Testing nonparametric shape restrictions

Komarova, Tatiana ORCID: 0000-0002-6581-5097 and Hidalgo, Javier (2023) Testing nonparametric shape restrictions. Annals of Statistics, 51 (6). 2299 - 2317. ISSN 0090-5364

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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.

Item Type:	Article
Official URL:	https://projecteuclid.org/journals/annals-of-stati...
Additional Information:	© Institute of Mathematical Statistics, 2023.
Divisions:	Economics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	18 Jan 2024 13:36
Last Modified:	29 Sep 2025 18:39
URI:	http://eprints.lse.ac.uk/id/eprint/121410

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