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http://hdl.handle.net/1942/4001
Title: | Likelihood ratio, score, and Wald tests in a constrained parameter space | Authors: | MOLENBERGHS, Geert VERBEKE, Geert |
Issue Date: | 2007 | Publisher: | AMER STATISTICAL ASSOC | Source: | AMERICAN STATISTICIAN, 61(1). p. 22-27 | Abstract: | Likelihood ratio, score, and Wald tests statistics are asymptotically equivalent. This statement is widely known to hold true under standard conditions. But what if the parameter space is constrained and the null hypothesis lies on the boundary of the parameter space, such as, for example, in variance component testing? Quite a bit is known in such situations too, but knowledge is scattered across the literature and considerably less well known among practitioners. Motivated from simple but generic examples, we show there is quite a market for asymptotic one-sided hypothesis tests, in the scalar as well as in the vector case. Reassuringly, the three standard tests can be used here as well and are asymptotically equivalent, but a somewhat more elaborate version of the score and Wald test statistics is needed. Null distributions take the form of mixtures of chi(2) distributions. Statistical and numerical considerations lead us to formulate pragmatic guidelines as to when to prefer which of the three tests. | Notes: | Hasselt Univ, Ctr Stat, Diepenbeek, Belgium. Katholieke Univ Leuven, Ctr Biostat, B-3000 Louvain, Belgium.MOLENBERGHS, G, Hasselt Univ, Ctr Stat, Diepenbeek, Belgium.geert.molenberghs@uhasselt.be geert.verbeke@med.kuleuven.be | Keywords: | boundary condition; dose response; generalized linear mixed model; likelihood ratio test; linear mixed model; one-sided test; score test; variance component; Wald test;boundary condition; dose response; generalized linear mixed model; likelihood ratio test; linear mixed model; one-sided test; score test; variance component; Wald test | Document URI: | http://hdl.handle.net/1942/4001 | Link to publication/dataset: | https://www.researchgate.net/publication/4741391_Likelihood_Ratio_Score_and_Wald_Tests_in_a_Constrained_Parameter_Space | ISSN: | 0003-1305 | e-ISSN: | 1537-2731 | DOI: | 10.1198/000313007X171322 | ISI #: | 000243781600003 | Rights: | (C) American Statisticial Association | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2008 |
Appears in Collections: | Research publications |
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