Self-normalized moderate deviations and lils

Let { X n,n⩾1} be i.i.d. R d -valued random variables. We prove partial moderate deviation principles for self-normalized partial sums subject to minimal moment assumptions. Applications to the self-normalized law of the iterated logarithm are also discussed.

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Bibliographic Details
Published inStochastic processes and their applications Vol. 75; no. 1; pp. 51 - 65
Main Authors Dembo, Amir, Shao, Qi-Man
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.06.1998
Elsevier Science
Elsevier
SeriesStochastic Processes and their Applications
Subjects
Exact sciences and technology
Law of the iterated logarithm
Limit theorems
Mathematics
Moderate deviations
Moderate deviations Self-normalized partial sums Law of the iterated logarithm
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Self-normalized partial sums
Self-normalized partial sums
Moderate deviations
Primary 60F10
Law of the iterated logarithm
60F15
Partial sum
Law of iterated logarithm
Stochastic process
Limit theorem
Online AccessGet full text
ISSN0304-4149
1879-209X
DOI10.1016/S0304-4149(98)00007-6

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Summary:Let { X n,n⩾1} be i.i.d. R d -valued random variables. We prove partial moderate deviation principles for self-normalized partial sums subject to minimal moment assumptions. Applications to the self-normalized law of the iterated logarithm are also discussed.
ISSN:0304-4149
1879-209X
DOI:10.1016/S0304-4149(98)00007-6