Large sample inference for a multivariate linear model with autocorrelated errors

S. Sethuraman; I. V. Basawa

doi:10.1016/0378-3758(94)90163-5

Large sample inference for a multivariate linear model with autocorrelated errors

S. Sethuraman
, I. V. Basawa

Mathematics

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

1 Scopus citations

Abstract

We consider a multivariate linear model with autocorrelated errors. The mean vector of the process is assumed to be linear in the time-trend parameter β and the within-group variation parameter γ. The least-squares estimators of β and γ, and the related estimators of the autoregressive parameter θ and the error covariance matrix Σ are derived and their asymptotic distributions are obtained. Large sample tests of H₁:γ=0 and H₂:β=0are derived and the limit distributions of the restricted least-squares estimators β̂_H₁ and γ̂_H₂ are obtained under H₁ and H₂, respectively.

Original language	English (US)
Pages (from-to)	187-204
Number of pages	18
Journal	Journal of Statistical Planning and Inference
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/0378-3758(94)90163-5
State	Published - Sep 1994

Keywords

Multivariate linear model
asymptotic tests
autoregressive processes
growth curves
least-squares estimation
limit distributions

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Access to Document

10.1016/0378-3758(94)90163-5

Cite this

@article{9b53e9275e0847df990ad337c26135c4,

title = "Large sample inference for a multivariate linear model with autocorrelated errors",

abstract = "We consider a multivariate linear model with autocorrelated errors. The mean vector of the process is assumed to be linear in the time-trend parameter β and the within-group variation parameter γ. The least-squares estimators of β and γ, and the related estimators of the autoregressive parameter θ and the error covariance matrix Σ are derived and their asymptotic distributions are obtained. Large sample tests of H1:γ=0 and H2:β=0are derived and the limit distributions of the restricted least-squares estimators {\^β}H1 and {\^γ}H2 are obtained under H1 and H2, respectively.",

keywords = "Multivariate linear model, asymptotic tests, autoregressive processes, growth curves, least-squares estimation, limit distributions",

author = "S. Sethuraman and Basawa, \{I. V.\}",

note = "Funding Information: I.V. Basawa{\textquoteright}s work was partially supported by a grant from the Office of Naval Research. We thank the referees for a careful reading and many constructive comments.",

year = "1994",

month = sep,

doi = "10.1016/0378-3758(94)90163-5",

language = "English (US)",

volume = "41",

pages = "187--204",

journal = "Journal of Statistical Planning and Inference",

issn = "0378-3758",

publisher = "Elsevier B.V.",

number = "2",

}

TY - JOUR

T1 - Large sample inference for a multivariate linear model with autocorrelated errors

AU - Sethuraman, S.

AU - Basawa, I. V.

N1 - Funding Information: I.V. Basawa’s work was partially supported by a grant from the Office of Naval Research. We thank the referees for a careful reading and many constructive comments.

PY - 1994/9

Y1 - 1994/9

N2 - We consider a multivariate linear model with autocorrelated errors. The mean vector of the process is assumed to be linear in the time-trend parameter β and the within-group variation parameter γ. The least-squares estimators of β and γ, and the related estimators of the autoregressive parameter θ and the error covariance matrix Σ are derived and their asymptotic distributions are obtained. Large sample tests of H1:γ=0 and H2:β=0are derived and the limit distributions of the restricted least-squares estimators β̂H1 and γ̂H2 are obtained under H1 and H2, respectively.

AB - We consider a multivariate linear model with autocorrelated errors. The mean vector of the process is assumed to be linear in the time-trend parameter β and the within-group variation parameter γ. The least-squares estimators of β and γ, and the related estimators of the autoregressive parameter θ and the error covariance matrix Σ are derived and their asymptotic distributions are obtained. Large sample tests of H1:γ=0 and H2:β=0are derived and the limit distributions of the restricted least-squares estimators β̂H1 and γ̂H2 are obtained under H1 and H2, respectively.

KW - Multivariate linear model

KW - asymptotic tests

KW - autoregressive processes

KW - growth curves

KW - least-squares estimation

KW - limit distributions

UR - https://www.scopus.com/pages/publications/33644680829

UR - https://www.scopus.com/pages/publications/33644680829#tab=citedBy

U2 - 10.1016/0378-3758(94)90163-5

DO - 10.1016/0378-3758(94)90163-5

M3 - Article

AN - SCOPUS:33644680829

SN - 0378-3758

VL - 41

SP - 187

EP - 204

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 2

ER -

Large sample inference for a multivariate linear model with autocorrelated errors

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this