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### 函数型变量倾斜分位回归模型及其应用

• 出版日期:2019-08-25 发布日期:2019-08-25

### Tilting Quantile Regression Modeling of Functional Data and Its Application

Tian Maozai & Mei Bo

• Online:2019-08-25 Published:2019-08-25

Abstract: This paper considers the functional features of data and develops a new type of tilting quantile regression model based on the definition of unconditional tilting quantile curve for two types of quantile regression models for functional data: functional-on-scalar regression model and functional-on-functional regression model. For the second type, this paper applies splines basis expansion on model coefficients and functional principal component basis expansion on the predictors and derives the generic formula of tilting quantile regression model. To improve the efficiency of parameter estimation, it adopts component-wise gradient boosting algorithm to minimize the weighted asymmetric loss function. In addition, this paper mathematically proves the asymptotic normal distribution of the estimates of parameters. Both the simulation and real data study shows that tilting quantile regression model fits better than the point-wise quantile regression model. According to the integral mean square prediction error (IMSPE), the model proposed here has better prediction than the existent models uniformly.