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Modeling univariate block maxima by the generalized extreme value distribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying stationary time series,…
Following the student t-statistic, normalization has been a widely used method in statistic and other disciplines including economics, ecology and machine learning. We focus on statistics taking the form of a ratio over (some power of) the…
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…
The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one…
We give the asymptotic behavior of the Mann-Whitney U-statistic for two independent stationary sequences. The result applies to a large class of short-range dependent sequences, including many non-mixing processes in the sense of…
We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…
Multivariate time series classification is a task with increasing importance due to the proliferation of new problems in various fields (economy, health, energy, transport, crops, etc.) where a large number of information sources are…
This work presents an introduction to feature-based time-series analysis. The time series as a data type is first described, along with an overview of the interdisciplinary time-series analysis literature. I then summarize the range of…
We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy…
Complex nonequilibrium systems are often effectively described by a `statistics of a statistics', in short, a `superstatistics'. We describe how to proceed from a given experimental time series to a superstatistical description. We argue…
We devise a general result on the consistency of model-based bootstrap methods for U- and V-statistics under easily verifiable conditions. For that purpose, we derive the limit distributions of degree-2 degenerate U- and V-statistics for…
Time series, as one of the most fundamental representations of sequential data, has been extensively studied across diverse disciplines, including computer science, biology, geology, astronomy, and environmental sciences. The advent of…
The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data systems. Its conservatism is studied through the use of the Gr\"{u}ss Inequality. It has been reported in the literature that fragmentation (or…
In this paper we study the distribution of hitting times for a class of random dynamical systems. We prove that for invariant measures with super-polynomial decay of correlations hitting times to dynamically defined cylinders satisfy…
We propose a general framework for constructing universal steering criteria that are applicable to arbitrary bipartite states and measurement settings of the steering party. The same framework is also useful for studying the joint…
A measure of primal importance for capturing the serial dependence of a stationary time series at extreme levels is provided by the limiting cluster size distribution. New estimators based on a blocks declustering scheme are proposed and…
Prevalent in many real-world settings such as healthcare, irregular time series are challenging to formulate predictions from. It is difficult to infer the value of a feature at any given time when observations are sporadic, as it could…
Applications of Strongly Convergent M-Estimators are discussed. Given the ubiquity of distributions across the sciences, multiple applications in the Physical, Biomedical and Social Sciences are elaborated. In one particular implementation…
We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of…
We develop the concept of exponential stochastic inequality (ESI), a novel notation that simultaneously captures high-probability and in-expectation statements. It is especially well suited to succinctly state, prove, and reason about…