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A Test of U-type for Goodness-of-fit in Regression Models Through martingale difference divergence

Acta Mathematicae Applicatae Sinica 2024年第4期40卷 979-1000页

作者： Kai XU Yan-qin NIE Dao-jiang HE School of Mathematics and Statistics Anhui Normal UniversityWuhu 241002China

Based on the martingale difference divergence,a recently proposed metric for quantifying conditional mean dependence,we introduce a consistent test of U-type for the goodness-of-fit of linear models under conditional mean ***,our test allows heteroscedastic regression models without imposing any condition on the distribution of the error,utilizes effectively important information contained in the distance of the vector of covariates,has a simple form,is easy to implement,and is free of the subjective choice of ***,our mathematical analysis is of own interest since it does not take advantage of the empirical process theory and provides some insights on the asymptotic behavior of U-statistic in the framework of model *** asymptotic null distribution of the proposed test statistic is derived and its asymptotic power behavior against fixed alternatives and local alternatives converging to the null at the parametric rate is also *** particular,we show that its asymptotic null distribution is very different from that obtained for the true error and their differences are interestingly related to the form expression for the estimated parameter vector embodied in regression function and a martingale difference divergence *** the asymptotic null distribution of the test statistic depends on data generating process,we propose a wild bootstrap scheme to approximate its null *** consistency of the bootstrap scheme is *** studies are undertaken to show the good performance of the new test.

关键词： bootstrap goodness-of-fit test linear mean regression martingale difference divergence martingale difference divergence matrix

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