Abstract
Quantile regression is a powerful statistical technique for estimating the quantiles of a conditional distribution on the values of covariates. It has been widely used in many fields. In this paper, an improved interior point algorithm for quantile regression is proposed. The algorithm introduces multiple centrality corrections technique into the interior point algorithm for quantile regression. The purpose of introducing the multiple centrality corrections technique is to reduce the overall solution time required to solve a quantile regression problem. The computational experiments results constitute evidence of the improvement obtained with the use of multiple centrality correction technique combined with the interior point algorithm.
Highlights
Most applied statistics can be regarded as an exposition of linear models and their associated least squares methods
The computational experiment results constitute evidence of the improvement obtained with the use of multiple centrality corrections technique combined with the interior point algorithm
The algorithm proposed in this paper introduces multiple centrality corrections technique into the interior point algorithm for quantile regression
Summary
Most applied statistics can be regarded as an exposition of linear models and their associated least squares methods. These approaches, as shown by Karmarkar [15] and subsequent authors, provide significantly better worst-case performance than simplex algorithms, and show impressive practical performance in the large-scale linear programming that appears in commercial and extensive numerical experiments Among these numerous interior point algorithms, the primal-dual interior point algorithm has been proved theoretically to have polynomial computational complexity, fast convergence and good robustness, so it has become one of the most widely used and efficient algorithms. According to a large number of numerical experimental results in Gondzio [27], the use of multiple centrality corrections technique can reduce computation time compared to the widely used predictor-corrector interior point algorithm. The computational experiment results constitute evidence of the improvement obtained with the use of multiple centrality corrections technique combined with the interior point algorithm This remainder of this article is organized as follows: Section II is devoted to describing quantile regression and converting it to the linear programming form.
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