Conditional mean estimation under asymmetric and heteroscedastic error by linear combination of quantile regressions

  • Authors:

  • Takafumi Kanamori;Ichiro Takeuchi

  • Affiliations:

  • Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan;Department of Information Engineering, Mie University, 1515 Kamihama-cho, Tsu, Mie 514-8507, Japan

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2006

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Abstract

In this paper we propose a new estimator for regression problems in the form of the linear combination of quantile regressions. The proposed estimator is helpful for the conditional mean estimation when the error distribution is asymmetric and heteroscedastic. It is shown that the proposed estimator has the consistency under heteroscedastic regression model: Y=@m(X)+@s(X).e, where X is a vector of covariates, Y is a scalar response, e is a zero mean random variable independent of X and @s(X) is a positive value function. When the error term e is asymmetric, we show that the proposed estimator yields better conditional mean estimation performance than the other estimators. Numerical experiments both in synthetic and real data are shown to illustrate the usefulness of the proposed estimator.