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New estimators for the mean and the covariance function for partially observed functional data are proposed using a detour via the fundamental theorem of calculus. The new estimators allow for a consistent estimation of the mean and…
The volatility of financial instruments is rarely constant, and usually varies over time. This creates a phenomenon called volatility clustering, where large price movements on one day are followed by similarly large movements on successive…
Change point detection in covariance structures is a fundamental and crucial problem for sequential data. Under the high-dimensional setting, most of the existing research has focused on identifying change points in historical data.…
The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…
The Maxwellian Average Cross Section (MACS) is usually calculated with help of the statistical codes that do not take into account fluctuations of individual resonance parameters. The actual MACS can substantially deviate from its…
The problem of local damage diagnosis (based on the detection of impulsive and periodic signals) is discussed. Both features should be checked, as fault frequency must be linked to the true value calculated for a given machine and speed.…
We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is only observed on a subinterval of length $\delta<1$, one has no…
A detailed discussion of semiclassical trace formulae is presented and it is demonstrated how a regularized trace formula can be derived while dealing only with finite and convergent expressions. Furthermore, several applications of trace…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
As semiconductor devices continue to scale down, process vari- ations become more relevant for circuit design. Facing such variations, statistical static timing analysis is introduced to model variations more accurately so that the…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
Functional data analysis has been extensively conducted. In this study, we consider a partially functional model, under which some covariates are scalars and have linear effects, while some other variables are functional and have…
The complex structure of a typical stratus cloud base height (or profile) time series is analyzed with respect to the variability of its fluctuations and their correlations at all experimentally observed temporal scales. Due to the…
Covariances and variances of linear statistics of a point process can be written as integrals over the truncated two-point correlation function. When the point process consists of the eigenvalues of a random matrix ensemble, there are often…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
A coupling of structural and thermodynamic fluctuations in the course of various-type insertion processes is investigated within a combination of Gibbsian statistics and the information theory approach. It is shown that the coupling makes…
This paper is concerned with the estimation of time-varying networks for high-dimensional nonstationary time series. Two types of dynamic behaviors are considered: structural breaks (i.e., abrupt change points) and smooth changes. To…
Inclusive and diffractive structure functions for electron-proton scattering are calculated in a semiclassical approach at large momentum transfer $Q^2$ and small values of the scaling variable $x$. The basic process is the production of a…
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…
Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new…