Likelihood ratio test for and against nonlinear inequality constraints.

*(English)*Zbl 1105.62022Summary: 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.

##### MSC:

62F03 | Parametric hypothesis testing |

62F30 | Parametric inference under constraints |

62E20 | Asymptotic distribution theory in statistics |

##### Keywords:

Nonlinear inequality constraints; Chi-bar-squared distribution; Likelihood ratio test; Asymptotic distribution; Optimal solution##### Software:

ACSSCode##### References:

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