Adaptive Inference in Multivariate Nonparametric Regression Models Under Monotonicity

Koohyun Kwon and Soonwoo Kwon

Papers from arXiv.org

Abstract: We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some or all of the arguments. We derive the minimax rate of convergence for confidence intervals (CIs) that adapt to the underlying smoothness, and provide an adaptive inference procedure that obtains this minimax rate. When the regression function is monotone in $k_{+}$ of its $k$ arguments, the minimax expected length over a H\"older class with exponent $\gamma'$ of CIs that maintain coverage over a rougher class with exponent $\gamma$ is of order $n^{-1/(2+k_{+}/\gamma'+(k-k_{+})/\gamma)}$. The rate is unchanged if the rougher class restricts the smoothness only at the point, along the nonmonotone arguments. Under monotonicity along a closed convex cone that contains no line, only the dimension of its linear span enters the rate. The procedure differs from that of Cai and Low (2004), intended to yield shorter CIs under practically relevant specifications. It is valid in finite samples under Gaussian errors with a known variance. The proposed method applies to general linear functionals of the regression function.

Date: 2020-11, Revised 2026-10
New Economics Papers: this item is included in nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://arxiv.org/pdf/2011.14219 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2011.14219

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().