Goodness-of-fit tests in parametric regression based on the estimation of the error distribution

被引：56

作者：

Van Keilegom, Ingrid ^{[2
]}

Manteiga, Wenceslao Gonzalez ^{[1
]}

Sellero, Cesar Sanchez ^{[1
]}

机构：

[1] Univ Santiago de Compostela, Fac Matemat, Dept Estadist, Santiago De Compostela 15706, Spain

[2] Univ Catholique Louvain, Inst Stat, B-1348 Louvain, Belgium

来源：

TEST | 2008年 / 17卷 / 02期

关键词：

bootstrap; goodness-of-fit; heteroscedastic regression; model check; nonlinear regression; nonparametric regression; residual distribution;

D O I：

10.1007/s11749-007-0044-z

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：

Consider a heteroscedastic regression model Y = m(X) + s(X) e, where m(X) = E(Y vertical bar X) and sigma(2)(X) = Var(Y vertical bar X) are unknown, and the error e is independent of the covariate X. We propose a new type of test statistic for testing whether the regression curve m(.) belongs to some parametric family of regression functions. The proposed test statistic measures the distance between the empirical distribution function of the parametric and of the nonparametric residuals. The asymptotic theory of the proposed test is developed, and the proposed testing procedure is illustrated by means of a small simulation study and the analysis of a data set.

引用

页码：401 / 415

页数：15

共 29 条

[1] Non-parametric estimation of the residual distribution [J].