Related papers: Measure Selection for Functional Linear Model

Statistical depth, a commonly used analytic tool in non-parametric statistics, has been extensively studied for multivariate and functional observations over the past few decades. Although various forms of depth were introduced, they are…

A new type of quadrature is developed. The Gaussian quadrature, for a given measure, finds optimal values of a function's argument (nodes) and the corresponding weights. In contrast, the Lebesgue quadrature developed in this paper, finds…

The existing Fr\'echet regression is actually defined within a linear framework, since the weight function in the Fr\'echet objective function is linearly defined, and the resulting Fr\'echet regression function is identified to be a linear…

Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…

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…

In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…

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 an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…

Analyzing the covariance structure of data is a fundamental task of statistics. While this task is simple for low-dimensional observations, it becomes challenging for more intricate objects, such as multivariate functions. Here, the…

Functional principal component analysis is one of the most commonly employed approaches in functional and longitudinal data analysis and we extend it to analyze functional/longitudinal data observed on a general $d$-dimensional domain. The…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data…

The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

The main purpose of this paper is to investigate the behaviour of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed…

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…

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…

Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…

Functional logistic regression is a popular model to capture a linear relationship between binary response and functional predictor variables. However, many methods used for parameter estimation in functional logistic regression are…

Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…