Covariance matrix estimation plays a significant role in both the theory and practice of portfolio analysis risk management. This paper deals with available data prior to developing factor model enhance covariance estimation. Our work has two main outcomes. First, for general linear unknown parameters, class best empirical Bayes estimators is established through kinds architectures improve accu...

Multivariate failure time data arise frequently in survival analysis. A commonly used technique is the working independence estimator for marginal hazard models. Two natural questions are how to improve the efficiency of the working independence estimator and how to identify the situations under which such an estimator has high statistical efficiency. In this paper, three weighted estimators ar...

Recently Martins-Filho and Yao (J Multivar Anal 100:309–333, 2009) have proposed a two-step estimator of nonparametric regression function with parametric error covariance and demonstrate that it is more efficient than the usual LLE. In the present paper we demonstrate that MY’s estimator can be further improved. First, we extend MY’s estimator to the multivariate case, and also establish the a...

Abstract We explore why many recently proposed robust estimation problems are efficiently solvable, even though the underlying optimization non-convex. study loss landscape of these problems, and identify existence ’generalized quasi-gradients’. Whenever quasi-gradients exist, a large family no-regret algorithms guaranteed to approximate global minimum; this includes commonly used filtering alg...

The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the ‘spectral estimator’) for the new class of ‘generalized elliptical distributions’ is presented. It is shown that the spectral estimator corresponds to an M-estimator proposed by Tyler (1983) in the context of elliptical distributions. Both the generalizati...

Estimation of high-dimensional covariance matrices is known to be a difficult problem, has many applications, and is of current interest to the larger statistics community. In many applications including so-called the “large p small n” setting, the estimate of the covariance matrix is required to be not only invertible, but also well-conditioned. Although many regularization schemes attempt to ...

The presence of multicollinearity in regression data is no exception in real life examples. Instead of applying ordinary regression methods, biased regression techniques such as Principal Component Regression and Ridge Regression have been developed to cope with such data sets. In this paper we consider Partial Least Squares (PLS) regression by means of the SIMPLS algorithm. Because the SIMPLS ...

This paper applies a method known in the engineering literature as Effective Independence Distribution (EID) to an approximation of the minimum volume ellipsoid, a high breakdown robust estimator of multivariate location and scale. The calculation of the minimum volume ellipsoid is an extremely computationally intensive task. Previous methods for approximating the MVE have focused on bootstrap-...

This paper considers state estimation for dynamic systems in the case of nonwhite, mutually correlated noise processes. Here, the problem is complicated by the fact, that only the individual covariances are known; cross covariances between random variables obtained by taking individual noise processes at different time steps and between different noise processes are completely unknown. New esti...