The correlation coefficient in the general linear model

Koerts, J.; Abrahamse, A. P. J.

doi:10.1016/0014-2921(70)90021-8

Cited by 25 publications

(15 citation statements)

References 2 publications

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“…But given that for a fixed η N the above statistic will converge to a diagonal quadratic form in standard normal random variables as N → ∞, we can use Koerts and Abrahamse (1969) implementation of Imhof (1961) procedure for evaluating the probability that a quadratic form of normals is less than a given value (see also Farebrother (1990)). …”

Section: B Estimating Finite-dimensional Specifications Of πmentioning

confidence: 99%

Underidentification?

Arellano¹,

Hansen²,

Sentana³

2009

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We develop methods for testing the hypothesis that an econometric model is underidentified and inferring the nature of the failed identification. By adopting a generalizedmethod-of moments perspective, we feature directly the structural relations and we allow for nonlinearity in the econometric specification. We establish the link between a test for overidentification and our proposed test for underidentification. If, after attempting to replicate the structural relation, we find substantial evidence against the overidentifying restrictions of an augmented model, this is evidence against underidentification of the original model. * This is an substantially revised and extended version of Arellano et al. (1999). We thank Javier Alvarez, Raquel Carrasco, Jesús Carro and especially Francisco Peñaranda and Javier Mencía for able research assistance at various stages of this project. Also, we thank Andres Santos and Azeem Shaikh for helpful conversations about our general approach to this problem.

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Section: B Estimating Finite-dimensional Specifications Of πmentioning

confidence: 99%

Underidentification?

Arellano¹,

Hansen²,

Sentana³

2009

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“…C C/tr(W 2 ) < x by a finite set of size 500. We use code for F C,W 2 (x) available from Ruud (2000) (Imhof 1961;Koerts and Abrahamse 1969;Farebrother 1990;Ruud 2000). For 400 matrices W 2 from a diffuse prior with K ∈ {1, 2, 3, 4, 5}, our numerical values for max C C/trW 2 <x F C,W 2 (c m ) range between 4.77% and 5.26%, and our numerical values for max C C/trW 2 <x F C,W 2 (c P ) range between 5.00% and 5.02%.…”

Section: Definition 2 (Patnaik Critical Value) Define the Patnaik Crmentioning

confidence: 99%

A Robust Test for Weak Instruments

Olea

Pflueger

2013

Journal of Business & Economic Statistics

769

298

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We develop a test for weak instruments in linear instrumental variables regression that is robust to heteroscedasticity, autocorrelation, and clustering. Our test statistic is a scaled nonrobust first-stage F statistic. Instruments are considered weak when the two-stage least squares or the limited information maximum likelihood Nagar bias is large relative to a benchmark. We apply our procedures to the estimation of the elasticity of intertemporal substitution, where our test cannot reject the null of weak instruments in a larger number of countries than the test proposed by Stock and Yogo in 2005. Supplementary materials for this article are available online.

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“…For instance, the sample serial correlation coefficient as defined in Anderson (1990) and discussed in Provost and Rudiuk (1995) as well as the sample innovation cross-correlation function for an ARMA time series whose asymptotic distribution was derived by McLeod (1979), have such a structure. Koerts and Abrahamse (1969) investigated the distribution of ratios of quadratic forms in the context of the general linear model. Shenton and Johnson (1965) derived the first few terms of the series expansions of the first and second moments of the sample circular serial correlation coefficient.…”

Section: Numerical Examples a Certain Weibull Densitymentioning

confidence: 99%

Polynomially Adjusted Saddlepoint Density Approximations

Provost

Sheng

2014

IJSP

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This thesis aims at obtaining improved bona fide density estimates and approximants by means of adjustments applied to the widely used saddlepoint approximation. Said adjustments are determined by solving systems of equations resulting from a moment-matching argument. A hybrid density approximant that relies on the accuracy of the saddlepoint approximation in the distributional tails is introduced as well. A certain representation of noncentral indefinite quadratic forms leads to an initial approximation whose parameters are evaluated by simultaneously solving four equations involving the cumulants of the target distribution. A saddlepoint approximation to the distribution of quadratic forms is also discussed. By way of application, accurate approximations to the distributions of the Durbin-Watson statistic and a certain portmanteau test statistic are determined. It is explained that the moments of the latter can be evaluated either by defining an expected value operator via the symbolic approach or by resorting to a recursive relationship between the joint moments and cumulants of sums of products of quadratic forms. As well, the bivariate case is addressed by applying a polynomial adjustment to the product of the saddlepoint approximations of the marginal densities of the standardized variables. Furthermore, extensions to the context of density estimation are formulated and applied to several univariate and bivariate data sets. In this instance, sample moments and empirical cumulant-generating functions are utilized in lieu of their theoretical analogues. Interestingly, the methodology herein advocated for approximating bivariate distributions not only yields density estimates whose functional forms readily lend themselves to algebraic manipulations, but also gives rise to copula density functions that prove significantly more flexible than the conventional functional type. ACKNOWLEDGEMENTSThere are many people I would like to thank for their support over the past three years.Firstly, I would like to express my gratitude to my supervisor, Dr. Serge Provost, for his valuable guidance, as well as his patience and keen enthusiasm to make this thesis possible.

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The correlation coefficient in the general linear model

Cited by 25 publications

References 2 publications

Underidentification?

Underidentification?

A Robust Test for Weak Instruments

Polynomially Adjusted Saddlepoint Density Approximations

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