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Central limit theorems revisited

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Central limit theorems revisited. / Majumdar, Suman; Kundu, Subrata; Mukherjee, Kanchan.
In: Statistics and Probability Letters, Vol. 47, No. 3, 15.04.2000, p. 265-275.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Majumdar, S, Kundu, S & Mukherjee, K 2000, 'Central limit theorems revisited', Statistics and Probability Letters, vol. 47, no. 3, pp. 265-275. https://doi.org/10.1016/S0167-7152(99)00164-9

APA

Majumdar, S., Kundu, S., & Mukherjee, K. (2000). Central limit theorems revisited. Statistics and Probability Letters, 47(3), 265-275. https://doi.org/10.1016/S0167-7152(99)00164-9

Vancouver

Majumdar S, Kundu S, Mukherjee K. Central limit theorems revisited. Statistics and Probability Letters. 2000 Apr 15;47(3):265-275. doi: 10.1016/S0167-7152(99)00164-9

Author

Majumdar, Suman ; Kundu, Subrata ; Mukherjee, Kanchan. / Central limit theorems revisited. In: Statistics and Probability Letters. 2000 ; Vol. 47, No. 3. pp. 265-275.

Bibtex

@article{68adf98ec82e45ebb41bec1369bacbe0,
title = "Central limit theorems revisited",
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. ",
keywords = "CLT, Hilbert space, Lindeberg condition, Martingale dierence array , Weak convergence",
author = "Suman Majumdar and Subrata Kundu and Kanchan Mukherjee",
year = "2000",
month = apr,
day = "15",
doi = "10.1016/S0167-7152(99)00164-9",
language = "English",
volume = "47",
pages = "265--275",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier",
number = "3",

}

RIS

TY - JOUR

T1 - Central limit theorems revisited

AU - Majumdar, Suman

AU - Kundu, Subrata

AU - Mukherjee, Kanchan

PY - 2000/4/15

Y1 - 2000/4/15

N2 - 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.

AB - 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.

KW - CLT

KW - Hilbert space

KW - Lindeberg condition

KW - Martingale dierence array

KW - Weak convergence

U2 - 10.1016/S0167-7152(99)00164-9

DO - 10.1016/S0167-7152(99)00164-9

M3 - Journal article

VL - 47

SP - 265

EP - 275

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 3

ER -