• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.383-388
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• 2009

In this paper we propose a variance function estimation method based on kernel trick for replicated data or data consisted of sample variances. Newton-Raphson method is used to obtain associated parameter vector. Furthermore, the generalized approximate cross validation function is introduced to select the hyper-parameters which affect the performance of the proposed variance function estimation method. Experimental results are then presented which illustrate the performance of the proposed procedure.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.523-533
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• 2020

This paper suggests three available methods for finding nonnegative estimates of variance components of the random effects in mixed models. The three proposed methods based on the concepts of projections are called projection method I, II, and III. Each method derives sums of squares uniquely based on its own method of projections. All the sums of squares in quadratic forms are calculated as the squared lengths of projections of an observation vector; therefore, there is discussion on the decomposition of the observation vector into the sum of orthogonal projections for establishing a projection model. The projection model in matrix form is constructed by ascertaining the orthogonal projections defined on vector subspaces. Nonnegative estimates are then obtained by the projection model where all the coefficient matrices of the effects in the model are orthogonal to each other. Each method provides its own system of linear equations in a different way for the estimation of variance components; however, the estimates are given as the same regardless of the methods, whichever is used. Hartley's synthesis is used as a method for finding the coefficients of variance components.

• Structural Monitoring and Maintenance
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• v.7 no.4
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• pp.319-344
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• 2020

Inverse analysis of non-linear reinforced concrete bridge pier using recursive Gaussian filtering for in-situ condition assessment is the main theme of this work. For this purpose, minimum variance unbiased estimation using unscented sigma points is adopted here. The uniqueness of this inverse analysis lies in its approach for strain based updating of engineering demand parameters, where appropriate bound and constrained conditions are introduced to ensure numerical stability and convergence. In this analysis, seismic input is also identified, which is an added advantage for the structures having no dedicated sensors for earthquake measurement. First, the proposed strategy is tested with a simulated example whose hysteretic properties are obtained from the slow-cyclic test of a frame to investigate its efficiency and accuracy. Finally, the experimental test data of a full-scale bridge pier is used to study its in-situ condition in terms of Park & Ang damage index. Overall the study shows the ability of the augmented minimum variance unbiased estimation based recursive time-marching algorithm for non-linear system identification with the aim to estimate the engineering damage parameters that are the fundamental information necessary for any future decision making for retrofitting/rehabilitation.

• The Korean Journal of Applied Statistics
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• v.30 no.2
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• pp.259-269
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• 2017

Due to the nonnegativity of variance, most of nonparametric estimations of discontinuous variance function have used the Nadaraya-Watson estimation with residuals. By the modification of Chen et al. (2009) and Yu and Jones (2004), Huh (2014, 2016a) proposed the estimators of the log-variance function instead of the variance function using the local linear estimator which has no boundary effect. Huh (2016b) estimated the variance function using the adjusted squared residuals by the estimated jump size in the discontinuous variance function. In this paper, we propose an estimator of the discontinuous log-variance function using the local linear estimator with the adjusted log-squared residuals by the estimated jump size of log-variance function like Huh (2016b). The numerical work demonstrates the performance of the proposed method with simulated and real examples.

• Journal of Korean Institute of Industrial Engineers
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• v.15 no.2
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• pp.103-108
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• 1989

PERT formulae for the mean and variance of activity time are near exact only over a short interval of the concentration parameter which is defined as the sum of the two shape parameters of the beta distribution. Aiming a better estimation of the mean and variance of activity time, we propose a method of subjectively estimating this concentration parameter via estimating the probability of completing the activity within a specified time interval.

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.155-166
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• 2018

Consider FARIMA time series with innovations that have infinite variances. We are interested in the estimation of self-similarities $H_n$ of FARIMA(0, d, 0) by using modified R/S statistic. We can confirm that the $H_n$ converges to Hurst parameter $H=d+\frac{1}{2}$. Finally, we figure out ARMA and minimum variance power spectrum density of FARIMA processes.

• Journal of the Korea Institute of Military Science and Technology
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• v.13 no.6
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• pp.982-989
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• 2010

This paper shows accuracy comparison results of reliability estimation methods for one-shot systems such as ammunitions. Quantal-response data, following a binomial distribution at each sampling time, characterizes lifetimes of one-shot systems. Various quantal-response data of different sample sizes are simulated using lifetime data randomly sampled from assumed weibull distributions with different shape parameters but the identical scale parameter in this paper. Then, reliability estimation methods in open literature are applied to the simulated quantal-response data to estimate true reliability over time. Rankings in estimation accuracy for different sample sizes are determined using t-test of SSE. Furthermore, MSE at each time, including both bias and variance of estimated reliability metrics for each method are analyzed to investigate how much both bias and variance contribute the SSE. From the MSE analysis, MSE provides reliability estimation trend for each method. Parametric estimation method provides more accurate reliability estimation results than the other methods for most of sample sizes.

• International Journal of Naval Architecture and Ocean Engineering
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• v.6 no.1
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• pp.74-86
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• 2014

The optimization techniques are explored in the direction of arrival (DOA) estimation based on single acoustic pressure gradient vector sensor (APGVS). By analyzing the working principle and measurement errors of the APGVS, acoustic intensity approaches (AI) and the minimum variance distortionless response beamforming approach based on single APGVS (VMVDR) are deduced. The radius to wavelength ratio of the APGVS must be not bigger than 0.1 in the actual application, otherwise its DOA estimation performance will degrade significantly. To improve the robustness and estimation performance of the DOA estimation approaches based on single APGVS, two modified processing approaches based on single APGVS are presented. Simulation and lake trial results indicate that the performance of the modified approaches based on single APGVS are better than AI and VMVDR approaches based on single APGVS when the radius to wavelength ratio is not bigger than 0.1, and the two modified DOA estimation methods have excellent estimation performance when the radius to wavelength ratio is bigger than 0.1.

• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.743-750
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• 2012

In this study, we propose definitions for the one-sided variance for asymmetric distribution. We consider to apply the one-sided variance to the construction to define modified $C_{pk}$, which is a definition for the process capability index for the asymmetric process distribution. Then we consider to obtain the consistent estimation for the one-sided variance and to apply to the various industrial fields.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.315-324
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• 2002

For estimating the error variance under the relative squared error loss in two-way analysis of variance models, we provide a class of hierarchical Bayes estimators and then derive a subclass of the hierarchical Bayes estimators, each member of which dominates the best multiple of the error sum of squares which is known to be minimax. We also identify a subclass of non-minimax hierarchical Bayes estimators.