On the rate of convergence of moments in the central limit theorem
1978 ◽
Vol 25
(2)
◽
pp. 250-256
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Keyword(s):
AbstractAn early extension of Lindeberg's central limit theorem was Bernstein's (1939) discovery of necessary and sufficient conditions for the convergence of moments in the central limit theorem. Von Bahr (1965) made a study of some asymptotic expansions in the central limit theorem, and obtained rates of convergence for moments. However, his results do not in general imply that the moments converge. Some better rates have been obtained by Bhattacharya and Rao for moments between the second and third. In this paper we give improved rates of convergence for absolute moments between the third and fourth.
1999 ◽
Vol 36
(4)
◽
pp. 974-986
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1999 ◽
Vol 36
(04)
◽
pp. 974-986
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1984 ◽
Vol s3-49
(3)
◽
pp. 423-444
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Keyword(s):
1983 ◽
pp. 561-575
◽
1985 ◽
Vol 22
(02)
◽
pp. 280-287
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