We consider the composite log-determinant optimization problem, arising from the `1 regularized Gaussian maximum likelihood estimator of a sparse inverse covariance matrix, in a high-dimensional setting with a very large number of variables. Recent work has shown this estimator to have strong statistical guarantees in recovering the true structure of the sparse inverse covariance matrix, or alt...

In this article, we propose a computationally efficient approach to estimate (large) p-dimensional covariance matrices of ordered (or longitudinal) data based on an independent sample of size n. To do this, we construct the estimator based on a k-band partial autocorrelation matrix with the number of bands chosen using an exact multiple hypothesis testing procedure. This approach is considerabl...

In classifying samples by Gaussian clas-siier, the covariance matrix estimated with a small number sample set becomes unstable, which leads to degrading the classiication accuracy. In this paper , we discuss the covariance matrix estimation problem for small number samples with high dimension setting based on Kullback-Leibler Information Measure. A new covariance matrix estimator is developed, ...

An exact formula of the inverse covariance matrix of an autoregressive stochastic process is obtained using the Gohberg}Semencul explicit inverse of the Toeplitz matrix. This formula is used to build an estimator of the inverse covariance matrix of a stochastic process based on a single realization. In this paper, we show that this estimator can be conveniently applied to maximum likelihood par...

Many statistical applications require an estimate of a covariance matrix and/or its inverse. Whenthe matrix dimension is large compared to the sample size, which happens frequently, the samplecovariance matrix is known to perform poorly and may suffer from ill-conditioning. There alreadyexists an extensive literature concerning improved estimators in such situations. In the absence offurther kn...

Medical imaging datasets used in clinical studies or basic research often comprise highly variable multi-subject data. Statistically-controlled inclusion of a subject in a group study, i.e. deciding whether its images should be considered as samples from a given population or whether they should be rejected as outlier data, is a challenging issue. While the informal approaches often used do not...

The classical unbiasedness condition utilized e.g. by the best linear unbiased estimator (BLUE) is very stringent. By softening the ”global” unbiasedness condition and introducing component-wise conditional unbiasedness conditions instead, the number of constraints limiting the estimator’s performance can in many cases significantly be reduced. In this work we investigate the component-wise con...