Related papers: Principal components analysis of regularly varying…
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…
Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has…
Principal component analysis continues to be a powerful tool in dimension reduction of high dimensional data. We assume a variance-diverging model and use the high-dimension, low-sample-size asymptotics to show that even though the…
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…
We consider functional data which are measured on a discrete set of observation points. Often such data are measured with additional noise. We explore in this paper the factor structure underlying this type of data. We show that the latent…
This article establishes a new and comprehensive estimation and inference theory for principal component analysis (PCA) under the weak factor model that allow for cross-sectional dependent idiosyncratic components under the nearly minimal…
We develop a robust Bayesian functional principal component analysis (RB-FPCA) method that utilizes the skew elliptical class of distributions to model functional data, which are observed over a continuous domain. This approach effectively…
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…
Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…
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 derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…
Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in…
We develop asymptotic theory for principal component analysis (PCA) of a high-dimensional factor model in which the working dimension $R$ is fixed and only required to satisfy $R \ge r$, where $r$ is the true number of factors. Building on…
In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to…
In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elements of a general metric space that lacks local or global…
A system with many degrees of freedom can be characterized by a covariance matrix; principal components analysis (PCA) focuses on the eigenvalues of this matrix, hoping to find a lower dimensional description. But when the spectrum is…
This article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude…
This article deals with the asymptotic behavior of fourth order differential equation where the coefficients are perturbations of linear constant coefficient equation. We introduce a change of variable and deduce that the new variable…