Abstract
I propose a simply method to estimate the regression parameters in quasi-likelihood model My main approach utilizes the dimension reduction technique to first reduce the dimension of the regressor X to one dimension before solving the quasi-likelihood equations. In addition, the real advantage of using dimension reduction technique is that it provides a good initial estimate for one-step estimator of the regression parameters. Under certain design conditions, the estimators are asymptotically multivariate normal and consistent. Moreover, a Monte Carlo simulation is used to study the practical performance of the procedures, and I also assess the cost of CPU time for computing the estimates.
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References
Brillinger, D. R. (1982). A generalized linear model with “Gaussian” regressor variables, A Festchrift for Erich L. Lehmann in Honor of His Sixty-Fifth Birthday (eds. P. J.Bickel, K.Doksum and J. L.Hodges), 97–114, Wadsworth International Group, Belmont, California.
Chanda, K. C. (1954). A note on the consistency and maxima of the roots of likelihood equations, Biometrika, 41, 56–61.
Cheng, K. F. and Wu, J. W. (1991). Adjusted least squares estimates for the scaled regression coefficients with censored data, Tech. Report, 90–108, National Central University, Chungli, Taiwan, R.O.C.
Cheng, K. F. and Wu, J. W. (1994). Testing goodness of fit for a parametric family of link function. J. Amer. Statist. Assoc., 89, 657–664.
Duan, N. and Li, K.-C. (1987). Distribution-free and link-free estimation for the sample selection model, J. Econometrics, 35, 25–35.
Duan, N. and Li, K.-C. (1991). Slicing regression: A link free regression method, Ann. Statist., 19, 505–530.
Fang, K. T., Kotz, S. and Ng, K. W. (1990). Symmetric Multivariate and Related Distributions, Chapman and Hall, New York.
Härdle, W. and Stoker, T. M. (1989). Investigating smooth multiple regression by the method of average derivative, J. Amer. Statist. Assoc., 84, 986–995.
Li, K.-C. (1991). Sliced inverse regression for dimension reduction, J. Amer. Statist. Assoc., 86, 316–342.
Li, K.-C. and Duan, N. (1989). Regression analysis under link violation, Ann. Statist., 17, 1009–1052.
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed., Chapman & Hall, London.
Müller, H.-G. (1984). Smooth optimum kernel, estimators of densities, regression curves and models, Ann. Statist., 12, 766–774.
Powell, J. L., Stock, J. H. and Stoker, T. M. (1989). Semiparametric estimation of index coefficients, Econometrica, 57, 1403–1430.
Prakasa Rao, B. L. S. (1983). Nonparametric Functional Estimation, Academic Press, New York.
Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics, John Wiley, New York.
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This research partially supported by the National Science Council, R.O.C. (Plan No. NSC 82-0208-M-032-023-T).
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Wu, JW. The quasi-likelihood estimation in regression. Ann Inst Stat Math 48, 283–294 (1996). https://doi.org/10.1007/BF00054791
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DOI: https://doi.org/10.1007/BF00054791