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Goodness-of-fit tests for linear regression models with missing response data. (English) Zbl 1096.62041
Summary: The authors show how to test the goodness-of-fit of a linear regression model when there are missing data in the response variable. Their statistics are based on the \(L_2\)-distance between nonparametric estimators of the regression function and a \(\sqrt{n}\)-consistent estimator of the same function under the parametric model. They obtain the limit distribution of the statistics and check the validity of their bootstrap version. Finally, a simulation study allows them to examine the behaviour of their tests, according the samples are either complete or not.

MSC:
62G10 Nonparametric hypothesis testing
62J05 Linear regression; mixed models
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62E20 Asymptotic distribution theory in statistics
62H12 Estimation in multivariate analysis
62G09 Nonparametric statistical resampling methods
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