Testing nonparametric shape restrictions
Tatiana Komarova, Javier Hidalgo
The Annals of Statistics · 2023 · Volume 51 · Issue 6
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
05A15, 05C38, 15A15, 15A18, B-splines, concavity, convexity, convexity in means, CUSUM transformation, distribution-free estimation, Log-convexity, Monotonicity, quasi-convexity, U-shape
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