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April, 1991 On Iterated Logarithm Laws for Linear Arrays and Nonparametric Regression Estimators
Peter Hall
Ann. Probab. 19(2): 740-757 (April, 1991). DOI: 10.1214/aop/1176990449


Laws of the iterated logarithm are derived for row sums of triangular arrays of independent random variables, in the context of nonparametric regression estimators. These laws provide exact strong convergence rates for kernel type nonparametric regression estimators. They apply to the important case where design points are conditioned upon, and permit the design to be multivariate. We impose minimal conditions on the error distribution; in fact, only finite variance is needed.


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Peter Hall. "On Iterated Logarithm Laws for Linear Arrays and Nonparametric Regression Estimators." Ann. Probab. 19 (2) 740 - 757, April, 1991.


Published: April, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0733.60047
MathSciNet: MR1106284
Digital Object Identifier: 10.1214/aop/1176990449

Primary: 60F15
Secondary: 60G50 , 62G05

Keywords: Fixed design , Law of the iterated logarithm , Nonparametric regression , strong convergence rate , triangular array

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.19 • No. 2 • April, 1991
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