Estimating coefficients of single-index regression models by minimizing variation |
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Authors: | Dongfang Lou Zhiyuan Ma |
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Institution: | 1. Department of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, People's Republic of China;2. Department of Public Economics and Administration, Shanghai University of Finance and Economics, Shanghai, People's Republic of China |
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Abstract: | This paper proposes a novel estimation of coefficients in single-index regression models. Unlike the traditional average derivative estimation Powell JL, Stock JH, Stoker TM. Semiparametric estimation of index coefficients. Econometrica. 1989;57(6):1403–1430; Hardle W, Thomas M. Investigating smooth multiple regression by the method of average derivatives. J Amer Statist Assoc. 1989;84(408):986–995] and semiparametric least squares estimation Ichimura H. Semiparametric least squares (sls) and weighted sls estimation of single-index models. J Econometrics. 1993;58(1):71–120; Hardle W, Hall P, Ichimura H. Optimal smoothing in single-index models. Ann Statist. 1993;21(1):157–178], the procedure developed in this paper is to estimate the coefficients directly by minimizing the mean variation function and does not involve estimating the link function nonparametrically. As a result, it avoids the selection of the bandwidth or the number of knots, and its implementation is more robust and easier. The resultant estimator is shown to be consistent. Numerical results and real data analysis also show that the proposed procedure is more applicable against model free assumptions. |
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Keywords: | Single-index regression model minimum variation estimation iterative marginal optimization |
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