相关论文: A note on MLE of covariance matrix

This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…

We show that the maximum likelihood estimator (MLE) is an effective tool for mitigating non-flow effects in flow analysis. To this end, one constructs two toy models that simulate non-flow contributions corresponding to particle decay and…

The Stein paradox has played an influential role in the field of high dimensional statistics. This result warns that the sample mean, classically regarded as the "usual estimator", may be suboptimal in high dimensions. The development of…

Minimax detection of Gaussian stochastic sequences (signals) with unknown covariance matrices is studied. For a fixed false alarm probability (1-st kind error probability), the performance of the minimax detection is being characterized by…

Linear models have found widespread use in statistical investigations. For every linear model there exists a matrix representation for which the ReML (Restricted Maximum Likelihood) can be constructed from the elements of the corresponding…

Providing theoretical guarantees for parameter estimation in exponential random graph models is a largely open problem. While maximum likelihood estimation has theoretical guarantees in principle, verifying the assumptions for these…

We show that in a common high-dimensional covariance model, the choice of loss function has a profound effect on optimal estimation. In an asymptotic framework based on the Spiked Covariance model and use of orthogonally invariant…

Graphical models are a framework for representing and exploiting prior conditional independence structures within distributions using graphs. In the Gaussian case, these models are directly related to the sparsity of the inverse covariance…

Maximum Likelihood Estimators (MLE) has many good properties. For example, the asymptotic variance of MLE solution attains equality of the asymptotic Cram{\'e}r-Rao lower bound (efficiency bound), which is the minimum possible variance for…

While the asymptotic normality of the maximum likelihood estimator under regularity conditions is long established, this paper derives explicit bounds for the bounded Wasserstein distance between the distribution of the maximum likelihood…

Factor models are widely applied to the analysis of multivariate data across disparate fields of research. However, modern scientific data are often incomplete, and estimating a factor model from partially observed data can be very…

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

Feature alignment methods are used in many scientific disciplines for data pooling, annotation, and comparison. As an instance of a permutation learning problem, feature alignment presents significant statistical and computational…

This paper deals with multivariate Gaussian models for which the covariance matrix is a Kronecker product of two matrices. We consider maximum likelihood estimation of the model parameters, in particular of the covariance matrix. There is…

In various applied areas such as reliability engineering, molecular biology, finance, etc., the measure of uncertainty of a probability distribution plays an important role. In the present work, we consider the estimation of a function of…

The inherent bias pathology of the maximum likelihood (ML) estimation method is confirmed for models with unknown parameters $\theta$ and $\psi$ when MLE $\hat \psi$ is function of MLE $\hat \theta.$ To reduce $\hat \psi$'s bias the…

Loss tomography has received considerable attention in recent years and a number of estimators based on maximum likelihood (ML) or Bayesian principles have been proposed. Almost all of the estimators are devoted to the tree topology despite…

This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension reduction strategy by selecting the pattern…

Our investigation concerns the estimation of predictive densities and a study of efficiency as measured by the frequentist risk of such predictive densities with integrated $L_2$ and $L_1$ losses. Our findings relate to a $p-$variate…

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…