门槛回归模型中门槛值和回归参数的估计

Estimation of threshold values and regression parameters in threshold regression model

门槛模型中有两个关键问题:门槛个数的选择和门槛参数的估计.本文提出的判罚光滑最小二乘方法同时解决这两个问题.本文的方法避免了为确定门槛个数所需的假设检验,计算简单.回归参数估计被证明是n-^(1/2)相合且渐近正态,门槛参数估计被证明是(n/h-)^(1/2)相合且渐近正态.数值模拟和实际例子结果显示本文方法有效可行.

There are two critical issues of threshold model： Parameter estimation and threshold number estimate problems. We propose penalized smoothed least square to solve these problems. Our estimation method avoids the hypothesis testing which is always used to determine the threshold numbers and is simple to compute.Estimator of regression is n-^1/2consistent and asymptotically normal, and estimator of threshold is （n/h-）^1/2consistent and asymptotically normal. Numerical simulation and practical example results show that the proposed method performs well.