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February 2014 Weighted approximations for Studentized $U$-statistics
Masoud M. Nasari
Braz. J. Probab. Stat. 28(1): 24-60 (February 2014). DOI: 10.1214/12-BJPS192


In this article, we employ the jackknife method of estimation and the concept of Studentized $U$-statistics to derive a new weak convergence result for nondegenerate $U$-statistics on the space $D[0,1]$. We drop the classical condition that the second moment of the kernel of the underlying $U$-statistic exists and derive a weighted weak convergence result for these Studentized statistics. This weak convergence is concluded from a weighted approximation in sup-norm $\|/q\|$, in probability, of Studentized $U$-statistics by partial sums of i.i.d. projections, where $q$ is in an appropriate class of positive weight functions.


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Masoud M. Nasari. "Weighted approximations for Studentized $U$-statistics." Braz. J. Probab. Stat. 28 (1) 24 - 60, February 2014.


Published: February 2014
First available in Project Euclid: 5 February 2014

zbMATH: 06291459
MathSciNet: MR3165427
Digital Object Identifier: 10.1214/12-BJPS192

Rights: Copyright © 2014 Brazilian Statistical Association


Vol.28 • No. 1 • February 2014
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