Related papers: Compositional splines for representation of densit…

Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…

Considering the context of functional data analysis, we developed and applied a new Bayesian approach via Gibbs sampler to select basis functions for a finite representation of functional data. The proposed methodology uses Bernoulli latent…

In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…

Functional Data Analysis represents a field of growing interest in statistics. Despite several studies have been proposed leading to fundamental results, the problem of obtaining valid and efficient prediction sets has not been thoroughly…

Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…

The present paper is concerned with new Besov-type space of variable smoothness. Nonlinear spline-approximation approach is used to give atomic decomposition of such space. Characterization of the trace space on hyperplane is also obtained.

It is well known that the minimax rates of convergence of nonparametric density and regression function estimation of a random variable measured with error is much slower than the rate in the error free case. Surprisingly, we show that if…

Bayes classifiers for functional data pose a challenge. This is because probability density functions do not exist for functional data. As a consequence, the classical Bayes classifier using density quotients needs to be modified. We…

In this paper we study dual bases functions in subspaces. These are bases which are dual to functionals on larger linear space. Our goal is construct and derive properties of certain bases obtained from the construction, with primary focus…

Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an…

This study introduces an efficient workflow for functional data analysis in classification problems, utilizing advanced orthogonal spline bases. The methodology is based on the flexible Splinets package, featuring a novel spline…

The spatial random-effects model is flexible in modeling spatial covariance functions, and is computationally efficient for spatial prediction via fixed rank kriging. However, the success of this model depends on an appropriate set of basis…

In several environmental applications data are functions of time, essentially con- tinuous, observed and recorded discretely, and spatially correlated. Most of the methods for analyzing such data are extensions of spatial statistical tools…

In this work, we present a general framework that unites the two primary strategies for constructing density functional approximations (DFAs): non-empirical (NE) constraint satisfaction and semi-empirical (SE) data-driven optimization. The…

Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…

A normalizing flow models a complex probability density as an invertible transformation of a simple base density. Flows based on either coupling or autoregressive transforms both offer exact density evaluation and sampling, but rely on the…

In this paper we show a density property for fractional weighted Sobolev spaces. That is, we prove that any function in a fractional weighted Sobolev space can be approximated by a smooth function with compact support. The additional…

Uncertainty estimation is critical in high-stakes machine learning applications. One effective way to estimate uncertainty is conformal prediction, which can provide predictive inference with statistical coverage guarantees. We present a…

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we…

We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $n$, the smoothing spline estimator can be expressed as a linear combination of $n$ basis functions,…