Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters
研究线性回归模型中系数受不等式约束时的假设检验问题，定义了库恩-塔克乘子检验统计量，并证明其与似然比检验、沃尔德检验的关系与等式约束情形相同，且渐近分布为卡方分布的混合。
This paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients. The Kuhn-Tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the Wald test are examined. It is shown, in particular, that these relationships are the same as in the equality constrained case. It is emphasized, however, that their common asymptotic distribution is a mixture of chi-square distributions under the null hypothesis.