A Score Test against One-Sided Alternatives

Silvapulle, Mervyn J.; Silvapulle, Paramsothy

doi:10.1080/01621459.1995.10476518

Cited by 93 publications

(74 citation statements)

References 15 publications

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“…Verbeke and Molenberghs (2003), using results by Silvapulle and Silvapulle (1995), have shown that similar results are obtained when a score test is used instead of a likelihood ratio test. The use of score tests for testing variance components under a constrained parameterization requires replacing the classical score test statistic by an appropriate one-sided version.…”

Section: The Score Testsupporting

confidence: 50%

“…For τ 2 negative, the score at zero is negative as well and the infimum in (6) is attained for b = 0, resulting in T S = 0. It follows from Silvapulle and Silvapulle (1995) that, under suitable regularity conditions, for N → ∞, the likelihood ratio and score test statistics satisfy T LR = T S + o p (1). This indicates that the equivalence of the score and likelihood ratio tests not only holds in the two-sided but also in the one-sided cases.…”

Section: The Score Testmentioning

confidence: 99%

“…The use of score tests for testing variance components under a constrained parameterization requires replacing the classical score test statistic by an appropriate one-sided version. This is where the general theory of Silvapulle and Silvapulle (1995) on onesided score tests proves very useful. They consider models parameterized through a vector θ = (λ , ψ ) , where testing a general hypothesis of the form H 0 : ψ = 0 versus H A : ψ ∈ C is of interest.…”

Section: The Score Testmentioning

confidence: 99%

“…They consider models parameterized through a vector θ = (λ , ψ ) , where testing a general hypothesis of the form H 0 : ψ = 0 versus H A : ψ ∈ C is of interest. Silvapulle and Silvapulle (1995) allow C to be a closed and convex cone in Euclidean space, with vertex at the origin. The advantage of such a general definition is that onesided, two-sided, and combinations of one-sided and two-sided hypotheses are included.…”

Section: The Score Testmentioning

confidence: 99%

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The Use of Score Tests for Inference on Variance Components

Verbeke¹,

Molenberghs²

2003

Biometrics

203

144

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Summary Whenever inference for variance components is required, the choice between one‐sided and two‐sided tests is crucial. This choice is usually driven by whether or not negative variance components are permitted. For two‐sided tests, classical inferential procedures can be followed, based on likelihood ratios, score statistics, or Wald statistics. For one‐sided tests, however, one‐sided test statistics need to be developed, and their null distribution derived. While this has received considerable attention in the context of the likelihood ratio test, there appears to be much confusion about the related problem for the score test. The aim of this paper is to illustrate that classical (two‐sided) score test statistics, frequently advocated in practice, cannot be used in this context, but that well‐chosen one‐sided counterparts could be used instead. The relation with likelihood ratio tests will be established, and all results are illustrated in an analysis of continuous longitudinal data using linear mixed models.

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Section: The Score Testsupporting

confidence: 50%

Section: The Score Testmentioning

confidence: 99%

Section: The Score Testmentioning

confidence: 99%

Section: The Score Testmentioning

confidence: 99%

See 2 more Smart Citations

The Use of Score Tests for Inference on Variance Components

Verbeke¹,

Molenberghs²

2003

Biometrics

203

144

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“…If the alternative = 0 is replaced by ¿0, according to Reference [18], the score test statistic should be modiÿed as where U = U (ÿ;ũ;˜ ; 0) is given in Section 3. Speciÿcally, the reference distribution of the score test statistic S * is then asymptotically 0:5( and N × N matrices B = diag{− exp(Á ij )}.…”

Section: Discussionmentioning

confidence: 99%

A score test for zero‐inflation in correlated count data

Xiang

Lee

Yau

et al. 2005

Statistics in Medicine

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SUMMARYTo account for the preponderance of zero counts and simultaneous correlation of observations, a class of zero-in ated Poisson mixed regression models is applicable for accommodating the within-cluster dependence. In this paper, a score test for zero-in ation is developed for assessing correlated count data with excess zeros. The sampling distribution and the power of the test statistic are evaluated by simulation studies. The results show that the test statistic performs satisfactorily under a wide range of conditions. The test procedure is further illustrated using a data set on recurrent urinary tract infections.

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