Simultaneous Spline Quantile Regression Under Shape Constraints

As data analysis methods, hypothesis testing and regression analysis are famous. However, the hypothesis testing can only detect significant differences between two groups divided by some characteristic or some empirical threshold, and the regression analysis can only construct one averaged model whose information is limited. Quantile regression is a robust and flexible analysis method, and can construct multilevel models, e.g., the median and the first and third quartiles. To make the most of the quantile regression, existing papers employed spline regression models as generalizations of polynomial regression models, but the regression of each level was individually executed. In this paper, we propose simultaneous spline quantile regression which considers the similarity between the adjacent quantiles. Further, the proposed method enforces the non-crossing and one shape (non-decreasing/non-increasing/convex/concave) constraints. Experiments demonstrate that the proposed method recovers harmonious quantiles.