Projection method for moment bounds on order statistics from restricted families. II: Independent case

DOI10.1006/jmva.1997.1720zbMath0906.62050OpenAlexW4241228350MaRDI QIDQ1383919

Tomasz Rychlik, Lestaw Gajek

Publication date: 16 February 1999

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmva.1997.1720

zbMATH Keywords

convex coneBernstein polynomialvariation diminishing propertyindependentidentically distributed random variablesdecreasing failure ratessymmetric unimodal distribution

Mathematics Subject Classification ID

Exact distribution theory in statistics (62E15) Order statistics; empirical distribution functions (62G30) Characterization and structure theory of statistical distributions (62E10)

Related Items (38)

Sharp Upper Bounds for Expectations of Differences of Order Statistics in Various Scale Units ⋮ Bounds on expectations of \(L\)-statistics from without replacement samples ⋮ Evaluations of expectations of order statistics and spacings based on IFR distributions ⋮ Sharp bounds on expectations of second record increments from decreasing density families ⋮ Sharp bounds for the mean of the total time on test for distributions with increasing generalized failure rate ⋮ Bounds on the expectations of \(L\)-statistics from iid symmetric populations in various scale units ⋮ On the choice of the optimal single order statistic in quantile estimation ⋮ Bounds on dispersion of order statistics based on dependent symmetrically distributed random variables ⋮ On Families of Distributions for Which Optimal Bounds on Expectations of GOS Can be Derived ⋮ Sharp bounds on the expectations of L-statistics expressed in the Gini mean difference units ⋮ Sharp bounds for expectations of spacings from DDA and DFRA families. ⋮ Non-positive upper bounds on expectations of small order statistics from DDA and DFRA populations ⋮ Refined solution to upper-bound problem for the expectations of order statistics from decreasing density on the average distributions ⋮ Projection bounds on expectations of generalized order statistics from DD and DDA families ⋮ Mean-variance bounds for order statistics from dependent DFR, IFR, DFRA and IFRA samples ⋮ Optimal bounds on expectations of order statistics and spacings from nonparametric families of distributions generated by convex transform order ⋮ Expectation bounds on linear estimators from dependent samples ⋮ Optimal bounds onl-statistics based on samples drawn with replacement from finite populations ⋮ Maximizing the expected range from dependent observations under mean–variance information ⋮ Sharp distribution-free bounds on the bias in estimating quantiles via order statistics ⋮ Sharp bounds on expectations of \(k\)th record spacings from restricted families ⋮ Projection Bounds on Expectations of Spacings of Generalized Order Statistics from DD and DDA Families ⋮ Variation diminishing property of densities of uniform generalized order statistics ⋮ Bounds on expectations of small order statistics from decreasing density populations ⋮ Projection bounds on expectations of spacings of generalized order statistics from DFR and DFRA families ⋮ Sharp upper mean-variance bounds for trimmed means from restricted families ⋮ On upper bounds on expectations of gOSs based on DFR and DFRA distributions ⋮ Lower Bounds on PositiveL-Statistics ⋮ Non-positive upper bounds on expectations of low rank order statistics from DFR populations ⋮ Tight evaluations for expectations of small order statistics from symmetric and symmetric unimodal populations ⋮ Projection bounds on expectations of generalized order statistics from DFR and DFRA families ⋮ Lower bounds on expectations of positiveL-statistics based on samples drawn with replacement ⋮ Sharp lower bounds on expectations of gOS based on DGFR distributions ⋮ Bounds on the expectations of \(L\)-statistics based on iid life distributions ⋮ Optimal evaluations for the bias of trimmed means of \(k\)th record values ⋮ Projection Mean–Variance Bounds on Expectations ofkth Record Values from Restricted Families ⋮ Maximal Expectations of Extreme Order Statistics from Increasing Density and Failure Rate Populations ⋮ Projection bounds on expectations of record statistics from restricted families

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Remarks on de la Vallée Poussin means and convex conformal maps of the circle
• Some finite sample results for the selection differential
• Inequalities of s-ordered distributions
• Projection method for moment bounds on order statistics from restricted families
• Divided Differences and Combinatorial Identities
• Bounds for expectation of l-estimates for dependent samples
• A class of unbiased kernel estimates of a probability density function
• Some Bounds for Expected Values of Order Statistics
• Inequalities for Linear Combinations of Order Statistics from Restricted Families
• LIMITS OF THE RATIO OF MEAN RANGE TO STANDARD DEVIATION
• Extremal Properties of Extreme Value Distributions
• A Modification of Schwarz's Inequality with Applications to Distributions
• The Maxima of the Mean Largest Value and of the Range
• Universal Bounds for Mean Range and Extreme Observation
• Über Erwartungswerte und Varianzen von Ranggrößen in kleinen Stichproben

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