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

✍ Scribed by Andrzej S. Kozek; Mirosław Pawlak

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
124 KB
Volume
58
Category
Article
ISSN
0167-7152

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✦ Synopsis

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 coincides with the L 1 -functional and with the conditional median.

📜 SIMILAR VOLUMES

NON-PARAMETRIC INFERENCE OF A FAILURE TI
NON-PARAMETRIC INFERENCE OF A FAILURE TIME DISTRIBUTION WHEN THE FAILURE TIMES ARE ESTIMATED
✍ HYUNGJIN MYRA KIM; STEPHEN W. LAGAKOS 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 925 KB

We consider the estimation of a failure time distribution F when, instead of N i.i.d. realizations TI, T z , .. . , T N from F, the observations consist of estimates of the Ti. If the T i could be observed, a natural non-parametric estimator of F would be the Kaplan-Meier estimator. Thus, we examine