Distributed estimation for large-scale expectile regression

Analysis of large volume of data is very complex due to not only the high level of skewness and heteroscedasticity of variance but also the difficulty of data storage. Expectile regression is a common alternative method to analyze heterogeneous data. Distributed storage can reduce effectively the storage burden of a single machine. In this paper, we consider fitting linear expectile regression model to estimate conditional expectile based on large-scale data. We store the data in a distributed manner and construct a gradient-enhanced loss (GEL) function as a proxy for the global loss function. A distributed algorithm is proposed for the optimization of the GEL function. The asymptotic properties of the proposed estimator are established. Simulation studies are conducted to assess the finite-sample performance of our proposed estimator. Applications to an analysis of the National Health Interview Survey data set demonstrate the practicability of the proposed method.