Bootstrap Approximations in Model Checks for Regression

Let M = m θ θ θ be a parametric model for an unknown regression function m. For example, M may consist of all polynomials or trigonometric polynomials with a given bound on the degree. To check the full model M (i.e., to test for H 0 : m ε M), it is known that optimal tests should be based on the em...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1998-03, Vol.93 (441), p.141-149
Main Authors: Stute, W., Manteiga, W. González, Quindimil, M. Presedo
Format: Article
Language:English
Subjects:
Approximation
Critical values
Estimators
Exact sciences and technology
Goodness of fit
Inference from stochastic processes
time series analysis
Linear inference, regression
Linear models
Linear regression
Marked empirical process
Mathematical functions
Mathematical models
Mathematics
P values
Parametric models
Polynomials
Probability and statistics
Regression analysis
Residuals
Sciences and techniques of general use
Statistical methods
Statistical models
Statistics
Theory and Methods
Wild bootstrap
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Summary:Let M = m θ θ θ be a parametric model for an unknown regression function m. For example, M may consist of all polynomials or trigonometric polynomials with a given bound on the degree. To check the full model M (i.e., to test for H 0 : m ε M), it is known that optimal tests should be based on the empirical process of the regressors marked by the residuals. In this article we show that the distribution of this process may be approximated by the wild bootstrap. The method is applied to simulated datasets as well as to real data.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1998.10474096