• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.807-814
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• 2012

We know that the exponentially weighted moving average (EWMA) control charts are sensitive to detecting relatively small shifts. Multivariate EWMA control charts are considered for monitoring of variance-covariance matrix when the distribution of process variables is multivariate normal. The performances of the proposed EWMA control charts are evaluated in term of average run length (ARL). The performance is investigated in three types of shifts in the variance-covariance matrix, that is, the variances, covariances, and variances and covariances are changed respectively. Numerical results show that all multivariate EWMA control charts considered in this paper are effective in detecting several kinds of shifts in the variance-covariance matrix.

• Journal of the Korean Data and Information Science Society
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• v.4
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• pp.31-44
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• 1993

Multivariate exponentially weighted moving average (EWMA) control charts for monitoring the variance-covariance matrix are investigated. A variable sampling interval (VSI) feature is considered in these charts. Multivariate EWMA control charts for monitoring the variance-covariance matrix are compared on the basis of their average time to signal (ATS) performances. The numerical results show that multivariate VSI EWMA control charts are more efficient than corrsponding multivariate fixed sampling interval (FSI) EWMA control charts.

• The Korean Journal of Applied Statistics
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• v.35 no.4
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• pp.569-577
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• 2022

Simulation studies are often conducted when it is difficult to compare the performance of nonparametric estimators theoretically. Kim and Kim (2021) showed that more systematic and accurate comparisons can be made if you analyze the simulation results using a regression model,. This study is a complementary study on Kim and Kim (2021). In the variance-covariance matrix for the error term of the regression model, only heteroscedasticity was considered and covariance was ignored in the previous study. When covariance is considered together with the heteroscedasticity, the variance-covariance matrix becomes a block diagonal matrix. In this study, a method of estimating and using the block diagonal variance-covariance matrix for the analysis was presented. This allows you to find more pairs of estimators with significant performance differences while ensuring the nominal confidence level.

• Journal of the Korean Institute of Telematics and Electronics
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• v.21 no.4
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• pp.7-12
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• 1984

A composite - discrete courier transform (CDFT) is developed, which can diagonalize a real symmetric circulant matrix. In general the circulant matrices can be diagonalized by the discrete Fourier transform (DFT). With the analysis of the variance distributions of the DFT and CDFT for the general symmetric covariance matrix of real signals, the DFT and CDFT are compared with respect to the rate distortion performance measure. The results show that the CDFT is more efficient than the DFT in bit rate reduction. In addition, for a particular 64$\times$64 points covariance matrix (f(q)=(0.95)q), the amount of the relative average bit rate reduction for the CDFT with respect to the DFT is obtained by 0.0095 bit with a numerical calculation.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.8
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• pp.78-86
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• 2002

The GPS carrier phase measurements include integer ambiguities and the decorrelation process on the variance-covariance matrix is necessary to resolve these ambiguities efficiently. In this paper, we introduce a new method for the ambiguity de-correlation. This method divides the variance-covariance matrix into 4 smaller blocks and decorrelates them separately. The decorrelation of each block is processed recursively so that the result of the previous step is not affected by the next step. A couple of numerical examples chosen in random show that this method is better than or comparable to other decorrelation methods, however, the speed of this is relatively faster because the computations are performed on small blocks of the variance-covariance matrix.

• The Korean Journal of Applied Statistics
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• v.5 no.2
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• pp.283-292
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• 1992

Updating algorithms are studied for the basic statistics (mean, variance). For a linear model, a recursive formulae for least squares estimators of regression coefficients, residual sum of squares and variance-covariance matrix are also studied. Hotelling's $T^2$ statistics can be calculated recursively using the recursive formulae of mean vector and variance-covariance matrix without computing the sample variance-covariance matrix at each stage.

• Journal of Korean Society for Quality Management
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• v.22 no.1
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• pp.54-65
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• 1994

Multivariate exponentially weighted moving average (EWMA) control charts for monitoring the variance-covariance matrix are investigated. Two basic approaches, "combine-accumulate" approach and "accumulate-combine" approach, for using past sample information in the developement of multivariate EWMA control charts are considered. Multivariate EWMA control charts for monitoring the variance-covariance matrix are compared on the basis of their average run length (ARL) performances. The numerical results show that multivariate EWMA control charts based on the accumulate-combine approach are more efficient than corresponding multivariate EWMA control charts based on the combine-accumulate approach.

• Journal of the Korean Data and Information Science Society
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• v.23 no.3
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• pp.617-626
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• 2012

Multivariate Shewhart control charts are considered for the simultaneous monitoring the variance-covariance matrix when the joint distribution of process variables is multivariate normal. The performances of the multivariate Shewhart control charts based on control statistic proposed by Hotelling (1947) are evaluated in term of average run length (ARL) for 2 or 4 correlated variables, 2 or 4 samples at each sampling point. The performance is investigated in three cases, that is, the variances, covariances, and variances and covariances are changed respectively.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.4
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• pp.137-152
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• 2014

In this paper, I suggest several techniques to estimate covariance matrix and compare the performance of the global minimum variance portfolio (GMVP) in terms of out of sample mean standard deviation and return. As a result, the return differences among the GMVPs are insignificant. The mean standard deviation of the GMVP using historical covariance is sensitive to the estimation window and the number of assets in the portfolio. Among the model covariance, the GMVP using constant systematic risk ratio model or using short sale restriction shows the best performance. The performance difference between the GMVPs using historical covariance and model covariance becomes insignificant as the historical covariance is estimated with longer estimation window. Lastly, the implied volatilities from ELW prices do not lead to superior performance to the historical variance.

• The Korean Journal of Applied Statistics
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• v.33 no.3
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• pp.281-296
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• 2020

Repeated outcomes from the same subjects are referred to as longitudinal data. Analysis of the data requires different methods unlike cross-sectional data analysis. It is important to model the covariance matrix because the correlation between the repeated outcomes must be considered when estimating the effects of covariates on the mean response. However, the modeling of the covariance matrix is tricky because there are many parameters to be estimated, and the estimated covariance matrix should be positive definite. In this paper, we consider analysis of multivariate longitudinal data via two modeling methodologies for the covariance matrix for multivariate longitudinal data. Both methods describe serial correlations of multivariate longitudinal outcomes using a modified Cholesky decomposition. However, the two methods consider different decompositions to explain the correlation between simultaneous responses. The first method uses enhanced linear covariance models so that the covariance matrix satisfies a positive definiteness condition; in addition, and principal component analysis and maximization-minimization algorithm (MM algorithm) were used to estimate model parameters. The second method considers variance-correlation decomposition and hypersphere decomposition to model covariance matrix. Simulations are used to compare the performance of the two methodologies.