Distribution-free consistency of kernel non-parametric M-estimators |
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| Institution: | 1. Department of Statistics, Brigham Young University, Provo, UT 84602-0001, USA;2. Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106-3110, USA;3. Department of Statistics, Colorado State University, Fort Collins, CO 80523-1877, USA |
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| Abstract: | 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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