Universal consistency of kernel nonparametric M-estimators
نویسنده
چکیده
We prove that in the case of independent and identically distributed random vectors (Xi, Yi) a class of kernel type M-estimators is universally and strongly consistent for conditional M-functionals. The term universal means that the strong consistency holds for all joint probability distributions of (X, Y ). The conditional M-functional minimizes (2.2) for almost every x. In the case M(y) = |y| the conditional M-functional coincides with the L1-functional and with the conditional median.
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