Abstract
This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator (MQLE) in quasi-likelihood nonlinear models (QLNM) with random regressors. The asymptotic results of generalized linear models (GLM) with random regressors are generalized to QLNM with random regressors.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chang, Y.I. Strong consistency of maximum quasi-likelihood estimate in generalized linear models via a last time. Statist. Probab. lett., 45: 237–246 (1999)
Chen, K., Hu, I., Ying, Z. Strong consistency of maximum quasi-likelihood estimation in generalized linear models with fixed and adaptive designs. Ann. Statist., 27: 1155–1163 (1999)
Fahrmer, L., Kaufmann, H. Consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models. Ann. Statist., 13: 342–368 (1985)
Ferguson, T.S. A course in large sample theory. Chapman & Hall, London, 1996
Heuser, H. Lehrbuch der Analysis, Teil 2. Teubner, Stuttgart, 1981
Lu, J.C., Chen, D., Zhou, W. Quasi-likelihood estimation for GLM with random Scales. J. Statist. Planning Inference., 136: 401–429 (2006)
McCullagh, P. Quasi likelihood functions. Ann. Statist., 11: 59–67 (1983)
McCullagh, P., Nelder, J.A. Generalized linear models. Chapman & Hall, London, 1989
Nelder, J.A., Wedderburn, R.W.M. Generalized linear models. J. R. Statist. Soc. A., 135: 370–384 (1972)
Padgett, W.Y., Taylor, R.L. Laws of large nunbers for normed linear spaces and certain fréchet space. Springer-Verlag, Berlin, 1973
Tzavelas, G., A note on the uniqueness of the quasi-likelihood estimator. Statist. Probab. Lett., 38: 125–130 (1998)
Xia, T., Kong, F.C. Rate of strong consistency of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models. Appl. Math. J. Chinese. Univ., 23: 391–400 (2008)
Xia, T., Kong, F.C., Wang, S.F., Wang, X.R. Asymptotic properties of maximum quasi-likelihood estimator in quasi-likelihood nonlinear models. Communications in Statistics-Theory and Methods, 37: 2358–2368 (2008)
Wedderburn, R.W.M. Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61: 439–447 (1974)
Wu, C.F. Asymptotic properties of nonlinear least squares estimators. Ann. Statist., 9: 501–513 (1981)
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by National Natural Science Foundation of China (No. 10761011, 10671139, 10901135), Natural Science Foundation of Yunnan Province(No. 2008CD081) and Special Foundation for Middle and Young Excellent Teachers of Yunnan University.
Rights and permissions
About this article
Cite this article
Xia, T., Wang, Sf. & Wang, Xr. Consistency and asymptotic normality of the maximum quasi-likelihood estimator in quasi-likelihood nonlinear models with random regressors. Acta Math. Appl. Sin. Engl. Ser. 26, 241–250 (2010). https://doi.org/10.1007/s10255-009-7168-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-009-7168-8
Keywords
- Asymptotic normality
- consistency
- maximum quasi-likelihood estimator
- quasi-likelihood nonlinear models with random regressors