Bounds for the variance of functions of random variables by orthogonal polynomials and Bhattacharya bounds

DOI10.1016/0167-7152(86)90033-7zbMath0583.62019OpenAlexW2037067636MaRDI QIDQ1069228

V. Papathanasiou, Theophilos Cacoullos

Publication date: 1986

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(86)90033-7

zbMATH Keywords

exponential familiesvariance boundsseries of orthogonal polynomialsChernoff's inequalityconvergence of Bhattacharya bounds

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Point estimation (62F10) Approximation by polynomials (41A10) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Statistical distribution theory (62E99)

Related Items (8)

First-order covariance inequalities via Stein's method ⋮ Umvu estimation for certain family of exponential distributions ⋮ An extended Stein-type covariance identity for the Pearson family with applications to lower variance bounds ⋮ Estimation based on the winsorized mean in the geometric distribution ⋮ An extension of the information inequality and related characterizations ⋮ Lower bounds for the variance in certain nonregular distributions ⋮ Bounds for the variance of functions of random variables by orthogonal polynomials and Bhattacharya bounds ⋮ Estimation in uniform distributions using orthogonal polynomials

Cites Work

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• On upper bounds for the variance of functions of random variables
• Bounds for the variance of functions of random variables by orthogonal polynomials and Bhattacharya bounds
• A note on an inequality involving the normal distribution
• An inequality for the multivariate normal distribution
• On upper and lower bounds for the variance of a function of a random variable
• The convergence of Bhattacharyya bounds
• On the Variance of Estimates

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