Cari Colleghi,
vorrei segnalarvi il seguente seminario che si terrà Mercoledi 24 Settembre alle ore 11:45
Louis H. Y. Chen (National University of Singapore)
On the error bound in a combinatorial central limit theorem
Il seminario si terrà in aula Giuseppe Volpato . (Dipartimento di Management, Campus San Giobbe, Cannaregio 873, 30121 Venezia Venezia)
Andrea Collevecchio
ABSTRACT The notion of exchangeable pair is central to Stein's method. The use of concentration inequalities is an effective means for bounding the Kolmogorov distance in normal approximation. Let $\{X_{ij}: i, j = 1, \cdots, n\}$ be independent random variables with finite 3rd moments and let $\pi$ be a random permutation of $(1, \dots,n)$, independent of the $X_{ij}$. Let $U = \sum_{i=1}^n X_{i\pi(i)}$ and let $W = (U - \mathbb{E} U)/(\mathrm{Var}(U))^{\frac{1}{2}}$. In this talk we will use exchangeable pairs and the concentration inequality approach to obtain a 3rd-moment error bound on $|P(W \le x) - \Phi(x)|$, where $\Phi$ is the standard normal distribution function. This result includes the case where the $X_{ij}$ are constants and the case of sampling without replacement from independent random variables. This talk is based on joint work with Xiao Fang.