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Title: Central Limit Theorems revisited
Authors: Kundu, S.
Majumdar, S.
Mukherjee, K. 
Keywords: Central Limit Theorem
Hilbert space
Lindeberg condition
Martingale difference array
Primary 60F05
Secondary 60B12
Weak convergence
Issue Date: 15-Apr-2000
Citation: Kundu, S.,Majumdar, S.,Mukherjee, K. (2000-04-15). Central Limit Theorems revisited. Statistics and Probability Letters 47 (3) : 265-275. ScholarBank@NUS Repository.
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. © 2000 Elsevier Science B.V.
Source Title: Statistics and Probability Letters
ISSN: 01677152
Appears in Collections:Staff Publications

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