Tatiana Komarova, Javier Hidalgo
arXiv 4 Sep 2019 · Statistics — Methodology · publishedThe Annals of Statistics (2023) · 4 citations (OpenAlex)
arXiv:1909.01675 · PDF · DOI · OpenAlex · Extracted main text
We describe and examine a test for a general class of shape constraints, such as constraints on the signs of derivatives, U-(S-)shape, symmetry, quasi-convexity, log-convexity, $r$-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 the standard Brownian motion, so that critical values are 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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Ghosal, S., Sen, A. and van der Vaart, A (2000) Testing monotonicity of regression | 0.874 | 7 | 2 | 100% |
| 2 | Stute, W (1997) Nonparametric model checks for regression | 0.874 | 5 | 2 | 100% |
| 3 | Brown, R.L., Durbin, J. and Evans, J.M (1975) Techniques for testing the constancy of regression relationships over time (with discussion) | 0.811 | 4 | 2 | 100% |
| 4 | Hall, P. and Heckman, N. E (2000) Testing for Monotonicity of a Regression Mean by Calibrating for Linear Functions | 0.811 | 4 | 2 | 100% |
| 5 | Khmaladze, E.V (1981) Martingale approach to the theory of goodness of fit tests | 0.811 | 4 | 2 | 100% |
| 6 | Bowman, A.W., Jones, M.C. and Gijbels, I (1998) Testing monotonicity of regression | 0.737 | 3 | 2 | 100% |
| 7 | Agarwal, G.G. and Studden, W.J (1980) Asymptotic Integrated Mean Square Error Using Least Squares and Bias Minimizing Splines | 0.644 | 4 | 2 | 50% |
| 8 | Andrews, D.W.K (1997) A Conditional Kolmogorov Test | 0.644 | 2 | 2 | 100% |
| 9 | Brunk, H. D (1955) Maximum likelihood estimates of monotone parameters | 0.644 | 2 | 2 | 100% |
| 10 | Durbin, J (1973) Distribution Theory for Tests Based on the Sample Distribution Function | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 92 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | A Projection Framework for Testing Shape Restrictions That Form Convex Cones | 0.511 | 2 | 1 |
| 2 | A Unifying Framework for Testing Shape Restrictions | 0.405 | 1 | 1 |
| 3 | Testing Shape Restrictions with Continuous Treatment: A Transformation Model Approach | 0.405 | 1 | 1 |