• Journal of the Korean Data and Information Science Society
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• v.27 no.3
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• pp.815-825
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• 2016

Marginalized random effects models (MREMs) are often used to analyze longitudinal categorical data. The models permit direct estimation of marginal mean parameters and specify the serial correlation of longitudinal categorical data via the random effects. However, it is not easy to estimate the random effects covariance matrix in the MREMs because the matrix is high-dimensional and must be positive-definite. To solve these restrictions, we introduce two modeling approaches of the random effects covariance matrix: partial autocorrelation and the modified Cholesky decomposition. These proposed methods are illustrated with the real data from Korean genomic epidemiology study.

• Proceedings of the KIEE Conference
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• 1992.07a
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• pp.453-456
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• 1992

A Data-based Covariance Matrix(DCM) is introduced in the Eigenvector(EV) method, among subspace methods of estimating multiple sinusoidal frequencies from finite white noisy measurements. It is shown that the EV with the DCM can obtain the true. frequencies from finite noiseless data Some asymptotic results and further improvement on the DCM are also presented mathematically. Monte-carlo simulations are statistically conducted from the view-points of means and standard deviations in the EV's of DCM and Conventional Covariance Matrix(CCM). Simulations show a great promise for using the DCM, particularly for the cases of short data records, closely spaced frequencies and high signal-to-noise ratios.

• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.301-311
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• 2020

Schwarz's Bayesian information criterion (BIC) is one of the most popular criteria for model selection, that was derived under the assumption of independent and identical distribution. For correlated data in longitudinal studies, Jones (Statistics in Medicine, 30, 3050-3056, 2011) modified the BIC to select the best linear mixed effects model based on the effective sample size where the number of parameters in covariance structure was not considered. In this paper, we propose an extended Jones' modified BIC by considering covariance parameters. We conducted simulation studies under a variety of parameter configurations for linear mixed effects models. Our simulation study indicates that our proposed BIC performs better in model selection than Schwarz's BIC and Jones' modified BIC do in most scenarios. We also illustrate an example of smoking data using a longitudinal cohort of cancer patients.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.19-30
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• 2003

Spatiotemporal statistical models are used for analyzing space-time data in many fields, such as environmental sciences, meteorology, geology, epidemiology, forestry, hydrology, fishery, and so on. It is well known that classical spatiotemporal process modeling requires the estimation of space-time variogram or covariance functions. In practice, the estimation of such variogram or covariance functions are computationally difficult and highly sensitive to data structures. We investigate a Bayesian hierarchical model which allows the specification of a more realistic series of conditional distributions instead of computationally difficult and less realistic joint covariance functions. The spatiotemporal model investigated in this study allows both spatial component and autoregressive temporal component. These two features overcome the inability of pure time series models to adequately predict changes in trends in individual sites.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.71-78
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• 2018

In this study, we consider the likelihood ratio test for the covariance matrix of the multivariate normal data. For this, we propose a method for obtaining null distributions of the likelihood ratio statistics by the Monte-Carlo approach when it is difficult to derive the exact null distributions theoretically. Then we compare the performance and precision of distributions obtained by the asymptotic normality and the Monte-Carlo method for the likelihood ratio test through a simulation study. Finally we discuss some interesting features related to the likelihood ratio test for the covariance matrix and the Monte-Carlo method for obtaining null distributions for the likelihood ratio statistics.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.577-590
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• 2018

Employing the covariance adjustment technique, we show that in the system of two seemingly unrelated multivariate regressions the estimator of regression coefficients can be expressed as a matrix power series, and conclude that the matrix series only has a unique simpler form. In the case that the covariance matrix of the system is unknown, we define a two-stage estimator for the regression coefficients which is shown to be unique and unbiased. Numerical simulations are also presented to illustrate its superiority over the ordinary least square estimator. Also, as an example we apply our results to the seemingly unrelated growth curve models.

• 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.

• International Journal of Aeronautical and Space Sciences
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• v.11 no.4
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• pp.326-337
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• 2010

This work addresses problems regarding trajectory planning for unmanned aerial vehicle sensors. Such sensors are used for taking measurements of large nonlinear systems. The sensor investigations presented here entails methods for improving estimations and predictions of large nonlinear systems. Thoroughly understanding the global system state typically requires probabilistic state estimation. Thus, in order to meet this requirement, the goal is to find trajectories such that the measurements along each trajectory minimize the expected error of the predicted state of the system. The considerable nonlinearity of the dynamics governing these systems necessitates the use of computationally costly Monte-Carlo estimation techniques, which are needed to update the state distribution over time. This computational burden renders planning to be infeasible since the search process must calculate the covariance of the posterior state estimate for each candidate path. To resolve this challenge, this work proposes to replace the computationally intensive numerical prediction process with an approximate covariance dynamics model learned using a nonlinear time-series regression. The use of autoregressive time-series featuring a regularized least squares algorithm facilitates the learning of accurate and efficient parametric models. The learned covariance dynamics are demonstrated to outperform other approximation strategies, such as linearization and partial ensemble propagation, when used for trajectory optimization, in terms of accuracy and speed, with examples of simplified weather forecasting.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.1
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• pp.259-264
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• 2006

It is well known that the uncertainty of the covariance parameters of the process noise (Q) and the observation errors (R) has a significant impact on Kalman filtering performance. Q and R influence the weight that the filter applies between the existing process information and the latest measurements. Errors in any of them may result in the filter being suboptimal or even cause it to diverge. The conventional way of determining Q and R requires good a priori knowledge of the process noises and measurement errors, which normally comes from intensive empirical analysis. Many adaptive methods have been developed to overcome the conventional Kalman filter's limitations. Starting from covariance matching principles, an innovative adaptive process noise scaling algorithm has been proposed in this paper. Without artificial or empirical parameters to be set, the proposed adaptive mechanism drives the filter autonomously to the optimal mode. The proposed algorithm has been tested using road test data, showing significant improvements to filtering performance.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.41 no.1
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• pp.35-44
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• 2004

We Propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization (CMF). Circulant matrix factorization is also very powerful tool used for spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. Schur algorithm is the method for a fast Cholesky factorization of Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR filter and for the case of the In filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).