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Testing nonparametric shape restrictions

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  • Tatiana Komarova
  • Javier Hidalgo

Abstract

We describe and examine a test for a general class of shape constraints, such as constraints on the signs of derivatives, U-(S-)shape, symmetry, quasi-convexity, log-convexity, $r$-convexity, among others, in a nonparametric framework using partial sums empirical processes. We show that, after a suitable transformation, its asymptotic distribution is a functional of the standard Brownian motion, so that critical values are available. However, due to the possible poor approximation of the asymptotic critical values to the finite sample ones, we also describe a valid bootstrap algorithm.

Suggested Citation

  • Tatiana Komarova & Javier Hidalgo, 2019. "Testing nonparametric shape restrictions," Papers 1909.01675, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:1909.01675
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    References listed on IDEAS

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    Cited by:

    1. Zheng Fang, 2021. "A Unifying Framework for Testing Shape Restrictions," Papers 2107.12494, arXiv.org, revised Aug 2021.

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