Approximation Theorems of Mathematical Statistics

By Robert Serfling. 1980

Subfields: Statistics and Probability, Statistical Learning Theory

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In Statistics and Probability

1. Bernhard Schölkopf
2. Jan Peters
3. Peter Buhlmann
4. Arthur Gretton
5. Jianqing Fan
6. Kenji Fukumizu
7. Mathias Drton
8. Le Song

In Statistical Learning Theory

1. Bernhard Schölkopf
2. Arthur Gretton
3. Kenji Fukumizu
4. Le Song
5. Jan Peters
6. Bharath K. Sriperumbudur
7. Alex Smola
8. Karsten M. Borgwardt

Citations in the corpus

• Kernel‐based tests for joint independence (2016, methodology): “Whereas U-statistics have been extensively studied (e.g. Serfling (1980)), results for V-statistics are often restricted to q= 2.”
• Structural properties and convergence results for contours of sample statistical depth functions (2000, methodology): “The arguments are similar to the proof of Theorem 2.3.2 of Serfling (1980) for univariate sample quantiles using probability inequalities of Hoeffding (1963).”
• Estimating conditional tail expectation with actuarial applications in view (2008, methodology): “For results and discussions on the subject, we refer, for example, to Puri and Sen (1971), Serfling (1980) and Shorack and Wellner (1986).”
• All Models are Wrong but many are Useful: Variable Importance for Black-Box, Proprietary, or Misspecified Prediction Models, using Model Class Reliance (2018, background): “Thus, under fairly minor conditions, êswitch(f) and êdivide(f) are unbiased, asymptotically normal, and have finite-sample probabilistic bounds (Hoeffding, 1948; Serfling, 1980).”
• ESTIMATION OF DISTRIBUTION FUNCTION AND QUANTILES USING THE MODEL-CALIBRATED PSEUDO EMPIRICAL LIKELIHOOD METHOD (2002, background): “The crucial argument that leads to this result is the Bernstein’s inequality (Serfling (1980), p.95).”
• Estimation of the generalized logistic distribution parameters: Comparative study (2009, unknown): “Using the central limit theorem ([22], P.”
• Matching As An Econometric Evaluation Estimator (1998, methodology): “We also make use of the results of Serfling (1980).”
• Empirical Likelihood Methods in Econometrics: Theory and Practice (2006, background): “For example, consider the following asymptotic efficiency criterion in terms of “large deviations” (see Chapter 10 of Serfling (1980) for discussions on large deviation theory).”
• Estimator and Tests for Common Coefficients of Variation in Normal Distributions (2009, unknown): “Then, by application of Theorem 3.1A in Serfling (1980), √ v Tv = √ v f(Uv) d→ N(f(γ2) , (f ′(γ2))2(2γ4 + 4γ6)), as v →∞, and (6) follows since (f ′(γ2))2(2γ4 + 4γ6) = γ2/2 + γ4.”