Bootstrapping regression quantiles

Abstract

Consider the fixed design heteroscedastic regression model where μ(.) and σ(.) are unknown smooth functions and η_i, i=1,…,n are i.i.d. random variables. We introduce a new resampling method for this nonparametric regression model and establish the asymptotic consistency of the bootstrap approximation for Stone's (1977) kernel estimator for F _x (y), the d.f. of the response y for a given value of x, and Cheng's (1984) regression quantile estimator for μ(x).

Keywords:

• Bootstrap approximation
• fixed design
• heteroscedastic model
• kernel estimator
• nonparametric regression
• regression quantiles

^∗AMS 1991 Subject Classification: Primary: 62G07, Secondary: 62009, 62G20.

^∗AMS 1991 Subject Classification: Primary: 62G07, Secondary: 62009, 62G20.

Notes

^∗AMS 1991 Subject Classification: Primary: 62G07, Secondary: 62009, 62G20.