Asymptotic Normality of U -Quantile-Statistics
نویسنده
چکیده
In 1948, W. Hoeffding introduced a large class of unbiased estimators called U -statistics, defined as the average value of a real-valued m-variate function h calculated at all possible sets of m points from a random sample. In the present paper, we investigate the corresponding robust analogue which we call U -quantile-statistics. We are concerned with the asymptotic behavior of the sample p-quantile of such function h instead of its average. Alternatively, U -quantile-statistics can be viewed as quantile estimators for a certain class of dependent random variables. Examples are given by a slightly modified HodgesLehmann estimator of location and the median interpoint distance among random points in space.
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