Zhang Feipeng, Li Qunhua
Department of Statistics, Pennsylvania State University, PA, 16802, USA.
Department of Statistics, Hunan University, Changsha, 410082, China.
Comput Stat Data Anal. 2017 Dec;116:49-66. doi: 10.1016/j.csda.2017.07.005. Epub 2017 Jul 29.
Expectile regression is a useful tool for exploring the relation between the response and the explanatory variables beyond the conditional mean. A continuous threshold expectile regression is developed for modeling data in which the effect of a covariate on the response variable is linear but varies below and above an unknown threshold in a continuous way. The estimators for the threshold and the regression coefficients are obtained using a grid search approach. The asymptotic properties for all the estimators are derived, and the estimator for the threshold is shown to achieve root-n consistency. A weighted CUSUM type test statistic is proposed for the existence of a threshold at a given expectile, and its asymptotic properties are derived under both the null and the local alternative models. This test only requires fitting the model under the null hypothesis in the absence of a threshold, thus it is computationally more efficient than the likelihood-ratio type tests. Simulation studies show that the proposed estimators and test have desirable finite sample performance in both homoscedastic and heteroscedastic cases. The application of the proposed method on a Dutch growth data and a baseball pitcher salary data reveals interesting insights. The proposed method is implemented in the package .
期望分位数回归是探索响应变量与条件均值之外的解释变量之间关系的有用工具。开发了一种连续阈值期望分位数回归，用于对协变量对响应变量的影响呈线性，但在未知阈值上下以连续方式变化的数据进行建模。使用网格搜索方法获得阈值和回归系数的估计值。推导了所有估计值的渐近性质，并证明了阈值估计值具有根n一致性。针对给定期望分位数处阈值的存在性，提出了一种加权CUSUM型检验统计量，并在原假设和局部备择模型下推导了其渐近性质。该检验仅需在无阈值的原假设下拟合模型，因此在计算上比似然比型检验更有效。模拟研究表明，所提出的估计量和检验在同方差和异方差情况下均具有理想的有限样本性能。将所提出的方法应用于荷兰生长数据和棒球投手薪资数据，揭示了有趣的见解。所提出的方法在 包中实现。
