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Deviation probability bound for martingales with applications to statistical estimation

✍ Scribed by R. Liptser; V. Spokoiny

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
132 KB
Volume
46
Category
Article
ISSN
0167-7152

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✦ Synopsis

Let Mt be a vector martingale and M t denote its predictable quadratic variation. In this paper we present a bound for the probability that z * M -1 t Mt ΒΏ z * M -1 t z with a ΓΏxed vector z and discuss some of its applications to statistical estimation in autoregressive and linear di usion models. Our approach is non-asymptotic and does not require any ergodic assumption on the underlying model.

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