Related papers: On a spiked model for large volatility matrix esti…
In this paper, we study limiting laws and consistent estimation criteria for the extreme eigenvalues in a spiked covariance model of dimension $p$. Firstly, for fixed $p$, we propose a generalized estimation criterion that can consistently…
How do statistical dependencies in measurement noise influence high-dimensional inference? To answer this, we study the paradigmatic spiked matrix model of principal components analysis (PCA), where a rank-one matrix is corrupted by…
A generalized spiked Fisher matrix is considered in this paper. We establish a criterion for the description of the support of the limiting spectral distribution of high-dimensional generalized Fisher matrix and study the almost sure limits…
We study symmetric spiked matrix models with respect to a general class of noise distributions. Given a rank-1 deformation of a random noise matrix, whose entries are independently distributed with zero mean and unit variance, the goal is…
This paper studies the asymptotic spectral properties of the sample covariance matrix for high dimensional compositional data, including the limiting spectral distribution, the limit of extreme eigenvalues, and the central limit theorem for…
Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of selected portfolios among a vast pool of assets, as demonstrated in Fan et al (2008). The required high-dimensional…
Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods…
Variational autoencoders (VAEs) are influential generative models with rich representation capabilities from the deep neural network architecture and Bayesian method. However, VAE models have a weakness that assign a higher likelihood to…
We introduce Group Spike-and-slab Variational Bayes (GSVB), a scalable method for group sparse regression. A fast co-ordinate ascent variational inference (CAVI) algorithm is developed for several common model families including Gaussian,…
We study the estimation of the high-dimensional covariance matrix andits eigenvalues under dynamic volatility models. Data under such modelshave nonlinear dependency both cross-sectionally and temporally. We firstinvestigate the empirical…
Conditional Value-at-Risk (CVaR) is a central tail-risk measure in stochastic structural mechanics, yet its accurate evaluation under high-dimensional, spatially correlated material uncertainty remains computationally prohibitive for…
We consider an Information-Plus-Noise type matrix where the Information matrix is a spiked matrix. When some eigenvalues of the random matrix separate from the bulk, we study how the corresponding eigenvectors project onto those of the…
In the realm of high-dimensional data analysis, the estimation of covariance matrices is a fundamental task, and this holds true for interval-valued data as well. However, there is no unified definition for the covariance matrix of…
In random matrix theory, the spectral distribution of the covariance matrix has been well studied under the large dimensional asymptotic regime when the dimensionality and the sample size tend to infinity at the same rate. However, most…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the…
Emergence of noise induced regularity or Coherence Resonance in nonlinear excitable systems is well known. We explain theoretically why the normalized variance ($V_{N}$) of inter spike time intervals, which is a measure of regularity in…
In many machine learning and data related applications, it is required to have the knowledge of approximate ranks of large data matrices at hand. In this paper, we present two computationally inexpensive techniques to estimate the…
The development of the manufacturing systems has made it increasingly necessary to monitor the data generated by multiple interconnected subsystems with rapid incoming of samples. Based on incremental Singular Value Decomposition (ISVD), we…
In this paper we study random matrix models where the matrices in question contain infinitely many spikes. Recent work has characterized the possible outliers in the spectrum of large deformed unitarily invariant models when the number of…