✦ LIBER ✦

Central Limit Theorems revisited

✍ Scribed by Subrata Kundu; Suman Majumdar; Kanchan Mukherjee

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 106 KB
Volume: 47
Category: Article
ISSN: 0167-7152
DOI: 10.1016/s0167-7152(99)00164-9

No coin nor oath required. For personal study only.

✦ Synopsis

A Central Limit Theorem for a triangular array of row-wise independent Hilbert-valued random elements with ÿnite second moment is proved under mild convergence requirements on the covariances of the row sums and the Lindeberg condition along the evaluations at an orthonormal basis. A Central Limit Theorem for real-valued martingale di erence arrays is obtained under the conditional Lindeberg condition when the row sums of conditional variances converge to a (possibly degenerate) constant. This result is then extended, ÿrst to multi-dimensions and next to Hilbert-valued elements, under appropriate convergence requirements on the conditional and unconditional covariances and the conditional Lindeberg condition along (orthonormal) basis evaluations. Extension to include Banach-(with a Schauder basis) valued random elements is indicated.

📜 SIMILAR VOLUMES

Central limit theorems under weak depend

Central limit theorems under weak dependence

✍ Richard C Bradley Jr. 📂 Article 📅 1981 🏛 Elsevier Science 🌐 English ⚖ 699 KB

Central limit theorems for weighted d[0,

Central limit theorems for weighted d[0,1]-valued mixing sequences i. functional central limit theorems for weighted sums.

✍ Ken-Ichi Yoshihara 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 228 KB

Almost sure central limit theorems for r

Almost sure central limit theorems for random fields

✍ István Fazekas; Zdzisław Rychlik 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 133 KB 👁 1 views

## Abstract A general almost sure limit theorem is presented for random fields. It is applied to obtain almost sure versions of some (functional) central limit theorems. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Central Limit Theorems for Markov-Connec

Central Limit Theorems for Markov-Connected Random Variables

✍ E. Liebscher 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 642 KB

## Abstract The paper provides some central limit theorems for triangular arrays of Markov‐connected random variables. It is assumed the Markov chain to satisfy condition (__D__~1~) which is an generalization of strong Doeblin's condition (__D~o~__). One result represents a central limit theorem wi

Almost sure central limit theorems under

Almost sure central limit theorems under minimal conditions

✍ István Berkes; Endre Csáki; Lajos Horváth 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 412 KB

Empirical central limit theorems for exc

Empirical central limit theorems for exchangeable random variables

✍ Xinxin Jiang; Marjorie G. Hahn 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 102 KB

This paper provides an empirical central limit theorem (CLT) for exchangeable random variables when the norming constants in the regular CLT are √ nh(n) with h(n) a slowly varying function. The situation with norming constants of the form nh(n) is also discussed.