Self-normalized Weak Limit Theorems for a Φ-mixing Sequence
نویسندگان
چکیده
Let {Xj , j ≥ 1} be a strictly stationary φ-mixing sequence of non-degenerate random variables with EX1 = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {Xj} under the condition that L(x) := EX2 1 I{|X1| ≤ x} is a slowly varying function at ∞, without any higher moment conditions.
منابع مشابه
Self-normalized limit theorems: A survey
Let X1,X2, . . . , be independent random variables with EXi = 0 and write Sn = ∑ n i=1 Xi and V 2 n = ∑ n i=1 X i . This paper provides an overview of current developments on the functional central limit theorems (invariance principles), absolute and relative errors in the central limit theorems, moderate and large deviation theorems and saddle-point approximations for the self-normalized sum S...
متن کاملJu n 20 09 Orthogonal series and limit theorems for canonical U - and V - statistics of stationary connected observations
The limit behavior is studied for the distributions of normalized U-and V-statistics of an arbitrary order with canonical (degenerate) kernels, based on samples of increasing sizes from a stationary sequence of observations satisfying ϕ-or α-mixing. The corresponding limit distributions are represented as infinite multilinear forms of a centered Gaussian sequence with a known covariance matrix.
متن کاملA Local Limit Theorem for random walks conditioned to stay positive
We consider a real random walk Sn = X1 + . . . + Xn attracted (without centering) to the normal law: this means that for a suitable norming sequence an we have the weak convergence Sn/an ⇒ φ(x)dx, φ(x) being the standard normal density. A local refinement of this convergence is provided by Gnedenko’s and Stone’s Local Limit Theorems, in the lattice and nonlattice case respectively. Now let Cn d...
متن کاملCentral limit theorems for Hilbert-space valued random fields satisfying a strong mixing condition
In this paper we study the asymptotic normality of the normalized partial sum of a Hilbert-space valued strictly stationary random field satisfying the interlaced ρ-mixing condition.
متن کاملON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS
The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010