Search results for "Scatter matrix"
showing 4 items of 14 documents
Tests of multinormality based on location vectors and scatter matrices
2007
Classical univariate measures of asymmetry such as Pearson’s (mean-median)/σ or (mean-mode)/σ often measure the standardized distance between two separate location parameters and have been widely used in assessing univariate normality. Similarly, measures of univariate kurtosis are often just ratios of two scale measures. The classical standardized fourth moment and the ratio of the mean deviation to the standard deviation serve as examples. In this paper we consider tests of multinormality which are based on the Mahalanobis distance between two multivariate location vector estimates or on the (matrix) distance between two scatter matrix estimates, respectively. Asymptotic theory is develop…
Affine equivariant multivariate rank methods
2003
The classical multivariate statistical methods (MANOVA, principal component analysis, multivariate multiple regression, canonical correlation, factor analysis, etc.) assume that the data come from a multivariate normal distribution and the derivations are based on the sample covariance matrix. The conventional sample covariance matrix and consequently the standard multivariate techniques based on it are, however, highly sensitive to outlying observations. In the paper a new, more robust and highly efficient, approach based on an affine equivariant rank covariance matrix is proposed and outlined. Affine equivariant multivariate rank concept is based on the multivariate Oja (Statist. Probab. …
Tests and estimates of shape based on spatial signs and ranks
2009
Nonparametric procedures for testing and estimation of the shape matrix in the case of multivariate elliptic distribution are considered. Testing for sphericity is an important special case. The tests and estimates are based on the spatial sign and rank covariance matrices. The estimates based on the spatial sign covariance matrix and symmetrized spatial sign covariance matrix are Tyler's [A distribution-free M-estimator of multivariate scatter, Ann. Statist. 15 (1987), pp. 234–251] shape matrix and and Dümbgen's [On Tyler's M-functional of scatter in high dimension, Ann. Inst. Statist. Math. 50 (1998), pp. 471–491] shape matrix, respectively. The test based on the spatial sign covariance m…
The Role of Covariance Matrix Forecasting Method in the Performance of Minimum-Variance Portfolios
2014
Providing a more accurate covariance matrix forecast can substantially improve the performance of optimized portfolios. Using out-of-sample tests, in this paper, we evaluate alternative covariance matrix forecasting methods by looking at (1) their forecast accuracy, (2) their ability to track the volatility of the minimum-variance portfolio, and (3) their ability to keep the volatility of the minimum-variance portfolio at a target level. We find large differences between the methods. Our results suggest that shrinkage of the sample covariance matrix improves neither the forecast accuracy nor the performance of minimum-variance portfolios. In contrast, switching from the sample covariance ma…