arXiv subjects

Leonid Torgovitski

Publications and source records attributed to Leonid Torgovitski.

4 recordsLinked to original sources

arXiv2016

A Darling-Erdős-type CUSUM-procedure for functional data II

This article considers testing for mean-level shifts in functional data. The class of the famous Darling-Erdős-type cumulative sums (CUSUM) procedures is extended to functional time series under short range dependence conditions which are satisfied by functional analogues of many popular time series models including the linear functional AR and the non-linear functional ARCH. We follow a data driven, projection-based approach where the lower-dimensional subspace is determined by (long run) functional principal components which are eigenfunctions of the long run covariance operator. This second-order structure is generally unknown and estimation is crucial - it plays an even more important role than in the classical univariate setup because it generates the finite-dimensional subspaces. We discuss suitable estimates and demonstrate empirically that altogether this change-point procedure performs well under moderate temporal dependence. Moreover, Darling-Erdős-type change-point estimates based on (long run) functional principal components as well as the corresponding "fully-functional" counterparts are provided and the testing procedure is finally applied to publicly accessible electricity data from a German power company.

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arXiv2015

Panel data segmentation under finite time horizon

We study the nonparametric change point estimation for common changes in the means of panel data. The consistency of estimates is investigated when the number of panels tends to infinity but the sample size remains finite. Our focus is on weighted denoising estimates, involving the group fused LASSO, and on the weighted CUSUM estimates. Due to the fixed sample size, the common weighting schemes do not guarantee consistency under (serial) dependence and most typical weightings do not even provide consistency in the i.i.d. setting when the noise is too dominant. Hence, on the one hand, we propose a consistent covariance-based extension of existing weighting schemes and discuss straightforward estimates of those weighting schemes. The performance will be demonstrated empirically in a simulation study. On the other hand, we derive sharp bounds on the change to noise ratio that ensure consistency in the i.i.d. setting for classical weightings.

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arXiv2015

Detecting changes in Hilbert space data based on "repeated" and change-aligned principal components

We study a CUSUM (cumulative sums) procedure for the detection of changes in the means of weakly dependent time series within an abstract Hilbert space framework. We use an empirical projection approach via a principal component representation of the data, i.e., we work with the eigenelements of the (long run) covariance operator. This article contributes to the existing theory in two directions: By means of a recent result of Reimherr (2015) we show, on one hand, that the commonly assumed "separation of the leading eigenvalues" for CUSUM procedures can be avoided. This assumption is not a consequence of the methodology but merely a consequence of the usual proof techniques. On the other hand, we propose to consider change-aligned principal components that allow to further reduce common assumptions on the eigenstructure under the alternative. This approach extends directly to multidirectional changes, i.e. changes that occur at different time points and in different directions, by fusing sufficient information on them into the first component. The latter findings are illustrated by a few simulations and compared with existing procedures in a functional data framework.

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arXiv2015

Algorithm for overlapping estimation of common change-sets in spatial data of fixed size

We propose a flexible class of estimates for "common change in the mean" sets in spatio-temporal data. We rely on a scan type approach by subdividing the spatial observations into suitable overlapping regions to which classical CUSUM (cumulative sums) estimates may then be applied separately. The aggregated "local" estimates are used to construct consistent "global" estimates of the change set(s) by taking the overlapping structure into account. The domain and the change regions may have irregular shapes and the suggested procedure is especially suited for estimation of multiple change regions. The performance is demonstrated in a simulation study.

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