Bootstrap tests for the error distribution in linear and nonparametric regression models

被引：19

作者：

Neumeyer, Natalie ^{[1
]}

Dette, Holger ^{[1
]}

Nagel, Eva-Renate ^{[1
]}

机构：

[1] Ruhr Univ Bochum, Fak Math, D-44780 Bochum, Germany

来源：

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS | 2006年 / 48卷 / 02期

关键词：

analysis of variance; goodness-of-fit; linear model; M-estimation; non-parametric regression; parametric bootstrap; residual process;

D O I：

10.1111/j.1467-842X.2006.00431.x

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：

In this paper we investigate several tests for the hypothesis of a parametric form of the error distribution in the common linear and non-parametric regression model, which are based on empirical processes of residuals. It is well known that tests in this context are not asymptotically distribution-free and the parametric bootstrap is applied to deal with this problem. The performance of the resulting bootstrap test is investigated from an asymptotic point of view and by means of a simulation study. The results demonstrate that even for moderate sample sizes the parametric bootstrap provides a reliable and easy accessible solution to the problem of goodness-of-fit testing of assumptions regarding the error distribution in linear and non-parametric regression models.

引用

页码：129 / 156

页数：28

共 50 条

[21] BOOTSTRAP AND CROSS-VALIDATION ESTIMATES OF THE PREDICTION ERROR FOR LINEAR-REGRESSION MODELS
BUNKE, O
DROGE, B
[J]. ANNALS OF STATISTICS, 1984, 12 (04): : 1400 - 1424
[22] A note on testing symmetry of the error distribution in linear regression models
Neumeyer, N
Dette, H
Nagel, ER
[J]. JOURNAL OF NONPARAMETRIC STATISTICS, 2005, 17 (06) : 697 - 715
[23] On the performance of nonparametric specification tests in regression models
Miles, D
Mora, J
[J]. COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2003, 42 (03) : 477 - 490
[24] BOOTSTRAP TOLERANCE INTERVALS FOR LINEAR REGRESSION MODELS
Abdel-Karim, Amany Hassan
[J]. ADVANCES AND APPLICATIONS IN STATISTICS, 2023, 87 (02) : 139 - 159
[25] Bootstrap LM tests for higher-order spatial effects in spatial linear regression models
Zhenlin Yang
[J]. Empirical Economics, 2018, 55 : 35 - 68
[26] Robust estimation of error scale in nonparametric regression models
Ghement, Isabella Rodica
Ruiz, Marcelo
Zamar, Ruben
[J]. JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2008, 138 (10) : 3200 - 3216
[27] Estimating functionals of the error distribution in parametric and nonparametric regression
Müller, UU
Schick, A
Wefelmeyer, W
[J]. JOURNAL OF NONPARAMETRIC STATISTICS, 2004, 16 (3-4) : 525 - 548
[28] Error variance function estimation in nonparametric regression models
Alharbi, Yousef F.
Patili, Prakash N.
[J]. COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2018, 47 (05) : 1479 - 1491
[29] Bootstrap LM tests for higher-order spatial effects in spatial linear regression models
Yang, Zhenlin
[J]. EMPIRICAL ECONOMICS, 2018, 55 (01) : 35 - 68
[30] Model specification tests in nonparametric stochastic regression models
Gao, JT
Tong, H
Wolff, R
[J]. JOURNAL OF MULTIVARIATE ANALYSIS, 2002, 83 (02) : 324 - 359

← 1 2 3 4 5 →