A power study of k-linear-r-ahead recursive residuals test for change-point in finite sequences

Abstract

A change-point problem in finite sequences is considered along with, so-called, k-linear-r-ahead recursive residuals and a test procedure proposed by Żoła¸dź et al. [Żoła¸dź, J.A., Szkutnik, Z., Majerczak, J. and Duda, K. 1998, Detection of change point in oxygen uptake during an incremental exercise test using recursive residuals: relationship to the plasma lactate accumulation and blood acid base balance. European Journal of Applied Physiology, 78, 369–377.]. Theoretical significance levels of that (conservative) test are compared with its simulated sizes. Numerical approximations to the powers against various alternatives are given. Properties of the k-linear-r-ahead recursive residuals are described and the consistency of the test is proved, when the noise level goes to zero.

Keywords:

• Change-point problem
• Recursive residuals
• Consistent test
• Incremental exercise test

2000 Mathematics Subject Classifications :

• 62F03
• 62P10

Acknowledgements

This research was partly supported by AGH local grant 10.420.03. The authors thank J.A. Żoła¸dź for the permission to use some real data from his physiological experiments for illustrative purposes. Suggestions of the reviewers of an early version of the manuscript are kindly acknowledged.