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Estimating the Error Distribution in a Single-Index Model

In: From Statistics to Mathematical Finance

Author

Listed:
  • 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)

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.

Suggested Citation

  • Hira L. Koul & Ursula U. Müller & Anton Schick, 2017. "Estimating the Error Distribution in a Single-Index Model," Springer Books, in: Dietmar Ferger & Wenceslao González Manteiga & Thorsten Schmidt & Jane-Ling Wang (ed.), From Statistics to Mathematical Finance, chapter 0, pages 209-233, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-50986-0_11
    DOI: 10.1007/978-3-319-50986-0_11
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