Browsing by Subject "U-statistics"
Now showing items 1-10 of 10
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Article
Consistent Testing for Pairwise Dependence in Time Series
(2017)We consider the problem of testing pairwise dependence for stationary time series. For this, we suggest the use of a Box–Ljung-type test statistic that is formed after calculating the distance covariance function among ...
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Article
A Kolmogorov inequality for U-statistics based on Bernoulli kernels
(1994)A Kolmogorov inequality for the class of U-statistics based on kernels which are Bernoulli random variables is presented. This class of statistics contains the sample average of i.i.d. Bernoulli random variables as a special ...
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Article
Maximal inequalities and convergence results for generalized U-statistics
(1990)We present some key probability inequalities and convergence results for multisample, or 'generalized' U-statistics. The reverse martingale structure of generalized U-statistic is exploited to obtain a useful Kolmogorov-type ...
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Article
Probability inequalities with exponential bounds for U-statistics
(1991)I present some probability inequalities with exponential bounds for U-statistics. In particular, I develop a probability inequality for U-statistics based on kernels which are Bernoulli random variables. In the special ...
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Article
Rate of convergence in the strong law of large numbers for a class of u-statistics and von Mises statistics
(1997)For the class of U-statistics based on multidimensionally indexed random variables introduced in Christofides (1987), an improved rate of convergence in the strong law of large numbers is obtained using martingale inequalities ...
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Article
Rate of convergence in the strong law of large numbers for U-statistics based on a multidimensionally indexed array of random variables
(1990)U-statistics based on a multidimensionally indexed array of random variables were introduced in Christofides (1987). In this paper, the rate of convergence in the strong law of large numbers for this class of U-statistics ...
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A strong law of large numbers for U-statistics
(1992)A U-statistic is defined based on a symmetric kernel h and on a collection of r-dimensionally indexed independent random variables from a distribution F. The simplest case of such a U-statistic is the sample mean of an ...
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Article
Subsampling Inference with K Populations and a Non-standard Behrens-Fisher Problem
(2012)We revisit the methodology and historical development of subsampling, and then explore in detail its use in hypothesis testing, an area which has received surprisingly modest attention. In particular, the general set-up ...
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Article
U-statistics on a lattice of I.I.D. random variables
(1998)Partial sums and sample means of r-dimensionally indexed arrays of independent random variables have been studied by Dunford (1951), Zygmund (1951), Kuelbs (1968), Wichura (1969), Smythe (1973), Gut (1978, 1992), Etemadi ...
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Article
U-statistics on associated random variables
(2004)We consider the class of U-statistics which are based on a collection of associated random variables. Since independent random variables are associated, the class of U-statistics introduced by Hoeffding (Ann. Math. Statist. ...