Estimating the covariance matrix and the generalized variance under a symmetric loss

1990 ◽  
Vol 42 (2) ◽  
pp. 331-343 ◽  
Author(s):  
Tatsuya Kubokawa ◽  
Yoshihiko Konno
Keyword(s):  
Covariance Matrix ◽  
Generalized Variance ◽  
Symmetric Loss

scholarly journals The use of principal components and univariate charts to control multivariate processes

2008 ◽  
Vol 28 (1) ◽  
pp. 173-196 ◽  
Author(s):  
Marcela A. G. Machado ◽  
Antonio F. B. Costa
Keyword(s):  
Dimensionality Reduction ◽  
Covariance Matrix ◽  
Principal Components ◽  
Control Charts ◽  
Principal Component ◽  
Multivariate Processes ◽  
Generalized Variance ◽  
Overall Performance ◽  
The Way

In this article, we evaluate the performance of the T² chart based on the principal components (PC X chart) and the simultaneous univariate control charts based on the original variables (SU charts) or based on the principal components (SUPC charts). The main reason to consider the PC chart lies on the dimensionality reduction. However, depending on the disturbance and on the way the original variables are related, the chart is very slow in signaling, except when all variables are negatively correlated and the principal component is wisely selected. Comparing the SU , the SUPC and the T² charts we conclude that the SU X charts (SUPC charts) have a better overall performance when the variables are positively (negatively) correlated. We also develop the expression to obtain the power of two S² charts designed for monitoring the covariance matrix. These joint S² charts are, in the majority of the cases, more efficient than the generalized variance chart.

A PROPOSAL FOR MULTI-ASSET GENERALIZED VARIANCE SWAPS

2019 ◽  
Vol 14 (04) ◽  
pp. 1950019
Author(s):  
SUBHOJIT BISWAS ◽  
DIGANTA MUKHERJEE
Keyword(s):  
Financial Markets ◽  
Covariance Matrix ◽  
Maximum Eigenvalue ◽  
Variance Swaps ◽  
Numerical Examples ◽  
Generalized Variance ◽  
Multiple Assets ◽  
Markov Modulated

This paper proposes swaps on two important new measures of generalized variance, namely the maximum eigenvalue and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for financial markets with Markov-modulated volatilities. We consider multiple assets in the portfolio for theoretical purpose and demonstrate our approach with numerical examples taking three stocks in the portfolio. The results obtained in this paper have important implications for the commodity sector where such swaps would be useful for hedging risk.

scholarly journals Monitoring bivariate process

2009 ◽  
Vol 29 (3) ◽  
pp. 547-562 ◽  
Author(s):  
Marcela A. G. Machado ◽  
Antonio F. B. Costa ◽  
Fernando A. E. Claro
Keyword(s):  
Covariance Matrix ◽  
Control Charts ◽  
Joint Control ◽  
Multivariate Processes ◽  
Generalized Variance ◽  
Main Drawback ◽  
The Mean ◽  
Sample Variances ◽  
Mean Vector

The T² chart and the generalized variance |S| chart are the usual tools for monitoring the mean vector and the covariance matrix of multivariate processes. The main drawback of these charts is the difficulty to obtain and to interpret the values of their monitoring statistics. In this paper, we study control charts for monitoring bivariate processes that only requires the computation of sample means (the ZMAX chart) for monitoring the mean vector, sample variances (the VMAX chart) for monitoring the covariance matrix, or both sample means and sample variances (the MCMAX chart) in the case of the joint control of the mean vector and the covariance matrix.

scholarly journals Asymptotic Comparison of Parameters Estimates of Two-parameter Weibull Distribution

2019 ◽  
Vol 67 (1) ◽  
pp. 253-263
Author(s):  
Tereza Konečná ◽  
Zuzana Hübnerová
Keyword(s):  
Weibull Distribution ◽  
Covariance Matrix ◽  
Asymptotic Efficiency ◽  
Parameter Estimates ◽  
Asymptotic Covariance Matrix ◽  
Generalized Variance ◽  
Asymptotic Covariance ◽  
Probability Plot ◽  
Efficiency Comparison ◽  
Two Parameter

The Weibull distribution is frequently applied in various fields, ranging from economy, business, biology, to engineering. This paper aims at estimating the parameters of two-parameter Weibull distribution are determined. For this purpose, the method of quantiles (three different choices of quantiles) and Weibull probability plot method is utilized. The asymptotic covariance matrix of the parameter estimates is derived for both methods. For optimal random choices of quantiles, the variance, covariance and generalized variance is computed. The main contribution of this study is the introduction of the best choice of percentiles for the method of quantiles and the joint asymptotic efficiency comparison of applied methods.

scholarly journals A New Generalized Variance Approach for Measuring Multidimensional Inequality and Poverty

2021 ◽  
Author(s):  
Ottó Hajdu
Keyword(s):  
Covariance Matrix ◽  
Composite Index ◽  
Multidimensional Poverty ◽  
Poverty Measurement ◽  
Multivariate Statistical ◽  
Generalized Variance ◽  
Multidimensional Inequality ◽  
Conventional Literature ◽  
Poverty Indicators ◽  
Special Complex

AbstractThe paper suggests a new generalized variance concept for measuring multidimensional inequality of a stratified society, based on multivariate statistical methods, where the members of society form a cloud in the oblique space of dimensions of inequality, such as income, expenditure and property. The cloud presents the multidimensional inequality capsulized in the cloud. The goal is to condense all the inequality information embodied by the cloud into a composite compact metric characterizing both the shape and the inner structure of the cloud. Contrary to the conventional literature that considers multidimensionality as a unidimensional weighted combination of the dimensions, our new composite index measures the inequality of the configuration of the points in the cloud. Our aim is twofold. First, we introduce the Inequality Covariance Matrix (ICM) assigned to the cloud, with elements measuring the correlations among dimensions. Having ICM, we propose the Generalized Variance (GV) of ICM to measure the composite Generalized Variance Inequality (GVI) level. Second, to evaluate the stratum-specific structure of the overall inequality, we suggest a new two-stage procedure. In the first stage, we divide the total GVI into between-groups and within-groups effects. Then, in the second stage the contributions of the strata to the within-groups inequality and, the contributions of the dimensions to the between-groups inequality are calculated. This GVI approach is sensitive to the correlation system, decomposable into stratum effects and, the number of dimensions is not limited. Moreover, including the log-dimensions in the analysis, GVI yields an Entropy Covariance Matrix giving a new Generalized Variance Entropy index. Finally, the GVI of censored poverty indicators means multidimensional poverty measurement. This special complex task is not yet solved in the traditional literature so far.

Multi-asset generalized variance swaps in Barndorff-Nielsen and Shephard model

2020 ◽  
Vol 07 (04) ◽  
pp. 2050051
Author(s):  
Subhojit Biswas ◽  
Diganta Mukherjee ◽  
Indranil SenGupta
Keyword(s):  
Financial Markets ◽  
Covariance Matrix ◽  
Maximum Eigenvalue ◽  
Variance Swaps ◽  
Numerical Examples ◽  
Generalized Variance ◽  
Multiple Assets

This paper proposes swaps on two important new measures of generalized variance, namely, the maximum eigenvalue and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for Barndorff-Nielsen and Shephard model used in financial markets. We consider multiple assets in the portfolio for theoretical purpose and demonstrate our approach with numerical examples taking three stocks in the portfolio. The results obtained in this paper have important implications for the commodity sector where such swaps would be useful for hedging risk.

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