Related papers: Estimating invertible processes in Hilbert spaces,…
The sharp asymptotics for the L^2-quantization errors of Gaussian measures on a Hilbert space and, in particular, for Gaussian processes is derived. The condition imposed is regular variation of the eigenvalues.
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We develop a new efficient algorithm for the analysis of large-scale time series data. We firstly define rolling averages, derive their analytical properties, and establish their asymptotic distribution. These theoretical results are…
This work is devoted to functional ARMA$(p, q)$ processes and approximating vector models based on functional PCA in the context of prediction. After deriving sufficient conditions for the existence of a stationary solution to both the…
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…
Using straightforward linear algebra we derive response operators describing the impact of small perturbations to finite state Markov processes. The results can be used for studying empirically constructed - e.g. from observations or…
We study estimation and prediction in linear models where the response and the regressor variable both take values in some Hilbert space. Our main objective is to obtain consistency of a principal components based estimator for the…
We consider an operator function (F(\lambda)) for (\lambda\in(\sigma,\tau)\subseteq\mathbb R) whose values are semibounded selfadjoint operators in Hilbert space (\mathfrak H). Our main goal is to estimate the number (\mathcal…
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
Time series prediction covers a vast field of every-day statistical applications in medical, environmental and economic domains. In this paper we develop nonparametric prediction strategies based on the combination of a set of 'experts' and…
The focus of the paper is functional output regression (FOR) with convoluted losses. While most existing work consider the square loss setting, we leverage extensions of the Huber and the $\epsilon$-insensitive loss (induced by infimal…
Spectral estimation is a fundamental problem for time series analysis, which is widely applied in economics, speech analysis, seismology, and control systems. The asymptotic convergence theory for classical, non-parametric estimators, is…
For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used FARIMA models with GARCH-type…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
This paper develops asymptotic theory of integrals of empirical quantile functions with respect to random weight functions, which is an extension of classical $L$-statistics. They appear when sample trimming or Winsorization is applied to…
The training algorithms for AI systems all introduce far-from-equilibrium dynamical processes, and understanding the irreversibility of these algorithms is a fundamental step towards understanding the learning dynamics of modern AI systems.…
We study random iterations of averaged operators in Hilbert spaces and prove that the associated residuals converge exponentially fast, both in expectation and almost surely. Our results provide quantitative bounds in terms of a single…
In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical…
Long Range Dependence (LRD) in functional sequences is characterized in the spectral domain under suitable conditions. Particularly, multifractionally integrated functional autoregressive moving averages processes can be introduced in this…
We propose a general white noise test for functional time series based on estimating a distance between the spectral density operator of a weakly stationary time series and the constant spectral density operator of an uncorrelated time…