Modal Regression Models Based On Nonparametric Quantile Estimations

Mean and quantile regression models are widely used because of the complete theories and rich algorithms.However,when the distributions of data are multimodal,heavy-tailed or biased,the mean and median regression functions cannot nicely sketch their centers.To remedy the shortcomings of classical regression models,the modal regression models come as an active research fields.With the complex data,the modal regression functions not only can do better in describing the data's center,but also contain the stronger robustness as the median than the mean to resist the outliers.The popular estimates of modal regression functions are based on density estimations.A new one uses the derivatives of the quantiles to estimate the modes.This paper presents a novel estimate of modal regression functions via the nonparametric quantile estimations.The consistency of the estimate is researched and simulations and application are given to show its performance.These works will rich the theories of regressions and provide some new choices for users of regression models.