一元线性回归模型突变的估计

On the estimation for liner regression model with change point

提出了变点回归的概念，建立了一元线性变点回归的数学模型，用拉格朗日乘数法对变点回归模型的参数进行了最小二乘估计。根据变点是否落在自变量的某一观测值上，把回归变点分为两种类型，回归变点最终位置和类型的统计推断，应使总体回归残差平方和最小。根据不同变点下总体残差平方和的性质，对回归变点的计算进行了简化。

A new concept of regression change point and its mathematical model is put forward, and the least square estimation of parameter in the model is also given with Lagrange multiplier method. The regression change points may be divided into two different types according to whether the change point is equal to one of observations or not. Location and type of change point must make overall residual sum of square to be minimal. Finally, a simple method of statistical inference of change point is given.