Chi-square approximation by Stein's method with application to Pearson's statistic

By Robert E. Gaunt, A. Pickett, Gesine Reinert. 2015

80 citations recorded by the source corpus.

This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve both the shape parameter and the order of the derivative. Subsequently Stein's method for chi-square approximation is applied to bound the distributional distance between Pearson's statistic and its limiting chi-square distribution, measured using smooth test functions. In combination with the use of symmetry arguments, Stein' method yields explicit bounds on this distributional distance of order $n^{-1}$.

Subfields: Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dde59bf4670962a8048ae97f0ad9a06bbfd68e1a

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In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

A multivariate Berry–Esseen theorem with explicit constants (2018, methodology): “Recently, Stein’s method has been used by Gaunt, Pickett and Reinert [15] to derive a convergence rate of order n−1, but for sufficiently smooth radially symmetric test functions rather than the indicators of centered balls.”
On Stein's method for products of normal random variables and zero bias couplings (2013, methodology): “Since then, Stein’s method has been extended to many other distributions, such as the Poisson [5], beta [8], [25], gamma [21], [29], [31], exponential [4], [34], Laplace [9], [36] and variance-gamma [13], [19]; for an overview see Reinert [37].”
Approximation of stable law in Wasserstein-1 distance by Stein’s method (2017, methodology): “Nowadays, Stein’s method has been extended and refined by many authors and become a very important tool for getting bounds of measure approximations, see [6, 10, 14, 22, 24, 29, 39, 46, 26, 27, 28, 33, 42, 43, 44, 47].”