Inference about the Point of Change in a Regression Model
研究了分段多项式回归模型中未知变化点的推断问题，推导了相对边际似然函数，并给出了估计多项式阶数的步骤，通过实际和模拟数据验证了方法。
SUMMARY Consider a sequence of (n1 + n2) independent ordered pairs of observations for which the relationship between variables can be represented by a segmented polynomial regression model with unknown point of change n 1. The relative marginal likelihood function for n 1 is derived and the expressions for the relative conditional and maximum likelihood functions are given. Either of the first two likelihoods, which account for the uncertainty about the value of the other parameters, are to be preferred to the maximum likelihood function, with the relative marginal likelihood function being examined more extensively here. In the case where the segmented regression model can be represented by two polynomials of unknown degrees p and q, a procedure is described for estimating p and q. The use of these methods is illustrated using two observed sets of data and three artificially generated sets.