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The sensitivity of OLS when variance matrix is (partially) unknown

The sensitivity of OLS when variance matrix is (partially) unknown
The sensitivity of OLS when variance matrix is (partially) unknown
We consider the standard linear regression model y=X?+u with all standard assumptions, except that the variance matrix is assumed to be ?2?(?), where ? depends on m unknown parameters ?1,…, ?m. Our interest lies exclusively in the mean parameters ? or X?. We introduce a new sensitivity statistic (B1) which is designed to decide whether y (or B) is sensitive to covariance misspecification. We show that the Durbin–Watson test is inappropriate in this context, because it measures the sensitivity of Image to covariance misspecification. Our results demonstrate that the estimator Image and the predictor Image are not very sensitive to covariance misspecification. The statistic is easy to use and performs well even in cases where it is not strictly applicable.
linear regression, least squares, autocorrelation, durbin–watson test, sensitivity
0304-4076
295-323
Banerjee, Anurag N.
4f772e58-24c0-4266-ba41-18f70a6108c4
Magnus, Jan R.
0aca9de5-9fa8-4d0b-9b02-8fe657aa3d92
Banerjee, Anurag N.
4f772e58-24c0-4266-ba41-18f70a6108c4
Magnus, Jan R.
0aca9de5-9fa8-4d0b-9b02-8fe657aa3d92

Banerjee, Anurag N. and Magnus, Jan R. (1999) The sensitivity of OLS when variance matrix is (partially) unknown. Journal of Econometrics, 92 (2), 295-323. (doi:10.1016/S0304-4076(98)00093-1).

Record type: Article

Abstract

We consider the standard linear regression model y=X?+u with all standard assumptions, except that the variance matrix is assumed to be ?2?(?), where ? depends on m unknown parameters ?1,…, ?m. Our interest lies exclusively in the mean parameters ? or X?. We introduce a new sensitivity statistic (B1) which is designed to decide whether y (or B) is sensitive to covariance misspecification. We show that the Durbin–Watson test is inappropriate in this context, because it measures the sensitivity of Image to covariance misspecification. Our results demonstrate that the estimator Image and the predictor Image are not very sensitive to covariance misspecification. The statistic is easy to use and performs well even in cases where it is not strictly applicable.

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More information

Published date: 1999
Keywords: linear regression, least squares, autocorrelation, durbin–watson test, sensitivity

Identifiers

Local EPrints ID: 32931
URI: http://eprints.soton.ac.uk/id/eprint/32931
ISSN: 0304-4076
PURE UUID: b8b6596d-91c7-4dc9-8635-67c02368d393

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Date deposited: 26 Jul 2006
Last modified: 15 Mar 2024 07:40

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Contributors

Author: Anurag N. Banerjee
Author: Jan R. Magnus

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