Optimum regression quantiles for the inference of the parameters of a simple regression model with exponential errors

 

A. K. M. E. Saleh and A. Adatia (2009). Optimum regression quantiles for the inference of the parameters of a simple regression model with exponential errors. Journal of Statistical Research, Vol. 43, No. 2, pp.  67-73.

 

Abstract

Consider the simple linear regression model:Y$ _{i}=\beta_{0}+\beta_{1}x_{i}+\sigma z_{i},\ (i=1,\ldots,n) $, where $ z_{1},\ldots,z_{n} $ are i.i.d. errors with exponential distribution, $ e^{-z},\ z\in R^{+}. $ This paper deals with the estimation and tests of hypothesis regarding the parameters, $ \boldsymbol{\theta}=(\beta_{0},\beta_{1},\sigma)' $ based on a few ``regression quantiles'' introduced by Koenker and Bassett (1978). The question of optimum regression quantiles is addressed for the problems. Further, estimation of the conditional regression function is also considered along with the related optimum regression quantiles. In every case the optimum spacings are independent of the design matrix.

 

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