New nonparametric tests for change-point detection based on the P-P and Q-Q plots processes
Résumé
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.