Cross‐Validation and U ‐Statistics
نویسندگان
چکیده
منابع مشابه
Lecture 4: U-Statistics & U-Process Minimizers
Hoeffding (1948a) developed the basic theory of U-Statistics, a family of estimates which includes many familiar and interesting examples. This lecture reviews this theory. Standard references for the material presented here include Serfling (1980, Chapter 5), Lehmman (1999, Chapter 6) and van der Vaart (1998, Chapters 11 & 12). The basic theory of U-Statistics allows for a presentation of larg...
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An important part of the legacy of Evarist Giné is his fundamental contributions to our understanding of U -statistics and U -processes. In this paper we discuss the estimation of the mean of multivariate functions in case of possibly heavy-tailed distributions. In such situations, reliable estimates of the mean cannot be obtained by usual U -statistics. We introduce a new estimator, based on t...
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In this paper, we investigate the asymptotic theory for U -statistics based on sample spacings, i.e. the gaps between successive observations. The usual asymptotic theory for U -statistics does not apply here because spacings are dependent variables. However, under the null hypothesis, the uniform spacings can be expressed as conditionally independent Exponential random variables. We exploit th...
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Strong laws of large numbers are given for L-statistics (linear com binations of order statistics) and for U -statistics (averages of kernels of ran dom samples) for ergodic stationary processes, extending classical theorems of Hoeffding and of Helmers for iid sequences. Examples are given to show that strong and even weak convergence may fail if the given sufficient conditions are not satisf...
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ژورنال
عنوان ژورنال: ETS Research Report Series
سال: 2019
ISSN: 2330-8516,2330-8516
DOI: 10.1002/ets2.12263