized linear models via a last time

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  • Chang, Yuan-chin Ivan

Abstract

In this paper, by using a last-time random variable, we show the strong consistency for the maximum quasi-likelihood estimate in generalized linear models with adaptive design variables and general link functions. Our approach is based on the Leray-Schauder Theorem and a last-time theorem. The last time that we defined here is based on a sum of martingale differences instead of independent random variables. Under some slightly stronger assumptions on the adaptive design variables, we obtain the almost sure convergence as well as the convergence rate of the estimate.

Suggested Citation

  • Chang, Yuan-chin Ivan, 1999. "Strong consistency of maximum quasi-likelihood estimate in generalized linear models via a last time," Statistics & Probability Letters, Elsevier, vol. 45(3), pages 237-246, November.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:3:p:237-246
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    Citations

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    Cited by:

    1. Yuan-chin Chang, 2005. "Application of Sequential Interval Estimation to Adaptive Mastery Testing," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 685-713, December.
    2. Arnoud V. den Boer, 2014. "Dynamic Pricing with Multiple Products and Partially Specified Demand Distribution," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 863-888, August.
    3. Xia, Tian & Jiang, Xuejun & Wang, Xueren, 2015. "Strong consistency of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models with stochastic regression," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 37-45.
    4. Yin, Changming & Wang, Zhanfeng & Zhang, Hong, 2014. "Asymptotic properties of maximum likelihood estimator for two-step logit models," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 135-143.
    5. Yuan-chin Chang & Hung-Yi Lu, 2010. "Online Calibration Via Variable Length Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 140-157, March.

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