# The rate of the normal approximation for jackknifingU-statistics

The rate of the normal approximation for jackknifingU-statistics LetU n be aU-statistic with symmetric kernelh(x, y) such thatEh(X1, X2)=θ and VarE[h(X1, X2)−θ|X 1]>0. Letf(x) be a function defined onR andf″ be bounded. Iff(θ) is the parameter of interest, a natural estimator isf(Un). It is known that the distribution function of $$z_n = \frac{{\sqrt n \{ Jf(Un) - f(\theta )\} }}{{S_n^* }}$$ converges to the standard normal distribution Φ(x) asn→∞, whereJf(Un) is: the jackknife estimator off(Un), andS n *2 is the jackknife estimator of the asymptotic variance ofn 1/2 Jf(Un). It is of theoretical value to study the rate of the normal approximation of the statisticz n. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# The rate of the normal approximation for jackknifingU-statistics

, Volume 2 (2) – Apr 6, 2005
6 pages

/lp/springer-journals/the-rate-of-the-normal-approximation-for-jackknifingu-statistics-7Ms0ftxu90
Publisher
Springer Journals
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF01539482
Publisher site
See Article on Publisher Site

### Abstract

LetU n be aU-statistic with symmetric kernelh(x, y) such thatEh(X1, X2)=θ and VarE[h(X1, X2)−θ|X 1]>0. Letf(x) be a function defined onR andf″ be bounded. Iff(θ) is the parameter of interest, a natural estimator isf(Un). It is known that the distribution function of $$z_n = \frac{{\sqrt n \{ Jf(Un) - f(\theta )\} }}{{S_n^* }}$$ converges to the standard normal distribution Φ(x) asn→∞, whereJf(Un) is: the jackknife estimator off(Un), andS n *2 is the jackknife estimator of the asymptotic variance ofn 1/2 Jf(Un). It is of theoretical value to study the rate of the normal approximation of the statisticz n.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Apr 6, 2005

### References

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