Likelihood inference m exponential families and directions of recession
Likelihood inference m exponential families and directions of recession
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DOI：
10.1214/08-ejs349
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发表时间：
2009-01-01
影响因子：
1.1
通讯作者：
Geyer, Charles J.
中科院分区：
文献类型：
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作者：
Geyer, Charles J.
当在完全指数族中不存在最大似然估计（MLE）时，MBE可能存在于族的Barndorff-Nielsen补全中。我们提出了一种实用算法，用于使用 R 贡献的包 rcdd 基于重复线性规划来查找补全中的 MBE，并用三个广义线性模型示例进行说明。当原假设的 MLE 处于完备状态时，模型比较的似然比检验与通常情况几乎没有变化。只需要调整自由度。当 MBE 处于完成状态时，置信区间与通常情况相比变化更大。自然参数的 MBE 可以被认为是在某个方向趋于无穷大，我们称之为衰退的通用方向。我们提出了一种新的单侧置信区间，它表示自然参数可能有多接近无穷大。这映射到平均值的单侧置信区间，显示它们与支持边界的接近程度。
When in a full exponential family the maximum likelihood estimate (MLE) does not exist, the MBE may exist in the Barndorff-Nielsen completion of the family. We propose a practical algorithm for finding the MBE in the completion based on repeated linear programming using the R contributed package rcdd and illustrate it with three generalized linear model examples. When the MLE for the null hypothesis lies in the completion, likelihood ratio tests of model comparison are almost unchanged from the usual case. Only the degrees of freedom need to be adjusted. When the MBE lies in the completion, confidence intervals are changed much more from the usual case. The MBE of the natural parameter can be thought of as having gone to infinity in a certain direction, which we call a generic direction of recession. We propose a new one-sided confidence interval which says how close to infinity the natural parameter may be. This maps to one-sided confidence intervals for mean values showing how close to the boundary of their support they may be.