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Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing. (English) Zbl 1293.62106
Summary: A new uniform expansion is introduced for sums of weighted kernel-based regression residuals from nonparametric or semiparametric models. This expansion is useful for deriving asymptotic properties of semiparametric estimators and test statistics with data-dependent bandwidths, random trimming, and estimated efficiency weights. Provided examples include a new estimator for a binary choice model with selection and an associated directional test for specification of this model’s average structural function. An appendix contains new results on uniform rates for kernel estimators and primitive sufficient conditions for high level assumptions commonly used in semiparametric estimation.

MSC:
62G20 Asymptotic properties of nonparametric inference
62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression
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