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Discussion Paper

Uniform Consistency of Nonstationary Kernel-Weighted Sample Covariances for Nonparametric Regression

We obtain uniform consistency results for kernel-weighted sample covariances in a nonstationary multiple regression framework that allows for both fixed design and random design coefficient variation. In the fixed design case these nonparametric sample covariances have different uniform convergence rates depending on direction, a result that differs fundamentally from the random design and stationary cases.