Exact Density Functions and Approximate Critical Regions for Likelihood Ratio Identifiability Test Statistics

Rhodes, George F.

doi:10.2307/1912516

Cited by 24 publications

(10 citation statements)

References 17 publications

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“…We use here the same notations as those in Phillips [19] for convenience of comparison with his marginal podX of n Note that the notation in (5.1), ). In view of (5.1), J8 L IML and X are not independent, so conditioning on X has an effect on the exact distribution of /3 LIML o The exact distribution of X was derived by Rhodes [20], and it depends on unknown parameters, so that X is not exactly ancillary. The exact conditional p.dof.…”

Section: Exact Conditional Distributionmentioning

confidence: 99%

“…of r, given X ? is obtained by (5 J ) divided by the marginal p.dX of X (Rhodes [20,Eq,3,4]), Since r and X are independent in the leading term of the exact joint p,d o f, ? nonexistence of the conditional moments follows.…”

Section: Exact Conditional Distributionmentioning

confidence: 99%

“…of the LIML estimator even though X is not maximal ancillary. The distributional properties of X were investigated in detail by Rhodes [20] and Kunitomo et al [15]. The statistic X is second-order asymptotically ancillary because its distribution does not depend on the parameters up to the order T~1 /2 under the null hypothesis, but not exactly ancillary.…”

Section: Introductionmentioning

confidence: 99%

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Ancillarity and the Limited Information Maximum-Likelihood Estimation of a Structural Equation in a Simultaneous Equation System

1989

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The concepts of the curved exponential family of distributions and ancillarity are applied to estimation problems of a single structural equation in a simultaneous equation model, and the effect of conditioning on ancillary statistics on the limited information maximum-likelihood (LIML) estimator is investigated. The asymptotic conditional covariance matrix of the LIML estimator conditioned on the second-order asymptotic maximal ancillary statistic is shown to be efficiently estimated by Liu and Breen's formula. The effect of conditioning on a second-order asymptotic ancillary statistic, i.e., the smallest characteristic root associated with the LIML estimation, is analyzed by means of an asymptotic expansion of the distribution as well as the exact distribution. The smallest root helps to give an intuitively appealing measure of precision of the LIML estimator.

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Section: Exact Conditional Distributionmentioning

confidence: 99%

Section: Exact Conditional Distributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ancillarity and the Limited Information Maximum-Likelihood Estimation of a Structural Equation in a Simultaneous Equation System

1989

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“…Three other related papers are Rhodes () that studies the exact distribution of the likelihood ratio statistic for testing the validity of overidentifying restrictions in a Gaussian simultaneous equations model; and Nielsen (, ) that study conditional tests of rank in bivariate canonical correlation analysis, which is related to the present problem when

k = 2

and

m_{W} = 1

. These papers do not provide results on asymptotic size or power.…”

Section: Introductionmentioning

confidence: 99%

A more powerful subvector Anderson Rubin test in linear instrumental variables regression

Guggenberger

Kleibergen

Mavroeidis

2019

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We study subvector inference in the linear instrumental variables model assuming homoskedasticity but allowing for weak instruments. The subvector Anderson and Rubin (1949) test that uses chi square critical values with degrees of freedom reduced by the number of parameters not under test, proposed by Guggenberger, Kleibergen, Mavroeidis, and Chen (2012), controls size but is generally conservative. We propose a conditional subvector Anderson and Rubin test that uses datadependent critical values that adapt to the strength of identification of the parameters not under test. This test has correct size and strictly higher power than the subvector Anderson and Rubin test by Guggenberger et al. (2012). We provide tables with conditional critical values so that the new test is quick and easy to use. Application of our method to a model of risk preferences in development economics shows that it can strengthen empirical conclusions in practice.

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“…The small sample properties of the null distributions of these statistics have been investigated by several econometricians. For instance, Rhodes [20] derived an expression of the exact null distribution of the likelihood ratio statistic using zonal polynomials. Since the exact distributions of statistics are too complicated to permit their interpretations and numerical evaluations (see [17]), Kunitomo et al [15] have derived the asymptotic expansions of the null distributions of these statistics both in the small-disturbance and the large sample asymptotic sequences.…”

Section: Introductionmentioning

confidence: 99%

Approximate Distributions and Power of Test Statistics for Overidentifying Restrictions in a System of Simultaneous Equations

Kunitomo

1988

Econ Theory

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We derive asymptotic expansions of the distributions of test statistics for over-identifying restrictions in a system of simultaneous equations under the null and the non-null hypotheses. We investigate the effects of the normality assumption for disturbances on the test statistics based on their asymptotic expansions. We also study the power functions of test statistics based on their asymptotic expansions. After modifying their critical regions to the same significance level, the power function of Basmann's statistic is larger than that of the likelihood ratio test when the variance of disturbances is sufficiently small. However, the difference in powers of the two test statistics disappears as the sample size grows larger.

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Exact Density Functions and Approximate Critical Regions for Likelihood Ratio Identifiability Test Statistics

Cited by 24 publications

References 17 publications

Ancillarity and the Limited Information Maximum-Likelihood Estimation of a Structural Equation in a Simultaneous Equation System

Ancillarity and the Limited Information Maximum-Likelihood Estimation of a Structural Equation in a Simultaneous Equation System

A more powerful subvector Anderson Rubin test in linear instrumental variables regression

Approximate Distributions and Power of Test Statistics for Overidentifying Restrictions in a System of Simultaneous Equations

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