Estimating the Error Distribution in a Single-Index Model

Hira L. Koul (), Ursula U. Müller and Anton Schick
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Hira L. Koul: Michigan State University, Department of Statistics and Probability
Ursula U. Müller: Texas A&M University, Department of Statistics
Anton Schick: Binghamton University, Department of Mathematical Sciences

Chapter Chapter 11 in From Statistics to Mathematical Finance, 2017, pp 209-233 from Springer

Abstract: Abstract This paper addresses the problem of estimating the error distribution in single-index regression models. We estimate the error distribution function with a weighted nonparametric residual empirical distribution function. Our main result is a first order uniform stochastic expansion of the estimator. This expansion makes it possible to derive asymptotically distribution free goodness-of-fit tests about the error distribution. Our approach is to regard the single-index model as a nonparametric regression model, but with estimated covariates (the estimated indices). However, the usual assumption in classical nonparametric regression, that the covariate distribution is quasi-uniform (bounded and bounded away from zero on its compact support), is not reasonable here. We handle this by introducing weights which restrict the estimation of the link function to intervals.

Keywords: Weighted residual empirical distribution function; local quadratic smoother (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-50986-0_11

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DOI: 10.1007/978-3-319-50986-0_11

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