Abstract
We propose nonparametric procedures for testing change-point by using the ℙ-ℙ and ℚ-ℚ plots processes. The limiting distributions of the proposed statistics are characterized under the null hypothesis of no change and also under contiguous alternatives. We give an estimator of the change-point coefficient and obtain its strong consistency. We introduce the bootstrapped version of ℙ-ℙ and ℚ-ℚ processes, requiring the estimation of quantile density, and obtain their limiting laws. Finally, we propose and investigate the exchangeable bootstrap of the empirical ℙ-ℙ plot and ℚ-ℚ plot processes which avoids the problem of the estimation of quantile density, which is of its own interest. These results are used for calculating p-values of the proposed test statistics. Emphasis is placed on the explanation of the strong approximation methodology.
ACKNOWLEDGMENTS
The authors are indebted to the Editor Nitis Mukhopadhyay and an Associate Editor.
Notes
Recommended by S. Lee