Central limit theorems revisited

Majumdar, Suman and Kundu, Subrata and Mukherjee, Kanchan (2000) Central limit theorems revisited. Statistics and Probability Letters, 47 (3). pp. 265-275. ISSN 0167-7152

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Abstract

A Central Limit Theorem for a triangular array of row-wise independent Hilbert-valued random elements with finite 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 difference 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, first 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.

Item Type:
Journal Article
Journal or Publication Title:
Statistics and Probability Letters
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1800/1804
Subjects:
ID Code:
65679
Deposited By:
Deposited On:
15 Jul 2013 09:11
Refereed?:
Yes
Published?:
Published
Last Modified:
15 Apr 2020 02:32