Related papers: Simultaneous Confidence Band for Stationary Covari…
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…
We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…
Individualized treatments are crucial for optimal decision making and treatment allocation, specifically in personalized medicine based on the estimation of an individual's dose-response curve across a continuum of treatment levels, e.g.,…
Load-sharing systems arise in many different reliability applications, for instance, when modeling tensile strength of fibrous composites in textile industry or lifetimes of redundant technical systems in engineering. Sequential order…
This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the…
A long-standing problem in the construction of asymptotically correct confidence bands for a regression function $m(x)=E[Y|X=x]$, where $Y$ is the response variable influenced by the covariate $X$, involves the situation where $Y$ values…
The specification of a covariance function is of paramount importance when employing Gaussian process models, but the requirement of positive definiteness severely limits those used in practice. Designing flexible stationary covariance…
We propose the use of indirect inference estimation to conduct inference in complex locally stationary models. We develop a local indirect inference algorithm and establish the asymptotic properties of the proposed estimator. Due to the…
We propose simultaneous confidence bands of the hyperbolic-type for the contrasts between several nonlinear (curvilinear) regression curves. The critical value of a confidence band is determined from the distribution of the maximum of a…
In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…
A bootstrap procedure for constructing prediction bands for a stationary functional time series is proposed. The procedure exploits a general vector autoregressive representation of the time-reversed series of Fourier coefficients appearing…
The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…
The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…
The convergence behavior of Stochastic Gradient Descent (SGD) crucially depends on the stepsize configuration. When using a constant stepsize, the SGD iterates form a Markov chain, enjoying fast convergence during the initial transient…
Network estimation and variable selection have been extensively studied in the statistical literature, but only recently have those two challenges been addressed simultaneously. In this paper, we seek to develop a novel method to…
Spectral bifurcation diagrams (SBDs) have recently emerged as an efficient tool for identifying dynamical transitions in nonlinear systems through frequency-domain analysis. Previous studies have been limited to numerical investigations,…
Spatial functional data arise in many settings, such as particulate matter curves observed at monitoring stations and age population curves at each areal unit. Most existing functional regression models have limited applicability because…
The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or ${\cal L}^\infty$) and the quadratic (or ${\cal…
Sequential Monte Carlo (SMC) algorithms represent a suite of robust computational methodologies utilized for state estimation and parameter inference within dynamical systems, particularly in real-time or online environments where data…
We establish the asymptotic validity of frequency-domain inference for stationary multivariate Hawkes processes under mild conditions, bridging the gap between theory and application. By developing upper-bounds on the reduced cumulant…