Testing the hypothesis of a general linear model using nonparametric regression estimation

摘要

Given the modelYi=m(χi)+ɛi,whereE(ɛi) =0,Xi≠Ci=1, ...,n, andCis ap-dimensional compact set, we have designed a new method for testing the hypothesis that the regression function follows a general linear model,m(·) ∈ {mθ(·) =At(·)θ}θ∈Θ⊂ℛq, withAa function fromℜptoℜq. The statistic, denoted ΔASE, used fortesting the given hypothesis is defined to be the difference between the average squared errors (ASE) associated with the non-parametric estimator$$hat m$$ofmand the minimum distance parametric estimator$$m_{hat theta } $$ofm. The asymptotic normality of both ΔASE and the minimum distance estimators is proved under general conditions. Alternative bootstrap versions of