Many different robust estimation approaches for the covariance or shape matrix of multivariate data have been established until today. Tyler's M-estimator has been recognized as the 'most robust' M-estimator for the shape matrix of elliptically symmetric distributed data. Tyler's Mestimators for...

Three main issues are explored in this thesis—volatility measurement, volatility spillover and large-dimension covariance matrices. For the first question of volatility measurement, this thesis compares two newly-proposed, high-frequency volatility measurement models, namely realized...

This paper presents a new random weighting estimation method for dynamic navigation positioning. This method adopts the concept of random weighting estimation to estimate the covariance matrices of system state noises and observation noises for controlling the disturbances of singular...

Recently, the world of cryptocurrencies has experienced an undoubted increase in interest. Since the first cryptocurrency appeared in 2009 in the aftermath of the Great Recession, the popularity of digital currencies has, year by year, risen continuously. As of February 2021, there are more than...

It is well known that in a vector autoregressive (VAR) model Granger non-causality is characterized by a set of restrictions on the VAR coefficients. This characterization has been derived under the assumption of non-singularity of the covariance matrix of the innovations. This note shows that...

In this paper we analyze a multivariate non-stationary regression model empirically. With the knowledge about unconditional heteroscedasticty of financial returns, based on univariate studies and a congruent paradigm in Gürtler and Rauh (2009), we test for a time-varying covariance structure...

The problem for choice of an optimum investment portfolio is considered. The square-law form of risk is presented as two-multiple convolution of covariant tensor of the covariance matrix and contravariant vector of weights. By means of reduction of covariance matrix to the diagonal form, the...

Let X1; : : : ;Xn be i.i.d. sample in Rp with zero mean and the covariance matrix . The classic principal component analysis esti- mates the projector P J onto the direct sum of some eigenspaces of by its empirical counterpart bPJ . Recent papers [20, 23] investigate the asymptotic distribution...