A nonparametric test of the non-convexity of regression

被引：8

作者：

Diack, CAT

Thomas-Agnan, C

机构：

[1] Univ Toulouse 3, Lab Stat & Probabilites, F-31062 Toulouse, France

[2] GREMAQ, Manufacture Tabacs, F-31000 Toulouse, France

来源：

JOURNAL OF NONPARAMETRIC STATISTICS | 1998年 / 9卷 / 04期

关键词：

least squares estimator; test of convexity; B-splines; modulus of continuity;

D O I：

10.1080/10485259808832749

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：

This paper proposes a nonparametric test of the non-convexity of a smooth regression function based on least squares or hybrid splines. By a simple formulation of the convexity hypothesis in the lcass of all polynomial cubic splines, we build a test which has an asymptotic size equal to the nominal level. It is shown that the test is consistent and is robust to nonnormality. The behavior of the lest under the local alternatives is studied.

引用

页码：335 / 362

页数：28

共 13 条

[1] ASYMPTOTIC INTEGRATED MEAN-SQUARE ERROR USING LEAST-SQUARES AND BIAS MINIMIZING SPLINES [J].