Distribution-free consistency of kernel non-parametric M-estimators

Andrzej S. Kozek; Mirosław Pawlak

doi:10.1016/S0167-7152(02)00106-2

Distribution-free consistency of kernel non-parametric M-estimators

Andrzej S. Kozek^*, Mirosław Pawlak

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We prove that in the case of independent and identically distributed random vectors (X_i, Y_i) 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 co-incides with the L₁-functional and with the conditional median.

Original language	English
Pages (from-to)	343-353
Number of pages	11
Journal	Statistics and Probability Letters
Volume	58
Issue number	4
DOIs	https://doi.org/10.1016/S0167-7152(02)00106-2
Publication status	Published - 15 Jul 2002

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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 co-incides with the L1-functional and with the conditional median.",

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N2 - 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 co-incides with the L1-functional and with the conditional median.

AB - 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 co-incides with the L1-functional and with the conditional median.

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JO - Statistics and Probability Letters

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Distribution-free consistency of kernel non-parametric M-estimators

Abstract

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