Abstract
The paper deals with kernel estimates of Nadaraya-Watson type for a regression function with square integrable response variable. For usual bandwidth sequences and smooth nonnegative kernels, e.g., Gaussian and quartic kernels, strongL 2-consistency is shown without any further condition on the underlying distribution. The proof uses a Tauberian theorem for Cesàro summability.
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Walk, H. Strong universal consistency of smooth kernel regression estimates. Ann Inst Stat Math 57, 665–685 (2005). https://doi.org/10.1007/BF02915432
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DOI: https://doi.org/10.1007/BF02915432