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Abstrakty
To investigate the features of the individual from the mixed-type model, a novel model, named the mixed-type generalized linear model, is proposed firstly in this work, which is verified to be realistic and useful. We consider the robustness of M-estimation to estimate the unknown parameters of the mixed-type generalized linear model. By applying the law of large numbers and the central limit theorem, the consistency and asymptotic normality of the M-estimation for the mixed-type generalized linear model are proved with regularity assumptions. At last, in order to evaluate the finite sample performance of the estimator for the new model, several applied instances are presented, which show the good performance of the estimator.
Czasopismo
Rocznik
Tom
Strony
209--223
Opis fizyczny
Bibliogr. 16 poz., tab.
Twórcy
autor
- Faculty of Science, Dalian Minzu University, Dalian, 116600, P.R. China
autor
- School of Mathematical Sciences, Dalian University of Technology, Dalian, 116023, P.R. China
autor
- School of Mathematical Sciences, Qufu Normal University, Shandong, Qufu, 273165, P.R. China
autor
- Nuclear Institute for Food and Agriculture, 446, Peshawar, Pakistan
Bibliografia
- [1] Z. D. Bai, C. R. Rao, and Y. Wu, M-estimation of multivariate linear regression parameters under a convex discrepancy function, Statist. Sinica 2 (1992), pp. 237-254.
- [2] Z. D. Bai, C. R. Rao, and Y. Wu, M-estimation of multivariate linear regression by minimizing the difference of two convex functions, Handbook of Statist., Vol. 15, 1997.
- [3] C. C. Heyde, Quasi-Likelihood and Its Application: A General Approach to Optimal Parameter Estimation, Springer, New York 1997.
- [4] Y. J. Huang and L. X. Song, M-estimator of a generalized linear model with measurement errors, Comm. Statist. Theory Methods 40 (2011), pp. 532-546.
- [5] P. J. Huber, Robust estimation of a location parameter, Ann. Math. Statist. 35 (1964), pp. 73-101.
- [6] P. J. Huber, The behavior of maximum likelihood estimates under nonstandard conditions, in: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 1, University of California Press, Berkeley 1967, pp. 221-233.
- [7] P. J. Huber, Robust regression: Asymptotics, conjectures and Monte Carlo, Ann. Statist. 5 (1973), pp. 799-821.
- [8] P. J. Huber, Robust Statistics, Wiley, New York 1981.
- [9] P. J. Huber, Robust Statistical Procedures, Society for Industrial Mathematics, Philadelphia 1989.
- [10] L. Mancini, E. Ronchetti, and F. Trojani, Optimal conditionally unbiased bounded-influence inference in dynamic location and scale models, J. Amer. Statist. Assoc. 105 (2005), pp. 628-641.
- [11] P. McCullagh and J. A. Nelder, Generalized Linear Models, second edition, Chapman and Hall, London 1989.
- [12] N. Muler and V. J. Yohai, Robust estimates for ARCH processes, J. Time Series Anal. 23 (2002), pp. 79-109.
- [13] J. A. Nelder and R. W. M. Wedderburn, Generalized linear models, J. Roy. Statist. Soc. Ser. B 135 (1972), pp. 370-384.
- [14] J. S. Preisser and B. F. Qaqish, Robust regression for clustered data with applications to binary regression, Biometrics 55 (1999), pp. 574-579.
- [15] S. K. Sinha, Robust analysis of generalized linear mixed models, J. Amer. Statist. Assoc. 99 (2004), pp. 451-460.
- [16] V. J. Yohai and R. A. Maronna, Asymptotic behavior of M-estimators for the linear model, Ann. Statist. 2 (1979), pp. 258-268.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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