Data reduction in tandem fusion systems

The sufficiency principle is the guiding principle for data reduction in statistical inference. There has been recent effort in developing the sufficiency principle for decentralized inference with a particular emphasis on the relationship between global sufficiency and local sufficiency. This paper studies the sufficiency based data reduction in tandem fusion systems when quantization is needed. We identify conditions such that it is optimal to implement data reduction using sufficient statistics prior to the quantization. They include the well known case when the data at decentralized nodes are conditionally independent as well as a class of problems with conditionally dependent data.