Related papers: Detecting a Structural Change in Functional Time S…
This paper introduces new scan statistics for multivariate functional data indexed in space. The new methods are derivated from a MANOVA test statistic for functional data, an adaptation of the Hotelling T2-test statistic, and a…
In modern industrial settings, advanced acquisition systems allow for the collection of data in the form of profiles, that is, as functional relationships linking responses to explanatory variables. In this context, statistical process…
Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Lo\`{e}ve expansion, which assumes a linear structure of the…
Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…
This paper introduces new methodology based on the field of Topological Data Analysis for detecting anomalies in multivariate time series, that aims to detect global changes in the dependency structure between channels. The proposed…
We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), and multi-fractal detrended fluctuation analysis (MFDFA), for investigating characteristics of vibration time series data from a friction brake.…
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…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…
Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). However, there is currently no widely accepted statistical…
Functional linear discriminant analysis (FLDA) is a powerful tool that extends LDA-mediated multiclass classification and dimension reduction to univariate time-series functions. However, in the age of large multivariate and incomplete…
Structural change detection problems are often encountered in analytics and econometrics, where the performance of a model can be significantly affected by unforeseen changes in the underlying relationships. Although these problems have a…
In this paper, we consider detecting and estimating breaks in heterogeneous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated and temporally dependent. A new test statistic…
In Structural Health Monitoring (SHM), sensor measurements and derived features such as eigenfrequencies often exhibit systematic daily patterns and can therefore be naturally represented as functional data. Furthermore, these patterns are…
The rise in data has led to the need for dimension reduction techniques, especially in the area of non-scalar variables, including time series, natural language processing, and computer vision. In this paper, we specifically investigate…
A major challenge of climate change adaptation is to assess the effect of changing weather on human health. In spite of an increasing literature on the weather-related health subject, many aspect of the relationship are not known, limiting…
Topological Data Analysis (TDA) is a modern approach to Data Analysis focusing on the topological features of data; it has been widely studied in recent years and used extensively in Biology, Physics, and many other areas. However,…
Identifying structural change is a crucial step in analysis of time series and panel data. The longer the time span, the higher the likelihood that the model parameters have changed as a result of major disruptive events, such as the…
Temporal data are ubiquitous in the financial services (FS) industry -- traditional data like economic indicators, operational data such as bank account transactions, and modern data sources like website clickstreams -- all of these occur…
The study of the dynamic behavior of cross-sectional ranks over time for functional data and the ranks of the observed curves at each time point and their temporal evolution can yield valuable insights into the time dynamics of functional…