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Testing nonparametric shape restrictions

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  • Komarova, Tatiana
  • Hidalgo, Javier

Abstract

We describe and examine a test for a general class of shape constraints, such as signs of derivatives, U-shape, quasi-convexity, log-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 a Brownian motion index by the c.d.f. of the regressor. As a result, the test is distribution-free and critical values are readily 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

  • Komarova, Tatiana & Hidalgo, Javier, 2023. "Testing nonparametric shape restrictions," LSE Research Online Documents on Economics 121410, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:121410
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    B-splines; concavity; convexity; convexity in means; CUSUM transformation; distribution-free estimation; log-convexity; Monotonicity; quasi-convexity; U-shape; AAM requested;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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