scholarly journals Inferences on a Normal Covariance Matrix and Generalized Variance with Monotone Missing Data

2001 ◽  
Vol 78 (1) ◽  
pp. 62-82 ◽  
Author(s):  
Jian Hao ◽  
K. Krishnamoorthy
Keyword(s):  
Missing Data ◽  
Covariance Matrix ◽  
Generalized Variance

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.

Estimation of the covariance matrix with two-step monotone missing data

2013 ◽  
Vol 45 (7) ◽  
pp. 1910-1922 ◽  
Author(s):  
Masashi Hyodo ◽  
Nobumichi Shutoh ◽  
Takashi Seo ◽  
Tatjana Pavlenko
Keyword(s):  
Missing Data ◽  
Covariance Matrix

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.

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