Testing nonparametric shape restrictions

Tatiana Komarova and Javier Hidalgo

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: B-splines; concavity; convexity; convexity in means; CUSUM transformation; distribution-free estimation; log-convexity; Monotonicity; quasi-convexity; U-shape; AAM requested (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2023-12-20
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Published in Annals of Statistics, 20, December, 2023, 51(6), pp. 2299 - 2317. ISSN: 0090-5364

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Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:121410

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