关键词: 函数型数据, 函数型主成分, 倾斜分位回归, 积分均分预测误差, 渐近分布, 多发性硬化症

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.

Key words: Functional Data, Functional PCA, Tilting Quantile Regression, IMSPE, Asymptotic Distribution, Multiple Sclerosis