复合零假设下非参数似然比检验的渐近性质

On the Asymptotic Properties of Nonparametric Likelihood Ratio Test Under Composite Null Hypothesis

给出了带估计参数的上界型和积分型两种非参似然比拟合优度检验统计量。对上界型检验统计量,研究了与之有关的一个极限性质;对积分型检验统计量,证明了其在复合零假设下的渐近分布。所得结论可以为进一步讨论非参似然比拟合优度检验提供一定的理论基础。

The supremum-type and the integral-type nonparametric likelihood ratio goodness-of-fit tests are investigated. The asymptotic property of the modified supremum-type statistic and the integral-type statistic under the composite null hypothesis are derived. The results can provide the theoretical basis for （generalized） nonparametric likelihood ratio of goodness of fit test with estimated parameters.