A universal strong law of large numbers for conditional expectations via nearest neighbors

For kn-nearest neighbor estimates of a regression Y on X (d-dimensional random vector X, integrable real random variable Y) based on observed independent copies of (X,Y), strong universal pointwise consistency is shown, i.e., strong consistency PX-almost everywhere for general distribution of (X,Y). With tie-breaking by indices, this means validity of a universal strong law of large numbers for conditional expectations E(YX=x).

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Year of publication:	2008
Authors:	Walk, Harro
Published in:	Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 99.2008, 6, p. 1035-1050
Publisher:	Elsevier
Keywords:	Conditional expectation Nearest neighbor regression estimation Strong universal pointwise consistency Strong law of large numbers

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005160484