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Likelihood ratio test for and against nonlinear inequality constraints. (English) Zbl 1105.62022
Summary: In applied statistics, a finite-dimensional parameter involved in the distribution function of the observed random variable is very often constrained by a number of nonlinear inequalities. This paper is devoted to studying the likelihood ratio test for and against the hypothesis that the parameter is restricted by some nonlinear inequalities. The asymptotic null distributions of the likelihood ratio statistics are derived by using the limits of the related optimization problems. The author also shows how to compute critical values for the tests.

62F03 Parametric hypothesis testing
62F30 Parametric inference under constraints
62E20 Asymptotic distribution theory in statistics
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