| Título: | Upper Bounds for Stein-Type Operators |
| Autores: | Daly, Fraser A; University of Nottingham |
| Fecha: | 2008-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Stein-type operator; Stein's method; central limit theorem; Poisson-Charlier approximation; stochastic ordering 60F05; 60J80; 62E17 |
| Descripción: | We present sharp bounds on the supremum norm of $\mathcal{D}^jSh$ for $j\geq2$, where $\mathcal{D}$ is the differential operator and $S$ the Stein operator for the standard normal distribution. The same method is used to give analogous bounds for the exponential, Poisson and geometric distributions, with $\mathcal{D}$ replaced by the forward difference operator in the discrete case. We also discuss applications of these bounds to the central limit theorem, simple random sampling, Poisson-Charlier approximation and geometric approximation using stochastic orderings. |
| Idioma: | No aplica |
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