相关论文: Applying Free Random Variables to Random Matrix An…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
We show how random matrix theory can be applied to develop new algorithms to extract dynamic factors from macroeconomic time series. In particular, we consider a limit where the number of random variables N and the number of consecutive…
In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…
Models which include domain constraints occur in myriad contexts such as econometrics, genomics, and environmetrics, though simulating from constrained distributions can be computationally expensive. In particular, repeated sampling from…
A Bayesian procedure is developed for multivariate stochastic volatility, using state space models. An autoregressive model for the log-returns is employed. We generalize the inverted Wishart distribution to allow for different correlation…
The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However,…
Recent work has explored data thinning, a generalization of sample splitting that involves decomposing a (possibly matrix-valued) random variable into independent components. In the special case of a $n \times p$ random matrix with…
We study the distribution of singular values of product of random matrices pertinent to the analysis of deep neural networks. The matrices resemble the product of the sample covariance matrices, however, an important difference is that the…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
The accurate prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the variances. Moreover, function…
This study introduces a new analytical framework for quantifying multivariate risk measures. Using the Wishart process, which is a stochastic process with values in the space of positive definite matrices, we derive several conditional tail…
We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse…
Modeling correlation (and covariance) matrices can be challenging due to the positive-definiteness constraint and potential high-dimensionality. Our approach is to decompose the covariance matrix into the correlation and variance matrices…
In this paper, we introduce two new matrix stochastic processes: fractional Wishart processes and $\varepsilon$-fractional Wishart processes with integer indices which are based on the fractional Brownian motions and then extend…
The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many…
The integration of physical relationships into stochastic models is of major interest e.g. in data assimilation. Here, a multivariate Gaussian random field formulation is introduced, which represents the differential relations of the…
We consider random matrices that have invariance properties under the action of unitary groups (either a left-right invariance, or a conjugacy invariance), and we give formulas for moments in terms of functions of eigenvalues. Our main tool…
In multivariate time series, the estimation of the covariance matrix of the observation innovations plays an important role in forecasting as it enables the computation of the standardized forecast error vectors as well as it enables the…
Correlations between asset returns are important in many financial applications. In recent years, multivariate volatility models have been used to describe the time-varying feature of the correlations. However, the curse of dimensionality…
We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced…