The COR criterion for optimal subset selection in distributed estimation

The problem of selecting an optimal subset in distributed regression is a crucial issue, as each distributed data subset may contain redundant information, which can be attributed to various sources such as outliers, dispersion, inconsistent duplicates, too many independent variables, and excessive data points, among others. Efficient reduction and elimination of this redundancy can help alleviate inconsistency issues for statistical inference. Therefore, it is imperative to track redundancy while measuring and processing data. We develop a criterion for optimal subset selection that is related to Covariance matrices, Observation matrices, and Response vectors (COR). We also derive a novel distributed interval estimation for the proposed criterion and establish the existence of optimal subset length. Finally, numerical experiments are conducted to verify the experimental feasibility of the proposed criterion.