The effects on convergence of substituting parameter estimates into U- statistics and other families of statistics

DOI10.1007/BF00340061zbMath0708.62024MaRDI QIDQ920500

Harald K. Iverson, Ronald Herman Randles

Publication date: 1989

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

strong convergenceweak convergenceorder statisticslimiting distributiondifferentialadaptive L-statisticsadaptive M-estimatorscross-validation assessment statisticslaw of the iterated logarithm for U-statisticssequential test for scale differences

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Robustness and adaptive procedures (parametric inference) (62F35) Strong limit theorems (60F15)

Related Items (15)

New class of exponentiality tests based on U-empirical Laplace transform ⋮ Large sample properties of cross-validation assessment statistics ⋮ New L2-type exponentiality tests ⋮ Weighted bootstrapping for \(U\)-quantiles ⋮ Resampling from centered data in the two-sample problem ⋮ Bootstrapping quantiles in the proportional hazards model of random censorship ⋮ Characterization-based approach for construction of goodness-of-fit test for Lévy distribution ⋮ Bahadur efficiency of EDF based normality tests when parameters are estimated ⋮ Comparison of efficiencies of some symmetry tests around an unknown centre ⋮ A quadratic bootstrap method and improved estimation in logistic regression. ⋮ Bootstrapping local polynomial estimators in likelihood-based models ⋮ Asymptotic distribution of certain degenerate V- and U-statistics with estimated parameters ⋮ Semiparametric inference based on a class of zero-altered distributions ⋮ New consistent exponentiality tests based on V-empirical Laplace transforms with comparison of efficiencies ⋮ Some improvements on the Birnbaum-McCarty bound for \(P(Y<X)\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Large sample properties of cross-validation assessment statistics
• A differential for L-statistics
• A note on differentials and the CLT and LIL for statistical functions, with application to M-estimates
• The asymptotic effect of substituting estimators for parameters in certain types of statistics
• On the asymptotic normality of statistics with estimated parameters
• Testing the Hypothesis That Two Populations Differ Only in Location
• Approximation Theorems of Mathematical Statistics
• On Tests Applied to Residuals
• Predictive Intervals Based on Reuse of the Sample
• A note on adaptive l-statistics
• An Adaptive M-Estimator and Its Application to a Selection Problem
• A New Proof of the Bahadur Representation of Quantiles and an Application
• SOME NONPARAMETRIC SEQUENTIAL TESTS WITH POWER ONE

This page was built for publication: The effects on convergence of substituting parameter estimates into U- statistics and other families of statistics