Related papers: Weakly dependent functional data
In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…
For spatially dependent functional data, a generalized Karhunen-Lo\`{e}ve expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient…
The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its…
Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary like precipitation, temperature, and wind speeds over time at a given weather station. We propose a multivariate functional…
We consider functional data which have only been observed on a subset of their domain. This paper aims to develop statistical tests to determine whether the function and the domain over which it is observed are independent. The assumption…
We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze…
Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…
The goal of data-driven learning of dynamical systems is to interpret time series as a continuous observation of an underlying dynamical system. This task is not well-posed for a variety of reasons - such as multiple co-existing…
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the…
Many recent studies use individual longitudinal data to analyze job search behaviors. Such data allow the use of fixed-effects models, which supposedly address the issue of dynamic selection and make it possible to identify the structural…
In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…
We extend two methods of independent component analysis, fourth order blind identification and joint approximate diagonalization of eigen-matrices, to vector-valued functional data. Multivariate functional data occur naturally and…
Motivated by modern observational studies, we introduce a class of functional models that expands nested and crossed designs. These models account for the natural inheritance of correlation structure from sampling design in studies where…
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling…
We measure the influence of different time-scales on the dynamics of financial market data. This is obtained by decomposing financial time series into simple oscillations associated with distinct time-scales. We propose two new time-varying…
This paper concerns the modeling of multi-way functional data where double or multiple indices are involved. We introduce a concept of weak separability. The weakly separable structure supports the use of factorization methods that…
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…
Mobile health applications, including those that track activities such as exercise, sleep, and diet, are becoming widely used. Accurately predicting human actions is essential for targeted recommendations that could improve our health and…
Mobile health studies often collect multiple within-day self-reported assessments of participants' behavior and well-being on different scales such as physical activity (continuous), pain levels (truncated), mood states (ordinal), and life…
This paper studies estimation in functional linear quantile regression in which the dependent variable is scalar while the covariate is a function, and the conditional quantile for each fixed quantile index is modeled as a linear functional…