Large-Scale Expectile Regression With Covariates Missing at Random

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. INDEX TERMS CSL function, expectile regression, large-scale data, missing at random, proximal ADMM algorithm.

Efficient Distributed Learning for Large-Scale Expectile Regression With Sparsity

“…Liao et al (2019) discussed the pros and cons of penalized quantile and expectile regression and conducted in-depth simulation studies to compare the finite sample performance of the two methods. Pan et al (2020) developed a communicationefficient distributed optimization method to solve the expectile regression problem with covariates missing at random. Although expectile regression has applications in various fields, few people, to the best of our knowledge, have used the penalized version of expectile regression in a distributed environment.…”

“…To address the problem of establishing the theoretical properties of parameter estimation under the distributed setting, Jordan et al (2019), Pan (2020) and Pan et al (2020) indicated that CSL function can be regarded as a valid proxy of global loss function. Inspired by CSL function, we propose a more generalized proxy loss function called gradient-enhanced loss (GEL) function, which includes the CSL function as a special case.…”