• Journal of the Korean Statistical Society
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• v.33 no.2
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• pp.233-244
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• 2004

The influence of observations is investigated in fitting proportional covariance matrices model. Local influence measures are obtained when all parameters or subsets of the parameters are of interest. We will also derive the local influence measure for investigating the influence of observations in testing the proportionality of covariance matrices. A numerical example is given for illustration.

• Communications for Statistical Applications and Methods
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• v.7 no.1
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• pp.55-64
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• 2000

We propose a criterion for testing homogeneity of matrix intraclass covariance matrices of K multivariate normal populations, It is based on a variable transformation intended to propose and develop a likelihood ratio criterion that makes use of properties of eigen structures of the matrix intraclass covariance matrices. The criterion then leads to a simple test that uses an asymptotic distribution obtained from Box's (1949) theorem for the general asymptotic expansion of random variables.

• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.929-938
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• 1999

We propose a criterion for testing homogeneity of diagonal covariance matrices of K multivariate normal populations. It is based on a factorization of usual likelihood ratio intended to propose and develop a criterion that makes use of properties of structures of the diagonal convariance matrices. The criterion then leads to a simple test as well as to an accurate asymptotic distribution of the test statistic via general result by Box (1949).

• Journal of the Korea Society of Computer and Information
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• v.15 no.5
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• pp.13-21
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• 2010

The Optimal results of Kalman Filtering on the Inverted Pendulum System requires an effective factor such as the noise covariance matrix Q, the measurement noise covariance matrix R and the initial error covariance matrix $P_0$. We present a special case where the optimality of the filter is not destroyed and not sensitive to scaling of these covariance matrix because these factors are unknown or are known only approximately in the practical situation. Moreover, the error covariance matrices issued by this method predict errors in the state estimate consistent with the scaled covariance matrices and not the issued state estimates. Various results using the scalar gain $\delta$ are derived to described the relations among the three covariance matrices, Kalman Gain and the error covariance matrices. This paper is described as follows: Section III a brief overview of the Inverted Pendulum system. Section IV deals with the mathematical dynamic model of the system used for the computer simulation. Section V presents a various simulation results using the scalar gain.

• Journal of the Korean Statistical Society
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• v.20 no.2
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• pp.191-201
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• 1991

Given a set of data pxN$_{i}$, matrices X$_{i}$ observed from p-variate normal populations $\prod$$_{i}$~N($\mu$$_{I}$, $\Sigma$$_{i}$) for i=1, …, K, the test for equality form of the covariance matrices is to choose a hypothetical model which best explains the homogeneity/heterogeneity structure across the covariance matrices among the hypothesized class of models. This paper describes a test procedure for selecting the best model. The procedure is based on a synthesis of Bayesian and a cross-validation or sample reuse methodology that makes use of a one-at-a-time schema of observational omissions. Advantages of the test are argued on two grounds, and illustrative examples and simulation results are given.are given.

• Journal of information and communication convergence engineering
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• v.9 no.2
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• pp.207-211
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• 2011

This paper presents a method for facial feature representation and recognition from the Covariance Matrices of the Gabor-filtered images. Gabor filters are a very powerful tool for processing images that respond to different local orientations and wave numbers around points of interest, especially on the local features on the face. This is a very unique attribute needed to extract special features around the facial components like eyebrows, eyes, mouth and nose. The Covariance matrices computed on Gabor filtered faces are adopted as the feature representation for face recognition. Geodesic distance measure is used as a matching measure and is preferred for its global consistency over other methods. Geodesic measure takes into consideration the position of the data points in addition to the geometric structure of given face images. The proposed method is invariant and robust under rotation, pose, or boundary distortion. Tests run on random images and also on publicly available JAFFE and FRAV3D face recognition databases provide impressively high percentage of recognition.

• Communications for Statistical Applications and Methods
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• v.22 no.4
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• pp.321-331
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• 2015

The K-means clustering algorithm is a popular and widely used method for clustering. For covariance matrices, we consider a geodesic clustering algorithm based on the K-means clustering framework in consideration of symmetric positive definite matrices as a Riemannian (non-Euclidean) manifold. This paper considers a geodesic clustering algorithm for data consisting of symmetric positive definite (SPD) matrices, utilizing the Riemannian geometric structure for SPD matrices and the idea of a K-means clustering algorithm. A K-means clustering algorithm is divided into two main steps for which we need a dissimilarity measure between two matrix data points and a way of computing centroids for observations in clusters. In order to use the Riemannian structure, we adopt the geodesic distance and the intrinsic mean for symmetric positive definite matrices. We demonstrate our proposed method through simulations as well as application to real financial data.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.1
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• pp.717-724
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• 2016

This paper proposes a change detection method based on the covariance matrices of color and edge gradient in a color video. The YCbCr color format was used instead of RGB. The color covariance matrix was calculated from the CbCr-channels and the edge gradient covariance matrix was calculated from the Y-channels. The covariance matrices were effectively calculated at each pixel by calculating the sum, squared sum, and sum of two values' multiplication of a rectangle area using the integral images from a background image. The background image was updated by a running the average between the background image and a current frame. The change areas in a current frame image against the background were detected using the Mahalanobis distance, which is a measure of the statistical distance using covariance matrices. The experimental results of an expressway color video showed that the proposed approach can effectively detect change regions for color and edge gradients against the background.

• Journal of the Korean Statistical Society
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• v.27 no.1
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• pp.11-23
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• 1998

A Bayes criterion for testing the equality of covariance matrices of two multivariate normal distributions is proposed and studied. Development of the criterion invloves calculation of Bayes factor using the imaginary sample method introduced by Spiegelhalter and Smith (1982). The criterion is designed to develop a Bayesian test criterion, so that it provides an alternative test criterion to those based upon asymptotic sampling theory (such as Box's M test criterion). For the constructed criterion, numerical studies demonstrate routine application and give comparisons with the traditional test criteria.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.463-472
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• 2005

In this paper, the problem of estimating a p-variate (p $\ge$4) normal mean vector is considered in decision-theoretic set up. Using a simple property of the noncentral chi-square distribution, a sequence of estimators dominating the Lindley type estimator with the cases of unknown covariance matrices has been produced and each improved estimator is better than previous one.