Author: Yonggang Yao, SAS
Quantile process regression (QPR) is a methodology for estimating the distribution of a response variable conditional on explanatory covariates. Because QPR is distribution-agnostic, QPR often surpasses other regression methods in its estimation flexibility and accuracy, especially for heteroscedastic data analysis. However, a major difficulty for the QPR practice is in its large computation cost. Fitting a QPR model needs to solve a sequence of quantile regression models on a quantile-level grid. Its computation complexity is usually believed to be proportional to the size of the grid: q, because QPR repeatedly fits each quantile regression model using all training data. This paper proposes a fast QPR algorithm by using a divide-and-conquer strategy whose computation complexity is roughly proportional to log 2 (q). This paper also illustrates the fast algorithm with a simulation study for evaluating its computing efficiency and estimating accuracy.
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