Asymptotic Properties of Koenker–Bassett Estimator in Regression Model with Long-Range Dependence

Abstract

This article deals with asymptotic distribution of Koenker-Bassett estimator in continuous time regression model with long-range dependent noise. It is proved that the asymptotic distribution of the normed estimator coincides with asymptotic distribution of the integral of an indicator random process generated by the random noise weighted by regression function gradient. A theorem is formulated also on asymptotic normality of the last integral.

Keywords:

• Asymptotic normality
• Hermite polynomials
• Hermite rank
• Koenker–Bassett estimator
• Long-range dependence
• Spectral measure of regression function

Mathematics Subject Classification:

• Primary 62J02
• Secondary 62J99