Related papers: Basis Expansions for Functional Snippets
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
We present and study semi-parametric estimators for the mean of functional outcomes in situations where some of these outcomes are missing and covariate information is available on all units. Assuming that the missingness mechanism depends…
We present new estimators for the statistical analysis of the dependence of the mean gap time length between consecutive recurrent events, on a set of explanatory random variables and in the presence of right censoring. The dependence is…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
A new framework is developed to intrinsically analyze sparsely observed Riemannian functional data. It features four innovative components: a frame-independent covariance function, a smooth vector bundle termed covariance vector bundle, a…
Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…
We place ourselves in a functional regression setting and propose a novel methodology for regressing a real output on vector-valued functional covariates. This methodology is based on the notion of signature, which is a representation of a…
Functional data, with basic observational units being functions (e.g., curves, surfaces) varying over a continuum, are frequently encountered in various applications. While many statistical tools have been developed for functional data…
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…
This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural…
The problem of estimating the mean of random functions based on discretely sampled data arises naturally in functional data analysis. In this paper, we study optimal estimation of the mean function under both common and independent designs.…
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected…
Semiparametric models are often considered for analyzing longitudinal data for a good balance between flexibility and parsimony. In this paper, we study a class of marginal partially linear quantile models with possibly varying…
Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the…
This paper examines robust functional data analysis for discretely observed data, where the underlying process encompasses various distributions, such as heavy tail, skewness, or contaminations. We propose a unified robust concept of…
This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…
We propose a summary measure defined as the expected value of a random variable over disjoint subsets of its support that are specified by a given grid of proportions, and consider its use in a regression modeling framework. The obtained…
Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods…
Functional data analysis tools, such as function-on-function regression models, have received considerable attention in various scientific fields because of their observed high-dimensional and complex data structures. Several statistical…