Randomized quantile regression estimation for heteroskedastic non parametric model |
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Authors: | Wei Xiong Maozai Tian Man-Lai Tang |
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Institution: | 1. School of Statistics, University of international Business and Economics, Beijing, China;2. Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, China;3. Department of Mathematics and Statistics, Hang Seng Management College, Shatin, N.T., Hong Kong |
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Abstract: | In this paper, we propose robust randomized quantile regression estimators for the mean and (condition) variance functions of the popular heteroskedastic non parametric regression model. Unlike classical approaches which consider quantile as a fixed quantity, our method treats quantile as a uniformly distributed random variable. Our proposed method can be employed to estimate the error distribution, which could significantly improve prediction results. An automatic bandwidth selection scheme will be discussed. Asymptotic properties and relative efficiencies of the proposed estimators are investigated. Our empirical results show that the proposed estimators work well even for random errors with infinite variances. Various numerical simulations and two real data examples are used to demonstrate our methodologies. |
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Keywords: | Asymptotic relative efficiency error density heterokcedastic variance function local linear regression randomized quantile regression |
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