Deviation probability bound for martingales with applications to statistical estimation
type: Item
instance of: scholarly article
title: Deviation probability bound for martingales with applications to statistical estimation
zbMATH Open document ID: 0953.62080
DOI: 10.1016/S0167-7152(99)00121-2
published in: Statistics \& Probability Letters
publication date: 2001-01-11T00:00:00Z
review text: The authors present an upper bound for the probability that \[ z^*\langle M\rangle_t^{-1}M_t>\lambda\sqrt{z^*\langle M\rangle_t^{-1}z} \] with a fixed vector \(z\) and \(\lambda\geq 1\). Here \(M_t\) is a vector martingale and \(\langle M\rangle_t\) denotes its predictable quadratic variation. They discuss some of its applications to statistical estimation in autoregressive and linear diffusion models. Their approach is non-asymptotic and does not require any ergodic assumption on the underlying model.
Mathematics Subject Classification ID: 62M02
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62M99
zbMATH DE Number: 1420539
zbMATH Keywords: martingales
zbMATH Keywords: deviation probability
zbMATH Keywords: autoregressive models
zbMATH Keywords: linear diffusions
zbMATH Keywords: maximum likelihood estimates
author: R. Liptser
author: V. G. Spokoiny
reviewed by: Yu. N. Lin'kov
MaRDI profile type: Publication
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full work available at URL: s0167-7152(99)00121-2
OpenAlex ID: W2082373836
Wikidata QID: Q127957472
description: scientific article; zbMATH DE number 1420539