Approximation Theorems of Mathematical Statistics

By I. Ser. 1980

Subfields: Statistics and Probability, Statistical Learning Theory

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Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Definition 3.4 (U -statistics and V -statistics, Serfling 1981).”
All Models are Wrong, but Many are Useful: Learning a Variable’s Importance by Studying an Entire Class of Prediction Models Simultaneously (2018, background): “…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., 2012).”
A Kernelized Stein Discrepancy for Goodness-of-fit Tests (2016, methodology): “…from the (unknown) p ( x ) , the form (3) also enables efﬁcient empirical estimation of S ( p, q ) via a U -statistic, (4) The distribution of ˆ S ( p, q ) can be well characterized using the theory of U -statistics (Hoeffding, 1948; Serﬂing, 2009), allowing us to reduce the testing of p = q to”
A Kernel Test of Goodness of Fit (2016, methodology): “The two concepts required to derive the distribution of the test statistic are: τ -mixing (Dedecker et al., 2007; Leucht & Neumann, 2013), and V-statistics (Serfling, 1980).”
A Wild Bootstrap for Degenerate Kernel Tests (2014, background): “The main results of the paper are based around two concepts: τ -mixing [10], which describes the dependence within the time series, and V -statistics [27], which constitute our test statistics.”
A low variance consistent test of relative dependency (2014, methodology): “The derivation of our test utilizes classical results of U -statistics (Hoeffding, 1963; Serfling, 1981; Arcones & Gine, 1993).”
Testing Hypotheses by Regularized Maximum Mean Discrepancy (2013, background): “Based on Hoeffding [14], Theorem A (p. 192) and Theorem B (p. 193) by Serfling [19], we can prove the following theorem: Theorem 2.”
B-tests: Low Variance Kernel Two-Sample Tests (2013, background): “It is shown in [9] that this simple asymptotic distribution makes it easy to optimize the Hodges and Lehmann asymptotic relative efficiency [19] over the family of kernels that define the statistic: in other words, to choose the kernel which gives the lowest Type II error (probability of wrongly acc”
Consistency of the MLE under mixture models (2016, unknown): “By applying Bernstein’s inequality to ∆j followed by the Borel–Cantelli Lemma as in Serfling (1980), we get max j ∆j Mǫ+ 8n −1 log n. Combining the two bounds leads to (3.8) sup θ {Fn(θ + ǫ)− Fn(θ)} ≤ 2Mǫ+ n−1 + 8n−1 log n almost surely.”
Asymptotics for Analysis of Variance When the Number of Levels is Large (2000, background): “Because the & are independent, by Liapanov’s theorem, it is enough to show that (see Serfling 1980, pp. 18, 30).”
Generalized Wald-type tests based on minimum density power divergence estimators (2014, background): “In testing of a composite null hypothesis, the restricted parameter space 0 ⊂ is often defined by a set of r restrictions of the form m(θ) = 0r, (17) where m : Rp → Rr (see [10]).”
Non-linear dynamics of a drill-string with uncertain model of the bit–rock interaction (2009, methodology): “The upper and lower envelopes of the confidence region are calculated using the method of quantiles [30].”
The Distribution of Robust Distances (2005, methodology): “Since 1 X and 1 X¤ are consistent estimators for 1, and S and c¡1S¤ (for some constant c) are consistent estimators for §, we know that the within sample and out of sample MSD are both asymptotically Â(2)p statistics (Mardia et al., 1979; Ser°ing, 1980).”