Abstract
Analysis of large volumes of data is very complex due to not only a high level of skewness and heteroscedasticity of variance but also the phenomenon of missing data. Expectile regression is a popular alternative method of analyzing heterogeneous data. In this paper, we consider fitting a linear expectile regression model for estimating conditional expectiles based on a large quantity of data with covariates missing at random. We construct a communication-efficient surrogate loss (CSL) function to estimate model parameters. The asymptotic normality of the proposed estimator is established. A proximal alternating direction method of multipliers (ADMM) algorithm is developed for distributed statistical optimization on a large quantity of data. Simulation studies are performed to assess the finite-sample performance of the proposed method. Survey data from the Behavioral Risk Factor Surveillance System (BRFSS) is used to demonstrate the utility of the proposed method in practice.
Highlights
Large-scale data, which arise in many fields such as online surveys, genomics and economics, are characterized by a high level of skewness, heteroscedasticity of variance and the phenomenon of missing information
We study a distributed optimization approach to analyzing large-scale data based on expectile regression with covariates missing at random
We study an efficient approach in an expectile regression framework for analyzing large-scale data with covariates missing at random
Summary
Large-scale data, which arise in many fields such as online surveys, genomics and economics, are characterized by a high level of skewness, heteroscedasticity of variance and the phenomenon of missing information. Y. Pan et al.: Large-Scale Expectile Regression With Covariates Missing at Random performed [16], [25]. We study a distributed optimization approach to analyzing large-scale data based on expectile regression with covariates missing at random. The CSL function can be regarded as a communication-efficient surrogate for the weighted global loss function, and can effectively solve the problems caused by large-scale data stored randomly on multiple machines. To establish the asymptotic properties of the proposed estimator, we apply the distributed optimization theory [10] and the Lindeberg-Feller central limit theorem Another challenge arises from the numerical calculation of the proposed estimator. The proofs of asymptotic properties are given in the Appendix
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