MARCIO VALK

Discrimination and classification time series becomes almost indispensable since the large amountof information available nowadays. The problem of time series discrimination and classification isdiscussed in [1]. In this work the authors propose a novel clustering algorithm based on a class ofquasi U-statistics and subgroup decomposition tests. The decomposition may be applied to any con-cave time-series distance. The resulting test statistics is proved to be asymptotically normal for eitheri.i.d. or non-identically distributed groups of time-series under mild conditions. In practice thereare many time series that are correlated among themselves. An example that can describe this fact isthe financial markets globalization. When one of these markets is affected by an exogenous factor, achain reaction can affect many others. So the independence condition fail.We are interested in analyzing how the correlation among the groups of time series can affectclassification and clustering methods especially the one proposed by [1]. Empirical results show thatthe proposed method is robust to the presence of correlation among time series. The convergence ofthe test statistic for dependent time series will be one of the goals in this work.

References[1]

Valk, M., Pinheiro, A. 2012: Time-series clustering via quasi U-statistics,J. Time Ser. Anal.,Vol. 33, 4, 608 -619.

Clustering methods are valuable tools for the identifcation of patterns in high dimensional data with applications in many scientifc felds. However, quantifying uncertainty in clustering is a challenging problem, particularly when dealing with High Dimension Low Sample Size (HDLSS) data. We develop a U-statistics based clustering approach that assesses statistical signifcance in clustering and is specifcally tailored to HDLSS scenarios. These non-parametric methods rely on very few assumptions about the data, and thus can be applied to a wide range of dataset for which the Euclidean distance captures relevant features. Our main result is the development of a hierarchical signifcance clustering method. In order to do so, we first introduce an extension of a relevant U-statistic and develop its asymptotic theory. Additionally, as a preliminary step, we propose a binary non-nested signifcance clustering method and show its optimality in terms of expected values. Our approach is tested through multiple simulations and found to have more statistical power than competing alternatives in all scenarios considered. They are further showcased in three applications ranging from genetics to image recognition problems.

The problem of time‐series discrimination and classification is discussed. We propose a novel clustering algorithm based on a class of quasi U‐statistics and subgroup decomposition tests. The decomposition may be applied to any concave time‐series distance. The resulting test statistics are proven to be asymptotically normal for either i.i.d. or non‐identically distributed groups of time‐series under mild conditions. We illustrate its empirical performance on a simulation study and a real data analysis. The simulation setup includes stationary vs. stationary and stationary vs. non‐stationary cases. The performance of the proposed method is favourably compared with some of the most common clustering measures available.