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Pointwise Estimation of Density of Heteroscedastistic Response in Regression

Hyun, Ji-Hoon;Kim, Si-Won;Lee, Sung-Dong;Byun, Wook-Jae;Son, Mi-Kyoung;Kim, Choong-Rak

  • Received : 2011.11.24
  • Accepted : 2012.01.16
  • Published : 2012.02.29

Abstract

In fitting a regression model, we often encounter data sets which do not follow Gaussian distribution and/or do not have equal variance. In this case estimation of the conditional density of a response variable at a given design point is hardly solved by a standard least squares method. To solve this problem, we propose a simple method to estimate the distribution of the fitted vales under heteroscedasticity using the idea of quantile regression and the histogram techniques. Application of this method to a real data sets is given.

Keywords

Conditional distribution function;heteroscedasticity;histogram;quantile regression

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)