Abstract: Generally, the range of tuning parameters in CUSUM type change-point estimation statistic is assumed to be (0,1) in theory. But the different values of tuning parameters often lead to the different estimation results in application. Here Monte Carlo method was used to study the influence of tuning parameters on the change-point estimation based on the jump change-point model. It was found that when the jump is large, the change-point estimate is not affected by the value of tuning parameters no matter where the true location of the change-point is. However, the value of tuning parameter has a significant effect on the change-point estimate when the jump is small. Especially, when the true location of change-point is close to one of the two trails, best estimation is obtained with the tuning parameter at 0.5. When the true location of change-point is near the center of sequence, it was observed that the smaller the tuning parameter, the better the estimation. On the basis of simulation and applications, a data-driven method was proposed to select appropriate tuning parameters from a set of possible values, which makes the CUSUM type change-point estimator more robust.

Key words: change-point, cumulative sum estimator, tuning parameter