Some uses of orthogonal polynomials in statistical inference. Issue 6 (31st January 2021)

• Record Type: Journal Article
• Authors: Barranco‐Chamorro, Inmaculada; Grentzelos, Christos
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 6(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-31
• Subjects: approximations of distributions -- chi‐square variables -- NEF‐QVF -- orthogonal polynomials -- UMVUE; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1144
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract: Every random variable (rv) X (or random vector) with finite moments generates a set of orthogonal polynomials, which can be used to obtain properties related to the distribution of X . This technique has been used in statistical inference, mainly connected to the exponential family of distributions. In this paper a review of some of its more relevant uses is provided. The first one deals with properties of expansions in terms of orthogonal polynomials for the Uniformly Minimum Variance Unbiased Estimator of a given parametric function, when sampling from a distribution in the Natural Exponential Family of distributions with Quadratic Variance Function. The second one compares two relevant methods, based on expansions in Laguerre polynomials, existing in the literature to approximate the distribution of linear combinations of independent chi‐square variables.