Related papers: Eigenvalue Distribution of Empirical Correlation M…
We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that…
A large i.i.d. random matrix with deterministic low-rank perturbation has been extensively studied, particularly in the aspects of the ESD (Empirical Spectral Distribution) and the outliers of eigenvalues. In this work, we investigate the…
Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform $[-1,1]$ deviates as pairwise correlations…
We study the eigenvalue of the Wishart matrix, which is created from a time series with temporal correlation. When there is no correlation, the eigenvalue distribution of the Wishart matrix is known as the Marchenko-Pastur distribution…
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 is concerned with the asymptotic empirical eigenvalue distribution of a non linear random matrix ensemble. More precisely we consider $M= \frac{1}{m} YY^*$ with $Y=f(WX)$ where $W$ and $X$ are random rectangular matrices with…
We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…
We propose a group model for correlations in stock markets. In the group model the markets are composed of several groups, within which the stock price fluctuations are correlated. The spectral properties of empirical correlation matrices…
We study distributions of eigenvalue curvatures for a block diagonal random matrix perturbed by a full random matrix. The most natural physical realization of this model is a quantum chaotic system with some inherent symmetry, such that its…
Modern evolvements of the technologies have been leading to a profound influence on the financial market. The introduction of constituents like Exchange-Traded Funds, and the wide-use of advanced technologies such as algorithmic trading,…
An expanded family of mixtures of multivariate power exponential distributions is introduced. While fitting heavy-tails and skewness has received much attention in the model-based clustering literature recently, we investigate the use of a…
The financial market and turbulence have been broadly compared on account of the same quantitative methods and several common stylized facts they shared. In this paper, the She-Leveque (SL) hierarchy, proposed to explain the anomalous…
We study the eigenvalue distributions for sums of independent rank-one $k$-fold tensor products of large $n$-dimensional vectors. Previous results in the literature assume that $k=o(n)$ and show that the eigenvalue distributions converge to…
We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…
This paper describes a model for power distribution network, which is hten utilized for eigenvalue behavior distribution analysis. We utilized the compensation theory to model the event that occurs in the network and derived the relation…
We propose a working strategy to describe the eigenvalue statistics of random spin systems along the whole phase diagram with thermal to many-body localization (MBL) transition. Our strategy relies on two random matrix (RM) models with…
Analytical understanding of how low-dimensional latent features reveal themselves in large-dimensional data is still lacking. We study this by defining a linear latent feature model with additive noise constructed from probabilistic…
Detailed study of the financial empirical correlation matrix of the 30 companies comprised by DAX within the period of the last 11 years, using the time-window of 30 trading days, is presented. This allows to clearly identify a nontrivial…
This work introduces a self and mutually exciting point process that embeds flexible residuals and intensity with discretely Markovian dynamics. By allowing the integration of diverse residual distributions, this model serves as an…
This paper investigates limiting properties of eigenvalues of multivariate sample spatial-sign covariance matrices when both the number of variables and the sample size grow to infinity. The underlying p-variate populations are general…