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This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that…

Numerical Analysis · Mathematics 2012-03-30 Guohui Song , Anne Gelb

The increasing interest in spatially correlated functional data has led to the development of appropriate geostatistical techniques that allow to predict a curve at an unmonitored location using a functional kriging with external drift…

Methodology · Statistics 2017-06-23 Maria Franco-Villoria , Rosaria Ignaccolo

Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…

Statistics Theory · Mathematics 2025-01-28 Shaojun Guo , Dong Li , Xinghao Qiao , Yizhu Wang

This paper proposes a novel localized Fourier extension method for approximating non-periodic functions via domain segmentation. By partitioning the computational domain into subregions with uniform discretization scales, the method…

Numerical Analysis · Mathematics 2025-08-29 Zhenyu Zhao , Yanfei Wang

We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…

Probability · Mathematics 2022-10-20 Zhaoyang Shi , Krishnakumar Balasubramanian , Wolfgang Polonik

We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…

Statistics Theory · Mathematics 2022-07-04 Teppei Ogihara

We study a non linear regression model with functional data as inputs and scalar response. We propose a pointwise estimate of the regression function that maps a Hilbert space onto the real line by a local linear method. We provide the…

Statistics Theory · Mathematics 2013-02-20 Alain Berlinet , Abdallah Elamine , André Mas

We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the…

Methodology · Statistics 2021-01-13 Mia Hubert , Peter J. Rousseeuw , Pieter Segaert

Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…

Statistics Theory · Mathematics 2025-02-13 Steven Golovkine , Nicolas Klutchnikoff , Valentin Patilea

This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…

Numerical Analysis · Mathematics 2024-05-13 David Levin

We study the problem of finding the one-dimensional structure in a given data set. In other words we consider ways to approximate a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of…

Analysis of PDEs · Mathematics 2016-08-31 Slav Kirov , Dejan Slepčev

The use of principal component methods to analyze functional data is appropriate in a wide range of different settings. In studies of ``functional data analysis,'' it has often been assumed that a sample of random functions is observed…

Statistics Theory · Mathematics 2016-08-16 Peter Hall , Hans-Georg Müller , Jane-Ling Wang

We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive…

Statistics Theory · Mathematics 2016-08-16 Frédéric Ferraty , André Mas , Philippe Vieu

In statistical physics and information theory, although the exponent of the partition function is often of our primary interest, there are cases where one needs more detailed information. In this paper, we present a general framework to…

Information Theory · Computer Science 2012-02-06 Ryuhei Mori , Toshiyuki Tanaka

Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems.…

Optimization and Control · Mathematics 2016-12-15 Patrick L. Combettes , Christian L. Müller

Most approximation methods in high dimensions exploit smoothness of the function being approximated. These methods provide poor convergence results for non-smooth functions with kinks. For example, such kinks can arise in the uncertainty…

Numerical Analysis · Mathematics 2019-02-19 Barbara Fuchs , Jochen Garcke

Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…

Methodology · Statistics 2024-03-11 Cory W. Natoli , Edward D. White , Beau A. Nunnally , Alex J. Gutman , Raymond R. Hill

We propose a new approach that combines multiple non-parametric likelihood-type components to build a data-driven approximation of the true likelihood function. Our approach is built on empirical likelihood, a non-parametric approximation…

Methodology · Statistics 2017-12-15 Adam Jaeger , Nicole Lazar

For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…

Statistics Theory · Mathematics 2015-09-10 János Marcell Benke , Gyula Pap

We construct an asymptotic approximation to the solution of a transmission problem for a body containing a region occupied by many small inclusions. The cluster of inclusions is characterised by two small parameters that determine the…

Analysis of PDEs · Mathematics 2016-07-22 Michael Nieves