Jump-preserving Estimation Of Nonparametric Quantile Regression Model Based On Complex Data

In the process of data collection,missing data or measurement errors often occur.For such scenarios,the classical estimation methods for the complete data will be invalid even lead to wrong results.Nonparametric regression model is one of very flexible modeling methods.Commonly,it is assumed that the regression function is smooth.However,because of some incidences,regression function often suffers from jump structure.In this paper,we study the jump-preserving estimation for the nonparametric quantile regression model with response variable missed and measurement errors.For the jump-preserving estimation for nonparametric quantile regression model with randomly missing response variables,firstly,we use local piecewise linear approximate the unknown regression function;Secondly,minimizing the inverse probability weighted quantile loss function,we obtain the regression function estimation;Thirdly,based on the left and right limit estimation the systematic clustering method is used to identify the regression function jump point.We also illustrate the effectiveness of the proposed method through several numerical simulation examples and a real data analysis.For the jump-preserving estimation for nonparametric quantile regression models with measurement errors in the covariates,firstly,the local linear function is used to approximate the unknown regression function;Secondly,the estimation of the regression function is obtained by minimizing the weighted quantile loss function.Thirdly,we weighted residual loss function to identify potential jump points.In the neighbour field of such pointes,the system clustering method is used to the left and right limit estimation of regression function.Forthly,based on the estimated value of the left and right limits of the regression function,the systematic clustering method is further used to identify the jumping point.Through some numerical simulation examples,we illustrate the effectiveness of the proposed method.