Multivariate normal approximations by Stein's method and size bias couplings

Multivariate normal approximations by Stein’s method and size bias couplings

Stein’s method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any nonnegative random vector. Theorem 1.2 requires multivariate size bias coupling, which we discuss in studying the approximation of distributions of sums of dependent random vectors. In the univariate case, we briefly illustrate ...

2 Sample Size Considerations in Multivariate Normal Classification by Seymour

Steins method, Malliavin calculus and infinite-dimensional Gaussian analysis

This expository paper is a companion of the four one-hour tutorial lectures given in the occasion of the special month Progress in Stein’s Method, held at the University of Singapore in January 2009. We will explain how one can combine Stein’s method with Malliavin calculus, in order to obtain explicit bounds in the normal and Gamma approximation of functionals of in…nite-dimensional Gaussian …...

Multivariate normal approximation using Stein’s method and Malliavin calculus

We combine Stein’s method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Our results generalize and refine the main findings by Peccati and Tudor (2005), Nualart and Ortiz-Latorre (2007), Peccati (2007) and Nourdin and Peccati (2007b, 2008); in particular, they apply to appr...

Concentration of measure for the number of isolated vertices in the Erdös-Rényi random graph by size bias couplings

Let Y be a nonnegative random variable with mean μ and let Y , defined on the same space as Y , have the Y -size biased distribution, that is, the distribution characterized by E[Y f(Y )] = μE[f(Y )] for all functions f for which these expectations exist. The size bias coupling of Y to Y s can be used to obtain the following concentration of measure result when Y counts the number of isolated v...