Local Sensitivity and Diagnostic Tests

Magnus, Jan R.; Vasnev, Andrey L.

doi:10.2139/ssrn.627366

Cited by 6 publications

(16 citation statements)

References 31 publications

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“…The matrix −E therefore has negative diagonal elements, and is a stable matrix (see [13, p. 165]), since −E − E is negative definite. By setting η kk = −e kk + g for all k ∈ J with g = e k k + χ, where e k k is the maximal diagonal element of E and χ is a positive constant, and by setting η kj = −e kj for all off-diagonal elements, we may express −E in the form −E = N − gI , where N ≡ [η kj ] is a Morishima matrix (see [1, p. 12]) under conditions (8) and (9). If E is also indecomposable, it follows from [13, pp.…”

Section: Resultsmentioning

confidence: 99%

“…For the case of a single endogenous variable, and hence n = 2, (8) and (9) have no force, with Proposition 2 implying:…”

Section: Propositionmentioning

confidence: 99%

“…, 3 + m, but not necessary. Since |E| > 0, the sign pattern of [d j ] = E −1 can be determined from the sign pattern of each e j without imposing conditions (8) and (9) in the 2 × 2 case where n − 1 = 2. For the case of n = 3, we may derive from Proposition 1 that the more general necessary and sufficient conditions for being able to sign θ k < 0 for any variable k = 2, .…”

Section: Propositionmentioning

confidence: 99%

“…Moreover, as Magnus and Vasnev [9] have recently emphasised, standard diagnostic tests may similarly provide little or no information about the sensitivity of parameter estimates to departures from the underlying assumptions of the model that is being estimated, but instead may indeed be (asymptotically) statistically independent from such sensitivity assessments. Diagnostic testing alone, upon which econometric practice has tended to concentrate, will therefore do little to fill the vacuum left by the relative neglect of the important questions which fall within the domain of sensitivity analysis.…”

Section: Introductionmentioning

confidence: 99%

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The determinants of cumulative endogeneity bias in multivariate analysis

Mayston

2009

Journal of Multivariate Analysis

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a b s t r a c tThe BLU properties of OLS estimators under known assumptions have encouraged the widespread use of OLS multivariate regression analysis in many empirical studies that are based upon a conceptual model of a single explanatory equation. However, such a model may well be an imperfect empirical approximation to the valid underlying conceptual model, that may well contain several important additional inter-relationships between the relevant variables. In this paper, we examine the conditions under which we can predict the direction of the resultant endogeneity bias that will prevail in the OLS asymptotic parameter estimates for any given endogenous or predetermined variable, and the extent to which we can rely upon simple heuristics in this process. We also identify the underlying structural parameters to which the magnitude of the endogeneity bias is sensitive. The importance of such sensitivity analysis has been underlined by an increasing awareness of the inability of standard diagnostic tests to shed light upon the extent of the endogeneity bias, rather than upon merely its existence. The paper examines the implications of the analysis for statistical inferences about the true value of the regression coefficients and the validity of associated t-statistics.

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Section: Resultsmentioning

confidence: 99%

“…For the case of a single endogenous variable, and hence n = 2, (8) and (9) have no force, with Proposition 2 implying:…”

Section: Propositionmentioning

confidence: 99%

Section: Propositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The determinants of cumulative endogeneity bias in multivariate analysis

Mayston

2009

Journal of Multivariate Analysis

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“…9 Jan Magnus and his collaborators have pursued a distinct but related approach to this problem that is noteworthy but not explored in the present paper. Magnus advocates a model-perturbation approach to sensitivity analysis that studies "the effect of small changes in model assumptions on an estimator of a parameter of interest" (see, e.g., Magnus and Vasnev 2007;Magnus 2007). that the theory of robust statistics exemplifies systematic thinking about how to secure evidence via a weakening strategy.…”

Section: Security Through Robust Statisticsmentioning

confidence: 99%

Strategies for securing evidence through model criticism

Staley

2011

Euro Jnl Phil Sci

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Some accounts of evidence regard it as an objective relationship holding between data and hypotheses, perhaps mediated by a testing procedure. Mayo's error-statistical theory of evidence is an example of such an approach. Such a view leaves open the question of when an epistemic agent is justif ied in drawing an inference from such data to a hypothesis. Using Mayo's account as an illustration, I propose a framework for addressing the justification question via a relativized notion, which I designate security, meant to conceptualize practices aimed at the justification of inferences from evidence. I then show how the notion of security can be put to use by showing how two quite different theoretical approaches to model criticism in statistics can both be viewed as strategies for securing claims about statistical evidence.

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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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Local Sensitivity and Diagnostic Tests

Cited by 6 publications

References 31 publications

The determinants of cumulative endogeneity bias in multivariate analysis

The determinants of cumulative endogeneity bias in multivariate analysis

Strategies for securing evidence through model criticism

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

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