A Class of Statistics with Asymptotically Normal Distribution

By W. Hoeffding. 1948

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In Statistics and Probability

Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Gretton et al. (2012a) proposes two distribution-free tests based on large deviation bounds (using Rademacher complexity and bound on U -statistics of Hoeffding (1948)) and the third one based on the asymptotic distribution of the test statistics.”
All Models are Wrong, but Many are Useful: Learning a Variable’s Importance by Studying an Entire Class of Prediction Models Simultaneously (2018, background): “Thus, under fairly minor conditions, these estimators are unbiased, asymptotically normal, and have finite-sample probabilistic bounds (Hoeffding, 1948, 1963; Serfling, 1980; see also DeLong et al., 1988 for an early use of U-statistics in machine learning, as well as caveats in Demler et al.,…”
Generalized random forests (2016, methodology): “…2.4), θ̃∗(x) is an infinite-order U -statistic whose order corresponds to the subsample size, and so the arguments of Mentch and Hooker (2016) or Wager and Athey (2018) can be used to study the averaged estimator θ̃∗(x) using results about U -statistics (Hoeffding, 1948; Efron and Stein, 1981).”
A Kernelized Stein Discrepancy for Goodness-of-fit Tests (2016, methodology): “where Ŝu(p, q) is a form of U -statistics (“U” stands for unbiasedness), which provides a minimum-variance unbiased estimator for S(p, q) (Hoeffding, 1948; Serfling, 2009).”
A low variance consistent test of relative dependency (2014, background): “Kernel Methods for Measuring Independence, Journal of Machine Learning Research, 6 , 2075-2129, - Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution.”
Recent and classical tests for exponentiality: a partial review with comparisons (2005, background): “More generally, Hoeffding (1949) shows that, under the condition EðX 2 Þ < 1, fGn� EðGnÞg=fVarðGnÞg 1=2 has a limiting standard normal distribution.”
The Use of Discrete Data in PCA: Theory, Simulations, and Applications to Socioeconomic Indices (2004, background): “In particular, those correlation coefficients are combinations of U -statistics which are known to be asymptotically normal (Hoeffding 1948, van der Vaart 1998). It follows from (41) that Kendall’sτ gives smaller weights to the pairs of observations that have drastically different ranks than Spearma”
Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask (2007, background): “and that Cn → C as n →. For more precise conditions under which this result holds, see, e.g., Hoeffding 1948 .”
Feature Selection via Dependence Maximization (2012, methodology): “Proof [Sketch] This follows directly from Serfling (1980, Theorem B, p. 193), which shows asymptotic normality of U-statistics.”
Design of fusion technique-based mining engine for smart business (2015, background): “In general case, the learning results meet the normal distribution [42].”
Nonparametric and semiparametric estimation of the three way receiver operating characteristic surface (2009, unknown): “} is an indicator function, one can use the projection method (Hoeffding, 1948) to derive the asymptotic variance formula (Nakas and Yiannoutsos, 2004).”
Consistency and asymptotic distribution of the Theil–Sen estimator (2008, methodology): “When establishing the asymptotic normality of the Theil-Sen estimator, Sen (1968) applied a theorem from Hoeffding (1948) that requires these Zi’s to be independent and identically distributed random vectors.”