• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.162-172
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• 2021

This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.483-487
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• 1986

The LQG/LTR method is applied to the real servomechanism with the unknown modeling error and system noise variance Q$_{2}$. The equivalent discretized LQG controller is implemented on the 16-bit microcomputer and the experimental results show the improved stability and the satisfactory performance when the noise variance Q$_{2}$ is increased infinitly.

• Journal of the Korean Data and Information Science Society
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• v.1
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• pp.59-65
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• 1990

The Edgeworth expansion, the Roy-Tiku method and the bootstrap method for approximating the distribution of the sample variance are compared through the Monte Carlo simulation study.

• Management Science and Financial Engineering
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• v.19 no.2
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• pp.37-42
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• 2013

This paper suggests a numerical method for valuation of European and American options under the two L$\acute{e}$vy Processes, Normal Inverse Gaussian Model and the Variance Gamma model. The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the existing numerical method, the lattice-based method.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.547-554
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• 2014

This paper discusses a method of estimating variance components for random effects model. Henderson's method I and III are discussed for the esimation of variance components. This paper shows how to use projections instead of using Henderson's methods for the calculation of sums of squares which are quadratic forms in the observations. It also discusses that eigenvalues can be used for getting the expectations of sums of squares in place of using the method of Hartley's synthesis. It shows the suggested method is much more effective than those methods.

• ETRI Journal
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• v.45 no.1
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• pp.131-137
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• 2023

The phase reconstruction process in digital holographic microscopy involves a trade-off between the phase error and the high-spatial-frequency components. In this reconstruction process, if the narrow region of the sideband is windowed in the Fourier domain, the phase error from the DC component will be reduced, but the high-spatial-frequency components will be lost. However, if the wide region is windowed, the 3D profile will include the high-spatial-frequency components, but the phase error will increase. To solve this trade-off, we propose the high-variance pixel averaging method, which uses the variance map of the reconstructed depth profiles of the windowed sidebands of different sizes in the Fourier domain to classify the phase error and the high-spatial-frequency components. Our proposed method calculates the average of the high-variance pixels because they include the noise from the DC component. In addition, for the nonaveraged pixels, the reconstructed phase data created by the spatial frequency components of the widest window are used to include the high-spatialfrequency components. We explain the mathematical algorithm of our proposed method and compare it with conventional methods to verify its advantages.

• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.369-377
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• 2006

This paper considers moving variance ratio (MVR) for valiance detection problem with time series data in progress. For testing purpose, parametric method based on F distribution and nonparametric method based on empirical distribution are compared via simulation study.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.177-198
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• 2002

The estimation of variance components or variance ratios in linear model is an important issue in plant or animal breeding fields, and various estimation methods have been devised to estimate variance components or variance ratios. However, many traits of economic importance in those fields are observed as dichotomous or polychotomous outcomes. The usual estimation methods might not be appropriate for these cases. Recently threshold linear model is considered as an important tool to analyze discrete traits specially in animal breeding field. In this note, we consider a hierarchical Bayesian method for the threshold animal model. Gibbs sampler for making full Bayesian inferences about random effects as well as fixed effects is described to analyze jointly discrete traits and continuous traits. Numerical example of the model with two discrete ordered categorical traits, calving ease of calves from born by heifer and calving ease of calf from born by cow, and one normally distributed trait, birth weight, is provided.

• Proceedings of the KIEE Conference
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• 2006.07d
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• pp.1858-1859
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• 2006

This paper presents a new fuzzy-neural-network based interacting multiple model (FNNBIMM) algorithm for tracking a maneuvering target. To effectively handle the unknown target acceleration, this paper regards it as additional noise, time-varying variance to target model. Each sub model characterized by the variance of the overall process noise, which is obtained on the basis of each acceleration interval. Since it is hard to approximate this time-varying variance adaptively owing to the unknown acceleration, the FNN is utilized to precisely approximate this time-varying variance. The gradient descendant method is utilized to optimize each FNN. To show the feasibility of the proposed algorithm, a numerical example is provided.