arXiv subjects

Adrian Röllin

Publications and source records attributed to Adrian Röllin.

40 records · Page 3Linked to original sources

arXiv2009

A Three-Parameter Binomial Approximation

We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the three parameters (the number of trials, the probability of success, and the shift amount) are chosen to match up the first three moments of the two distributions. We give a bound on the approximation error in terms of the total variation metric using Stein's method. A numerical study is discussed that shows shifted binomial approximations typically are more accurate than Poisson or standard binomial approximations. The application of the approximation to solving a problem arising in Bayesian hierarchical modeling is also discussed.

math.PR↗

arXiv2008

A note on the exchangeability condition in Stein's method

We show by a surprisingly simple argument that the exchangeability condition, which is key to the exchangeable pair approach in Stein's method for distributional approximation, can be omitted in many standard settings. This is achieved by replacing the usual antisymmetric function by a simpler one, for which only equality in distribution is required. In the case of normal approximation we also slightly improve the constants appearing in previous results. For Poisson approximation, a different antisymmetric function is used, and additional error terms are needed if the bound is to be extended beyond the exchangeable setting.

math.PR↗

arXiv2007

Translated Poisson approximation using exchangeable pair couplings

It is shown that the method of exchangeable pairs introduced by Stein [Approximate Computation of Expectations (1986) IMS, Hayward, CA] for normal approximation can effectively be used for translated Poisson approximation. Introducing an additional smoothness condition, one can obtain approximation results in total variation and also in a local limit metric. The result is applied, in particular, to the anti-voter model on finite graphs as analyzed by Rinott and Rotar [Ann. Appl. Probab. 7 (1997) 1080--1105], obtaining the same rate of convergence, but now for a stronger metric.

math.PR↗

arXiv2006

Symmetric and centered binomial approximation of sums of locally dependent random variables

Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric Binomial distribution. Under appropriate smoothness properties of the summands, the same order of accuracy as in the Berry-Essen Theorem is achieved. The approximation of the total number of points of a point processes is also considered. The results are applied to the exceedances of the $r$-scans process and to the Matérn hardcore point process type I.

math.PR↗