Sharp bounds on l-estimates and their expectations for dependent samples

DOI10.1080/03610928308831073zbMath0786.62046OpenAlexW2122658535MaRDI QIDQ4275779

Tomasz Rychlik

Publication date: 31 January 1994

Published in: Communications in Statistics - Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03610928308831073

zbMATH Keywords

order statisticsupportidentically distributed random variablessymmetric random variablesbounded random variablesdependent samplebounds on expectations\(L\)-estimates of arbitrary finite samplescentral absolute momentgiven expectation

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Nonparametric estimation (62G05) Exact distribution theory in statistics (62E15) Order statistics; empirical distribution functions (62G30)

Related Items (23)

Bounds on expectation of order statistics from a finite population ⋮ Unimodality of uniform generalized order statistics, with applications to mean bounds ⋮ Exact bounds for the mean of total time on test under type II censoring samples ⋮ Reliability and expectation bounds for coherent systems with exchangeable components ⋮ Polygonal smoothing of the empirical distribution function ⋮ SHARP BOUNDS FOR THE MEAN OFkTH RECORD VALUE ⋮ Extremal properties of order statistic distributions for dependent samples with partially known multidimensional marginals ⋮ Sharp bounds on change in expected values and variances for single risk analysis in the flood catastrophe model ⋮ Bounds on expectations ofL-estimates for maximally and minimally stable samples ⋮ Bounds on dispersion of order statistics based on dependent symmetrically distributed random variables ⋮ P-norm bounds for moments of progressive type II censored order statistics. ⋮ Bounds on the mean residual lifetime of progressive type II right censored order statistics ⋮ Lower bounds on expectations of positive \(L\)-statistics from without-replacement models ⋮ Evaluations of quantiles of system lifetime distributions ⋮ Multivariate copulas with hairpin support ⋮ Mean-variance bounds for order statistics from dependent DFR, IFR, DFRA and IFRA samples ⋮ Maximizing the expected range from dependent observations under mean–variance information ⋮ Evaluations of the mean residual lifetime of an \(m\)-out-of-\(n\) system ⋮ BOUNDS ON THE BIAS OF WINSORIZED MEANS ⋮ Sharp bounds on distribution functions and expectations of mixtures of ordered families of distributions ⋮ Lower Bounds on Spacings Based on With-Replacement Model ⋮ Sharp bounds on the expectations of second record values from symmetric populations ⋮ Bounds on the expectations of \(L\)-statistics based on iid life distributions

Cites Work

• p-norm bounds on the expectation of the maximum of a possibly dependent sample
• Some finite sample results for the selection differential
• Bounds on expectations of linear systematic statistics based on dependent samples
• Distribution-Free Bounds on the Mean of the Maximum of a Dependent Sample
• Maximal Deviation Between Sample and Population Means in Finite Populations
• Bounds on Differences of Order Statistics
• Maximally dependent random variables
• Schwarz, Regression, and Extreme Deviance
• Best bounds for order statistics and their expectations in range and mean units with applications
• Inequalities of Chebyshev Type Involving Conditional Expectations
• On the Bounds of the Range of Order Statistics

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