Deviation probability bound for martingales with applications to statistical estimation

R. Liptser; V. Spokoiny

doi:10.1016/s0167-7152(99)00121-2

Deviation probability bound for martingales with applications to statistical estimation

R. Liptser^*, V. Spokoiny

^*Corresponding author for this work

Engineering General

Weierstrass Institute for Applied Analysis and Stochastics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

Let M_t 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〉_t^-1M _t>λz^*〈M〉_t ^-1z with a fixed vector z and discuss some of its applications to statistical estimation in autoregressive and linear diffusion models. Our approach is non-asymptotic and does not require any ergodic assumption on the underlying model.

Original language	English
Pages (from-to)	347-357
Number of pages	11
Journal	Statistics and Probability Letters
Volume	46
Issue number	4
DOIs	https://doi.org/10.1016/s0167-7152(99)00121-2
State	Published - 15 Feb 2000

Keywords

62G05
Autoregression
Deviation probability
Linear diffusion
Martingale
Maximum likelihood estimate
Secondary 62M99

Access to Document

10.1016/s0167-7152(99)00121-2

Cite this

@article{6f8c95818a924298ae58b2e8aa70f649,

title = "Deviation probability bound for martingales with applications to statistical estimation",

abstract = "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〉t-1M t>λz*〈M〉t -1z with a fixed vector z and discuss some of its applications to statistical estimation in autoregressive and linear diffusion models. Our approach is non-asymptotic and does not require any ergodic assumption on the underlying model.",

keywords = "62G05, Autoregression, Deviation probability, Linear diffusion, Martingale, Maximum likelihood estimate, Secondary 62M99",

author = "R. Liptser and V. Spokoiny",

year = "2000",

month = feb,

day = "15",

doi = "10.1016/s0167-7152(99)00121-2",

language = "אנגלית",

volume = "46",

pages = "347--357",

journal = "Statistics and Probability Letters",

issn = "0167-7152",

publisher = "Elsevier B.V.",

number = "4",

}

TY - JOUR

T1 - Deviation probability bound for martingales with applications to statistical estimation

AU - Liptser, R.

AU - Spokoiny, V.

PY - 2000/2/15

Y1 - 2000/2/15

N2 - 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〉t-1M t>λz*〈M〉t -1z with a fixed vector z and discuss some of its applications to statistical estimation in autoregressive and linear diffusion models. Our approach is non-asymptotic and does not require any ergodic assumption on the underlying model.

AB - 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〉t-1M t>λz*〈M〉t -1z with a fixed vector z and discuss some of its applications to statistical estimation in autoregressive and linear diffusion models. Our approach is non-asymptotic and does not require any ergodic assumption on the underlying model.

KW - 62G05

KW - Autoregression

KW - Deviation probability

KW - Linear diffusion

KW - Martingale

KW - Maximum likelihood estimate

KW - Secondary 62M99

UR - http://www.scopus.com/inward/record.url?scp=0042527921&partnerID=8YFLogxK

U2 - 10.1016/s0167-7152(99)00121-2

DO - 10.1016/s0167-7152(99)00121-2

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0042527921

SN - 0167-7152

VL - 46

SP - 347

EP - 357

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 4

ER -

Deviation probability bound for martingales with applications to statistical estimation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this