Adjusted empirical likelihood and its properties
Adjusted empirical likelihood and its properties
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DOI：
10.1198/106186008x321068
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发表时间：
2008-06-01
影响因子：
2.4
通讯作者：
Abraham, Bovas
中科院分区：
文献类型：
--
作者：
Chen, Jiahua;Variyath, Asokan Mulayath;Abraham, Bovas
计算剖面经验似然函数是经验似然应用的关键步骤，它涉及到约束最大化。然而，在某些情况下，所需的数值问题没有解决方案。在这种情况下，惯例是将零值分配给剖面经验似然。这种策略至少有两个局限性。首先，在数值上很难确定没有解;其次，没有提供关于似然性被设置为零的参数值的相对似然性的信息。在这篇文章中，我们提出了一种新的调整经验似然保留所有的最优性属性，并保证在任何参数值的可能性的合理值。再加上这种调整，我们引入了一个迭代算法，保证收敛。我们的模拟表明，调整后的经验似然比配置文件的经验似然要快得多的计算。通过调整后的经验似然构造的置信区域被发现有覆盖概率接近标称水平，而不采用复杂的程序，如Bartlett校正或自举校准。该方法也被证明是有效的，在解决与经验似然的几个实际问题。
Computing a profile empirical likelihood function, which involves constrained maximization, is a key step in applications of empirical likelihood. However, in some situations, the required numerical problem has no solution. In this case, the convention is to assign a zero value to the profile empirical likelihood. This strategy has at least two limitations. First, it is numerically difficult to determine that there is no solution; second, no information is provided on the relative plausibility of the parameter values where the likelihood is set to zero. In this article, we propose a novel adjustment to the empirical likelihood that retains all the optimality properties, and guarantees a sensible value of the likelihood at any parameter value. Coupled with this adjustment, we introduce an iterative algorithm that is guaranteed to converge. Our simulation indicates that the adjusted empirical likelihood is much faster to compute than the profile empirical likelihood. The confidence regions constructed via the adjusted empirical likelihood are found to have coverage probabilities closer to the nominal levels without employing complex procedures such as Bartlett correction or bootstrap calibration. The method is also shown to be effective in solving several practical problems associated with the empirical likelihood.