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TESTING NONPARAMETRIC SHAPE RESTRICTIONS
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DOI：10.1214/23-AOS2311.png)
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Abstract
En 中文
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:
Monotonicity
convexity
concavity
U-shape
quasi-convexity
log-convexity
convexity in means
B-splines
CUSUM transformation
distribution-free estimation
Journal
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3.7
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2.8K
Citations:
2.9W