# Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises

D. Fourdrinier, V. Konev, S. Pergamenshchikov

Research output: Contribution to journalArticle

6 Citations (Scopus)

### Abstract

For a first-order non-explosive autoregressive process with dependent noise, we propose a truncated sequential procedure with a fixed mean-square accuracy. The asymptotic distribution of the estimator depends on the type of the noise distribution: it is normal when the noise has a Kotz's distribution, while it is a mixture of normal distributions if the noise distribution is a variance mixture of normal distrbutions as well. In both cases, the convergence to the limiting distribution is uniform in the unknown parameter.

Original language English 43-58 16 Mathematical Methods of Statistics 18 1 https://doi.org/10.3103/S1066530709010037 Published - 1 Mar 2009

### Fingerprint

Sequential Estimation
Autoregressive Process
First-order
Dependent
Mixture of Normal Distributions
Sequential Procedure
Limiting Distribution
Unknown Parameters
Mean Square
Asymptotic distribution
Estimator
Autoregressive process

### Keywords

• autoregression model
• truncated sequential estimators
• uniform normality

### ASJC Scopus subject areas

• Statistics, Probability and Uncertainty
• Statistics and Probability

### Cite this

Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises. / Fourdrinier, D.; Konev, V.; Pergamenshchikov, S.

In: Mathematical Methods of Statistics, Vol. 18, No. 1, 01.03.2009, p. 43-58.

Research output: Contribution to journalArticle

title = "Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises",
abstract = "For a first-order non-explosive autoregressive process with dependent noise, we propose a truncated sequential procedure with a fixed mean-square accuracy. The asymptotic distribution of the estimator depends on the type of the noise distribution: it is normal when the noise has a Kotz's distribution, while it is a mixture of normal distributions if the noise distribution is a variance mixture of normal distrbutions as well. In both cases, the convergence to the limiting distribution is uniform in the unknown parameter.",
keywords = "autoregression model, truncated sequential estimators, uniform normality",
author = "D. Fourdrinier and V. Konev and S. Pergamenshchikov",
year = "2009",
month = "3",
day = "1",
doi = "10.3103/S1066530709010037",
language = "English",
volume = "18",
pages = "43--58",
journal = "Mathematical Methods of Statistics",
issn = "1066-5307",
publisher = "Allerton Press Inc.",
number = "1",

}

TY - JOUR

T1 - Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises

AU - Fourdrinier, D.

AU - Konev, V.

AU - Pergamenshchikov, S.

PY - 2009/3/1

Y1 - 2009/3/1

N2 - For a first-order non-explosive autoregressive process with dependent noise, we propose a truncated sequential procedure with a fixed mean-square accuracy. The asymptotic distribution of the estimator depends on the type of the noise distribution: it is normal when the noise has a Kotz's distribution, while it is a mixture of normal distributions if the noise distribution is a variance mixture of normal distrbutions as well. In both cases, the convergence to the limiting distribution is uniform in the unknown parameter.

AB - For a first-order non-explosive autoregressive process with dependent noise, we propose a truncated sequential procedure with a fixed mean-square accuracy. The asymptotic distribution of the estimator depends on the type of the noise distribution: it is normal when the noise has a Kotz's distribution, while it is a mixture of normal distributions if the noise distribution is a variance mixture of normal distrbutions as well. In both cases, the convergence to the limiting distribution is uniform in the unknown parameter.

KW - autoregression model

KW - truncated sequential estimators

KW - uniform normality

UR - http://www.scopus.com/inward/record.url?scp=84859509830&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84859509830&partnerID=8YFLogxK

U2 - 10.3103/S1066530709010037

DO - 10.3103/S1066530709010037

M3 - Article

AN - SCOPUS:84859509830

VL - 18

SP - 43

EP - 58

JO - Mathematical Methods of Statistics

JF - Mathematical Methods of Statistics

SN - 1066-5307

IS - 1

ER -