NONPARAMETRIC KERNEL REGRESSION WITH MULTIPLE PREDICTORS AND MULTIPLE SHAPE CONSTRAINTS

被引：75

作者：

Du, Pang ^{[1
]}

Parmeter, Christopher F. ^{[2
]}

Racine, Jeffrey S. ^{[3
]}

机构：

[1] Virginia Tech, Dept Stat, Blacksburg, VA 24061 USA

[2] Univ Miami, Dept Econ, Coral Gables, FL 33124 USA

[3] McMaster Univ, Dept Econ, Dept Math & Stat, Grad Program Stat, Hamilton, ON L8S 4M4, Canada

来源：

STATISTICA SINICA | 2013年 / 23卷 / 03期

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

Hypothesis testing; multivariate kernel estimation; nonparametric regression; shape restrictions; DENSITY-ESTIMATION; SMOOTHING SPLINES; MONOTONE; ESTIMATORS; SUBJECT; CONVEX;

D O I：

10.5705/ss.2012.024

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Nonparametric smoothing under shape constraints has recently received much well-deserved attention. Powerful methods have been proposed for imposing a single shape constraint such as monotonicity and concavity on univariate functions. In this paper, we extend the monotone kernel regression method in Hall and Huang (2001) to the multivariate and multi-constraint setting. We impose equality and/or inequality constraints on a nonparametric kernel regression model and its derivatives. A bootstrap procedure is also proposed for testing the validity of the constraints. Consistency of our constrained kernel estimator is provided through an asymptotic analysis of its relationship with the unconstrained estimator. Theoretical underpinnings for the bootstrap procedure are also provided. Illustrative Monte Carlo results are presented and an application is considered.

引用

页码：1347 / 1371

页数：25

共 51 条

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