Adaptive Quantile Regressions For Massive Datasets

Compared with traditional Regression analysis,Quantile Regression(QR)can more comprehensively describe the conditional distribution of explained variables.It can be used to analyze the conditional expectation of independent variables as well as the influence of independent variables on the conditional quantiles of dependent variables.Moreover,the advantage of QR is that it does not require the assumption that the error term is subject to the normal distribution,so when the random error is not subject to the normal distribution,the QR unknown parameter estimator is more robust.With the advent of the digital era,people are constantly collecting and storing data,which makes the scale of data sets larger and larger.Therefore,it is necessary to constantly develop new statistical methods to improve computing efficiency.Quantile regression is often modeled and analyzed by using the conditional quantile of response variables,which can comprehensively describe the distribution of response variables and is one of the important means and methods to explore objective laws.Many existing quantile regression methods for massive data are based on the dial-and-conquer method(DC),which has the same accuracy as full-data analysis under=(9)~2),whereis the full data size and9)is the subset data size.And quantile regression needs to solve the non-smooth optimization problem,for a large number of data sets,the amount of calculation is quite large.In this paper,a new estimation method for the unknown parameter₀ is developed for adaptive quantile regression(AQR),which is called adaptive smooth quantile regression(ASQR)method.For mass data processing,this paper proposes a divide-and-conquer ASQR method(DC-ASQR)without the condition=(9)~2),which has high computational efficiency and relatively accurate estimation results.