Homogeneity and change-point detection tests for multivariate data using rank statistics

By Alexandre Lung-Yut-Fong, C. L'evy-Leduc, Olivier Capp'e. 2011

100 citations recorded by the source corpus.

Detecting and locating changes in highly multivariate data is a major concern in several current statistical applications. In this context, the first contribution of the paper is a novel non-parametric two-sample homogeneity test for multivariate data based on the well-known Wilcoxon rank statistic. The proposed two-sample homogeneity test statistic can be extended to deal with ordinal or censored data as well as to test for the homogeneity of more than two samples. We also provide a detailed analysis of the power of the proposed test statistic (in the two sample case) against asymptotic local shift alternatives. The second contribution of the paper concerns the use of the proposed test statistic to perform retrospective change-point detection. It is first shown that the approach is computationally feasible even when looking for a large number of change-points thanks to the use of dynamic programming. Computable asymptotic p-values for the test are available in the case where a single potential change-point is to be detected. The proposed approach is particularly recommendable in situations where the correlations between the coordinates of the data are moderate, the marginal distributions are not well modelled by usual parametric assumptions (e.g., in the presence of outliers) and when faced with highly variable change patterns, for instance, if the potential changes only affect subsets of the coordinates of the data.

Subfields: Artificial Intelligence, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/cbc29a381b38445ac7dbe3039531bc7561b1a6a3

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Citations in the corpus

A Nonparametric Approach for Multiple Change Point Analysis of Multivariate Data (2013, methodology): “Nonparametric approaches often rely heavily on the estimation of density functions (Kawahara and Sugiyama 2011), though they have also been performed using rank statistics (Lung-Yut-Fong, Lévy-Leduc, and Cappé 2011).”
Selective review of offline change point detection methods (2020, methodology): “The resulting algorithm has been applied on DNA 526 sequences [93] and network traffic data [28, 29].”
Asymptotic distribution-free change-point detection for multivariate and non-Euclidean data (2017, background): “cross-sample copy number variation analysis, Zhang et al. (2010)), images (e.”
ecp: An R Package for Nonparametric Multiple Change Point Analysis of Multivariate Data (2013, background): “5 E−Agglo Results for Individual 10 Index S ig na l MultiRank Results for Individual 10 0 500 1000 1500 2000 − 3 − 1 1 GFL Results for Individual 15 Index S ig na l 0 500 1000 1500 2000 − 3 − 1 1 E−Divisive Results for Individual 15 Index S ig na l 0 500 1000 1500 2000 − 3 − 1 1 E−Agglo Results for ”
A review of change point detection methods (2018, methodology): “ detection: the calculation of the rank statistics, in O(dTlogT) operations, and the calculation of the matrix b r, in O(d2T+ d3) operations. The resulting algorithm has been applied on DNA sequences [92] and network trac data [28, 29]. 4.2.3. Kernel-based detection A kernel-based method has been pr”