Showing papers on "U-statistic published in 2021"
TL;DR: In this paper, the problem of variance estimation of cross-validation risk is addressed in the form of a general U-statistic and the authors focus on estimating the risk in the context of cross validation.
Abstract: This paper concerns the problem of variance estimation of cross-validation. We consider the unbiased cross-validation risk estimate in the form of a general U-statistic and focus on estimating the ...
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TL;DR: In this paper, a class of U-statistics of overlapping spacings of order two is considered and the asymptotic distribution of the statistics under the null hypothesis and under a sequence of local alternatives are derived.
Abstract: For testing goodness of fit, we consider a class of U-statistics of overlapping spacings of order two, and investigate their asymptotic properties. The standard U-statistic theory is not directly applicable here as the overlapping spacings form a dependent random sequence. The asymptotic distribution of the statistics under the null hypothesis and under a sequence of local alternatives are derived. In terms of the Pitman ARE, the U-statistic based on Gini's mean square difference of overlapping spacings is found to be the asymptotically locally most powerful. Interestingly, this test has the same efficacy as the Greenwood test based on overlapping spacings.