Abstract The covariance matrix is an important element of many asset allocation strategies. widely used sample estimator unstable especially when the number time observations small and assets large or high-dimensional data involved in computation. In this study, we focus on most estimators that are applied a group Markowitz-type strategies also recently introduced method based hierarchical tree...

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to ∞ as the sample size n increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the covariance matrix. The factors are observa...

Abstruct-The determination of the state-space equations of a time-varying finite-dimensional linear system with a prescribed output covariance matrix is considered when the system is excited by Gaussian whitenoise inputs. It is shown that a symmetric state covariance matrix provides the key link between the statespace equations of a system and the system output covariance matrix. Furthermore, s...

Question: Is the pattern of phenotypic divergence among populations influenced by constraint in the form of the genetic covariances among characters? Background: Quantitative genetic theory predicts that when evolutionary lineages diverge simultaneously by genetic drift, the pattern of among-population divergence will parallel the pattern of within-population genetic variation and covariation. ...

We consider here the problem of estimating p×p scale matrix Σ a multivariate linear regression model when distribution observed belongs to large class elliptically symmetric distributions. Any estimator Σˆ is assessed through data-based loss tr(S+Σ(Σ−1Σˆ−Ip)2) where S sample covariance and S+ its Moore–Penrose inverse.

Markowitz’s portfolio selection problem chooses weights for stocks in a portfolio based on a covariance matrix of stock returns. Our study proposes to reduce noise in the estimated covariance matrix using a Tikhonov filter function. In addition, we propose a new strategy to resolve the rank deficiency of the covariance matrix, and a method to choose a Tikhonov parameter which determines a filte...