Self-normalized sumsStein’s methodWe study the self-normalized sums of independent random variables from the perspective of the Malliavin calculus. We give the chaotic expansion for them and we prove a Berry–Esséen bound with respect to several distances....
We show that the distribution of self-normalized sums of free self-adjoint random variables converges weakly to Wigner's semicircle law under appropriate conditions and estimate the rate of convergence in terms of the Kolmogorov distance. In the case of free identically distributed self-adjoint bounde...
摘要: We determine the cluster sets of certain self-normalized sums of i.i.d. random variables. In the process, we obtain a refined large deviation result for sums in the domain of attraction of a stable law.关键词:Self-normalized sums stable laws cluster sets ...
self-normalized sumsLet X, X (1) , X (2) , . . . be a sequence of strictly stationary I center dot-mixing random variables with zero means. In this paper, we show that a self-normalized version of almost sure central limit theorem holds under the assumptions that the mixing ...
Finally, they are also very useful in practice themselves, e.g., the self-normalized sums are closely related to the commonly used Studentt-statistics in inference. In this paper, we shall briefly review some of the results for sums and self-normalized sums of independent random variables. ...
This paper briefly surveys recent developments on self-normalized saddle point approximations; limiting distributions of self-normalized sums; weak invariance principle for self-normalized partial sum processes; Darling-Erds type theorem... Qi-Man Shao\t - Probability, Finance And Insurance 被引量: 54...
1) Self-normalized partial sums 自正则化部分和 2) partial regularity 部分正则性 1. his peper is concerned with thepartial regularityof weak solutions to certain obstacleproblems involving p-Laplacian type elliptic systems with natural growth conditions. ...
We establish a Cram\'er-type moderate deviation result for self-normalizedsums of weakly dependent random variables, where the moment requirement is muchweaker than the non-self-normalized counterpart. The range of the moderatedeviation is shown to depend on the moment condition and the degree of...
An extension of almost sure central limit theorem for self-normalized products of sums for mixing sequences: Communications in Statistics - Theory and Methods: Vol 45, No 22doi:10.1080/03610926.2014.963619Almostsurecentrallimittheoremφ-Mixing
作者: Qi-Man Shao\t 摘要: This paper briefly surveys recent developments on self-normalized saddle point approximations; limiting distributions of self-normalized sums; weak invariance principle for self-normalized partial sum processes; Darling-Erds type theorem; self-normalized empirical processes; se...