The Power of Change-Point Test for Two-Phase Regression


In this paper, the roughness of the model function to the basis functions and its properties have been considered. We also consider some conditions to take the limit of the roughness when the observations are i.i.d. An explicit formula to calculate the power of change-point test for the two phases regression through the roughness was obtained.

Share and Cite:

Ban, T. and Quyen, N. (2014) The Power of Change-Point Test for Two-Phase Regression. Applied Mathematics, 5, 2994-3000. doi: 10.4236/am.2014.519286.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Aue, A., Horvath, L., Huskova, M. and Kokoszka, P. (2008) Testing for Changes in Polynomial Regression. Bernoulli, 14, 637-660.
[2] Berkes, I., Horvath, L. and Schauer, J. (2011) Asymptotics of Trimmed CUSUM Statistics. Bernoulli, 17, 1344-1367.
[3] Worsley, K.J. (1983) Testing for a Two-Phase Multiple Regression. Technometrics, 25, 35-42.
[4] Koul, H.L. and Qian, L. (2002) Asymptotics of Maximum Likelihood Estimator in a Two-Phase Linear Regression Model. Journal of Statistical Planning and Inference, 108, 99-119.
[5] Jaruskova, D. (1998) Testing Appearance of Linear Trend. Journal of Statistical Planning and Inference, 70, 263-276.
[6] Lehmann, E.L. and Romano, J.P. (2005) Testing Statistical Hypotheses. 3th Edition, Springer, New York, USA, 277-282.
[7] Ban, T.V., Quyen, N.T. and Ha, P.T. (2013) The Roughness of the Model Function to the Basis Functions. Journal of Mathematics and System Science, 3, 385-390.
[8] Bischoff, W. and Miller, F. (2000) Asymptotically Optimal Test and Optimal Designs for Testing the Mean in Regression Models with Applications to Change-Point Problems. Annals of the Institute of Statistical Mathematics, 52, 658-679.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.