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

Banerjee, Anurag; Magnus, Jan R.

doi:10.1016/s0304-4076(98)00093-1

Cited by 26 publications

(81 citation statements)

References 20 publications

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“…Now that S(0) = S and dΩ −1 (θ )/dθ θ=0 = −A (see [3], equation 2.5). Setting θ = 0 in (A.2) we obtain κ(0) = S −1 X AXS −1 .…”

Section: Discussionmentioning

confidence: 99%

“…In the context that is of interest to us here, studies by Banerjee and Magnus [3,4] and Magnus and Vasnev [5] developed a theory of sensitivity analysis for the linear model. Banerjee and Magnus [3] proposed a sensitivity statistic for the OLS estimator.…”

Section: Introductionmentioning

confidence: 99%

“…Banerjee and Magnus [3] proposed a sensitivity statistic for the OLS estimator. They found that the OLS coefficient estimator is not very sensitive to covariance misspecification.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the sensitivity of the one-sided t test to covariance misspecification

Qin

Wan

Zou

2009

Journal of Multivariate Analysis

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a b s t r a c tSensitivity analysis stands in contrast to diagnostic testing in that sensitivity analysis aims to answer the question of whether it matters that a nuisance parameter is non-zero, whereas a diagnostic test ascertains explicitly if the nuisance parameter is different from zero. In this paper, we introduce and derive the finite sample properties of a sensitivity statistic measuring the sensitivity of the t statistic to covariance misspecification. Unlike the earlier work by Banerjee and Magnus [A. Banerjee, J.R. Magnus, On the sensitivity of the usual t-and F -tests to covariance misspecification, Journal of Econometrics 95 (2000) 157-176] on the sensitivity of the F statistic, the theorems derived in the current paper hold under both the null and alternative hypotheses. Also, in contrast to Banerjee and Magnus' [see the above cited reference] results on the F test, we find that the decision to accept the null using the OLS based one-sided t test is not necessarily robust against covariance misspecification and depends much on the underlying data matrix. Our results also indicate that autocorrelation does not necessarily weaken the power of the OLS based t test.

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“…Now that S(0) = S and dΩ −1 (θ )/dθ θ=0 = −A (see [3], equation 2.5). Setting θ = 0 in (A.2) we obtain κ(0) = S −1 X AXS −1 .…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the sensitivity of the one-sided t test to covariance misspecification

Qin

Wan

Zou

2009

Journal of Multivariate Analysis

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“…The sensitivity of b to the data in y and X can be connected to Cook's (1986) de nition of likelihood displacement; see also Cook (1979). For a study on sensitivity of the variance estimator, see Banerjee and Magnus (1999). In this paper, we simply focus to present the de nitions in a systematic approach and provide further results as we see that these sensitivity results are needed and important in dealing with such issues as estimator approximations and comparisons, model mis-speci cation studies, and regression diagnostics for outliers or in uential observations.…”

Section: De Nitionmentioning

confidence: 99%

Sensitivity analysis in linear models

Liu

2016

Special Matrices

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Abstract:In this work, we consider the general linear model or its variants with the ordinary least squares, generalised least squares or restricted least squares estimators of the regression coe cients and variance. We propose a newly uni ed set of de nitions for local sensitivity for both situations, one for the estimators of the regression coe cients, and the other for the estimators of the variance. Based on these de nitions, we present the estimators' sensitivity results. We include brief remarks on possible links of these de nitions and sensitivity results to local in uence and other existing results.

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“…autocorrelation in the model error term, which can be captured by sensitivity in AR(1) direction introduced by Banerjee and Magnus (1999), 2. asymmetry in the error distribution as the yield cannot be negative, which can be captured by sensitivity to skewness introduced by Magnus and Vasnev (2007).…”

Section: Absolute Sensitivitymentioning

confidence: 99%

Practical Use of Sensitivity in Econometrics with an Illustration to Forecast Combinations

Vasnev

Magnus

2013

SSRN Journal

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Sensitivity analysis is important for its own sake and also in combination with diagnostic testing. We consider the question how to use sensitivity statistics in practice, in particular how to judge whether sensitivity is large or small. For this purpose we distinguish between absolute and relative sensitivity and highlight the context-dependent nature of any sensitivity analysis. Relative sensitivity is then applied in the context of forecast combination and sensitivity-based weights are introduced. All concepts are illustrated through the European yield curve. In this context it is natural to look at sensitivity to autocorrelation and normality assumptions. Different forecasting models are combined with equal, fit-based and sensitivity-based weights, and compared with the multivariate and random walk benchmarks. We show that the fit-based weights and the sensitivity-based weights are complementary. For long-term maturities the sensitivity-based weights perform better than other weights. March 6, 2013Abstract Sensitivity analysis is important for its own sake and also in combination with diagnostic testing. We consider the question how to use sensitivity statistics in practice, in particular how to judge whether sensitivity is large or small. For this purpose we distinguish between absolute and relative sensitivity and highlight the context-dependent nature of any sensitivity analysis. Relative sensitivity is then applied in the context of forecast combination and sensitivity-based weights are introduced. All concepts are illustrated through the European yield curve. In this context it is natural to look at sensitivity to autocorrelation and normality assumptions. Different forecasting models are combined with equal, fit-based and sensitivity-based weights, and compared with the multivariate and random walk benchmarks. We show that the fit-based weights and the sensitivity-based weights are complementary. For long-term maturities the sensitivity-based weights perform better than other weights.

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

Cited by 26 publications

References 20 publications

On the sensitivity of the one-sided t test to covariance misspecification

On the sensitivity of the one-sided t test to covariance misspecification

Sensitivity analysis in linear models

Practical Use of Sensitivity in Econometrics with an Illustration to Forecast Combinations

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