Related papers: A review and comparative study on functional time …

This paper deals with study of Birkhoff-James orthogonality of a linear operator to a subspace of operators defined between arbitrary Banach spaces. In case the domain space is reflexive and the subspace is finite dimensional we obtain a…

Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…

We consider $\alpha$-mixing observations and deal with the estimation of the conditional mode of a scalar response variable $Y$ given a random variable $X$ taking values in a semi-metric space. We provide a convergence rate in $L^p$ norm of…

We study ordinal-indexed, multi-layer iterations of bounded operator transforms and prove convergence to spectral/ergodic projections under functional-calculus hypotheses. For normal operators on Hilbert space and polynomial or holomorphic…

Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…

Using notions from the geometry of Banach spaces we introduce square functions $\gamma(\Omega,X)$ for functions with values in an arbitrary Banach space $X$. We show that they have very convenient function space properties comparable to the…

We consider nonparametric functional regression when both predictors and responses are functions. More specifically, we let $(X_1,Y_1),...,(X_n,Y_n)$ be random elements in $\mathcal{F}\times\mathcal{H}$ where $\mathcal{F}$ is a semi-metric…

This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel…

A Ritt operator T : X --> X on Banach space is a power bounded operator such that the sequence of all n(T^{n} -T^{n-1}) is bounded. When X=Lp for some 1<p<\infty, we study the validity of square functions estimates Norm{(\sum_k k |T^{k}(x)…

We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a…

Lecture note topics: 1. Some tools from real and complex analysis, 2. Hilbert spaces, 3. Banach spaces, 4. Compact operators and their spectra, 5. Intermezzo: reproducing kernel Hilbert spaces, 6. Banach algebras ,7. Spectral theory of…

We consider frames F in a given Hilbert space, and we show that every F may be obtained in a constructive way from a reproducing kernel and an orthonormal basis in an ambient Hilbert space. The construction is operator-theoretic, building…

The existence of a Banach limit as a translation invariant positive continuous linear functional on the space of bounded scalar sequences which is equal to 1 at the constant sequence (1,1,...,1,...) is proved in a first course on functional…

Time series analysis has become crucial in various fields, from engineering and finance to healthcare and social sciences. Due to their multidimensional nature, time series often need to be embedded into a fixed-dimensional feature space to…

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…

Financial time series are characterised by their nonstationarity and autocorrelation. Even if these time series are differenced, technically ensuring their stationarity, they experience regular covariate shifts and concept drifts. Against…

Time series data is a collection of chronological observations which is generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting, and clustering have been…

Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…

In functional linear regression, the parameters estimation involves solving a non necessarily well-posed problem and it has points of contact with a range of methodologies, including statistical smoothing, deconvolution and projection on…

We develop an estimation methodology for a factor model for high-dimensional matrix-valued time series, where common stochastic trends and common stationary factors can be present. We study, in particular, the estimation of (row and column)…