LIC criterion for optimal subset selection in distributed interval estimation.

Distributed interval estimation in linear regression may be computationally infeasible in the presence of big data that are normally stored in different computer servers or in cloud. The existing challenge represents the results from the distributed estimation may still contain redundant information about the population characteristics of the data. To tackle this computing challenge, we develop an optimization procedure to select the best subset from the collection of data subsets, based on which we perform interval estimation in the context of linear regression. The procedure is derived based on minimizing the length of the final interval estimator and maximizing the information remained in the selected data subset, thus is named as the LIC criterion. Theoretical performance of the LIC criterion is studied in this paper together with a simulation study and real data analysis.

Taylor quasi-likelihood for limited generalized linear models.

It is a major research topic of limited generalized linear models, namely, generalized linear models with limited dependent variables. The models are developed in many research fields. However, quasi-likelihood estimation of the models is an unresolved issue, due to including limited dependent variables. We propose a novel quasi-likelihood, called Taylor quasi-likelihood, to handle with the unified estimation problem of the limited models. It is based on Taylor expansion of distribution function or likelihood function. We also extend the likelihood to a generalized version and an adaptive version and propose a distributed procedure to obtain the likelihood estimator. In low-dimensional setting, we give selection criteria for the proposed method and make arguments for the consistency and asymptotic normality of the estimator. In high-dimensional setting, we discuss feature selection and oracle properties of the proposed method. Simulation results confirm the advantages of the proposed method.