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Consistent nonparametric change point detection combining CUSUM and marked empirical processes
- Publication Year :
- 2019
-
Abstract
- A weakly dependent time series regression model with multivariate covariates and univariate observations is considered, for which we develop a procedure to detect whether the nonparametric conditional mean function is stable in time against change point alternatives. Our proposal is based on a modified CUSUM type test procedure, which uses a sequential marked empirical process of residuals. We show weak convergence of the considered process to a centered Gaussian process under the null hypothesis of no change in the mean function and a stationarity assumption. This requires some sophisticated arguments for sequential empirical processes of weakly dependent variables. As a consequence we obtain convergence of Kolmogorov-Smirnov and Cram\'er-von Mises type test statistics. The proposed procedure acquires a very simple limiting distribution and nice consistency properties, features from which related tests are lacking. We moreover suggest a bootstrap version of the procedure and discuss its applicability in the case of unstable variances.<br />Comment: 35 pages (including 5 pages of supplementary material), 4 figures, 2 tables
- Subjects :
- Mathematics - Statistics Theory
Primary 62M10, Secondary 62G08, 62G09, 62G10
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1901.08491
- Document Type :
- Working Paper