非参数模型的稳健跳点检测估计

Robust Jump-Detection-Based Estimation for Nonparametric Models

非参数模型是统计学中常用的一类模型.在实际应用中,回归函数可能不是连续的,即在某些未知的位置上存在跳点.检测这些跳点对于回归函数的估计非常重要.本文基于B样条和众数估计,提出一个稳健跳点检测方法.然后利用检测出的跳点给出了回归函数的稳健有效估计量,并讨论了参数的选择.数值模拟和实例分析验证了所提方法在有限样本下的表现.

Nonparametric models are commonly used models in statistics.In practical applications,the regression function may be discontinuous,namely,some jump points exist at some unknown positions.Detecting such jump points is important for estimating the regression function.This article proposes a robust jump detection method based on the B-spline and modal regression.Using the detected jump points,we provide a robust jump-detection-based estimator for the regression function,and then the selection of parameters is discussed.Numerical studies and a real data analysis are conducted to assess the finite sample performance of the proposed method.