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Communications in Statistics - Theory and Methods, 1986
For a class of distributions which are invariant under a group of transformations, we propose an estimator ot an estimable parameter. The estimator, which we call the invariant U-statistic, is the uniformly minimum variance unbiased estimator of the corresponding estimable parameter for the class of all continuous distributions which are invariant ...
Hajime Yamato, Yoshihiko Maesono
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For a class of distributions which are invariant under a group of transformations, we propose an estimator ot an estimable parameter. The estimator, which we call the invariant U-statistic, is the uniformly minimum variance unbiased estimator of the corresponding estimable parameter for the class of all continuous distributions which are invariant ...
Hajime Yamato, Yoshihiko Maesono
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U-Statistic Hierarchical Clustering
Psychometrika, 1978A monotone invariant method of hierarchical clustering based on the Mann-Whitney U-statistic is presented. The effectiveness of the complete-link, single-link, and U-statistic methods in recovering tree structures from error perturbed data are evaluated.
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Large Deviations of U-Statistics. II
Lithuanian Mathematical Journal, 2003Large deviation results are proved for non-degenerate \(U\)-statistics of degree \(m\) of the form \[ U_n={(m-1)\cdots 2\cdot 1 \over{(n-1)\cdots (n-m+1) } } \sum_{1\leq i_1 < \cdots < i_m \leq n } h(X_{i_1}, \ldots, X_{i_m}), \] where \(X_1,\ldots X_n\) be independent and identically distributed random variables, taking values in a measurable space ...
Borovskikh, Yu. V., Weber, N. C.
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Hermite ranks and $$U$$ U -statistics
Metrika, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lévy-Leduc, C., Taqqu, M. S.
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Weighted bootstrapping of U-statistics
Journal of Statistical Planning and Inference, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Acta Applicandae Mathematicae, 1994
Let \(B\) be a real separable Banach space with the norm \(\|\cdot\|\). Let \(X_ 1,\dots, X_ n\) be independent random elements with values in a measurable space \(({\mathcal X},{\mathcal A})\) and having identical distribution \(P\). Each symmetric function \(\Phi: {\mathcal X}^ m\to B\) defines a so-called \(UB\)-statistic \[ U_{mn}= {n\choose m}^{-1}
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Let \(B\) be a real separable Banach space with the norm \(\|\cdot\|\). Let \(X_ 1,\dots, X_ n\) be independent random elements with values in a measurable space \(({\mathcal X},{\mathcal A})\) and having identical distribution \(P\). Each symmetric function \(\Phi: {\mathcal X}^ m\to B\) defines a so-called \(UB\)-statistic \[ U_{mn}= {n\choose m}^{-1}
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Empirical U-statistics processes
Journal of Statistical Planning and Inference, 1992Let \(\xi_ 1,\xi_ 2,\dots\) be independent and identically distributed random elements defined on a probability space \((\Omega,{\mathcal E},P)\) with values in a measurable space \(X_ 2\) with \(\sigma\)-field \(\mathcal A\) and let \(h: X^ q\to R^ r\) be an \(({\mathcal A}^ q,{\mathcal B}^ r)\)- measurable mapping \((q,r\in N)\) (\(h\) being ...
Ruymgaart, F.H., Zuijlen, M.C.A. van
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Tail probability approximations for U-statistics
Statistics & Probability Letters, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Keener, Robert W. +2 more
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2018
U statistics are a large and important class of statistics. Indeed, any U-statistic (with finite variance) is the non-parametric minimum variance estimator of its expectation \( \theta \). Many common statistics and estimators are either U-statistics or approximately so.
Arup Bose, Snigdhansu Chatterjee
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U statistics are a large and important class of statistics. Indeed, any U-statistic (with finite variance) is the non-parametric minimum variance estimator of its expectation \( \theta \). Many common statistics and estimators are either U-statistics or approximately so.
Arup Bose, Snigdhansu Chatterjee
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