Related papers: Properties of Design-Based Functional Principal Co…
Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…
We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique…
Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…
Factor models have been widely used in economics and finance. However, the heavy-tailed nature of macroeconomic and financial data is often neglected in the existing literature. To address this issue and achieve robustness, we propose an…
In many longitudinal studies, a large number of variables are measured repeatedly over time, with substantial missing data. Existing methods, such as probabilistic principal component analysis (PPCA), are ill-equipped to handle such…
Principal component analysis (PCA) is a most frequently used statistical tool in almost all branches of data science. However, like many other statistical tools, there is sometimes the risk of misuse or even abuse. In this paper, we…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…
We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
We analyse the properties of the Principal Fitted Components (PFC) algorithm proposed by Cook. We derive theoretical properties of the resulting estimators, including sufficient conditions under which they are $\sqrt{n}$-consistent, and…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
This paper investigates the intrinsic group structures within the framework of large-dimensional approximate factor models, which portrays homogeneous effects of the common factors on the individuals that fall into the same group. To this…
Sparse functional data arise when measurements are observed infrequently and at irregular time points for each subject, often in the presence of measurement error. These characteristics introduce additional challenges for functional…