Orthogonal Polynomials in Stein's Method
Copyright policy )Orthogonal Polynomials in Stein's Method
The paper systematically develops a relationship between the classical families of orthogonal polynomials and Stein's method as applied to the distributions in the Pearson and Ord families, that was also discussed by \textit{P. Diaconis} and \textit{S. Zabell} [Stat. Sci. 6, No. 3, 284-302 (1991)]. Here, the two are related by way of a generator approach to Stein's method, in conjunction with the birth and death processes associated with the orthogonal polynomials of \textit{S. Karlin} and \textit{J.L. McGregor}'s [Trans. Am. Math. Soc. 85, 489-546 (1957; Zbl 0091.13801)] spectral representation. This leads, in particular, to Stein equations for the Student's \(t\) and beta distributions.
- KU Leuven Belgium
- Katholieke Universiteit Leuven Belgium
- Technical University Eindhoven Netherlands
Markov processes, Applied Mathematics, distributions, General harmonic expansions, frames, birth and death processes, Approximations to statistical distributions (nonasymptotic), Applications of branching processes, Pearson's class, Ord's class, Stein's method, approximation, orthogonal polynomials, Analysis
Markov processes, Applied Mathematics, distributions, General harmonic expansions, frames, birth and death processes, Approximations to statistical distributions (nonasymptotic), Applications of branching processes, Pearson's class, Ord's class, Stein's method, approximation, orthogonal polynomials, Analysis
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