Mathematical Sciences: Partial Ancillarity, Partial Sufficiency and Generalized Principles for Inference

在有滋扰参数的情况下，将研究在给定这种部分辅助统计量的值的情况下，根据条件分布进行推断时所涉及的信息损失的部分辅助因素的替代定义。同样，当推论是基于这种部分充分性统计的边际分布时，将从信息损失的角度研究部分充分性的定义。最后，在干扰参数存在的情况下，用广义似然原理对感兴趣的参数进行推理。这是统计学中关于数据结构的基础性研究，它与研究兴趣以外的变量混淆。基于部分信息的统计方法在实践中已经变得相当普遍，这项基础性工作是必要的和及时的。

Alternative definitions of partial ancillarity, in the presence of nuisance parameters, will be examined with regard to loss of information involved when inference is based on the conditional distribution given the values of such partial ancillary statistics. Similarly, definitions of partial sufficiency will be examined with respect to loss of information when inference is based on the marginal distribution of such partial sufficiency statistics. Finally, a generalized likelihood principle will be formulated for inference concerning parameters of interest in the presence of the nuisance parameters. This is foundational research in statistics for data structures confounded with variables other than those of research interest. Statistical methods based on partial information have become quite popular in practice and this foundational work is needed and timely.