• Journal of the Korean Mathematical Society
• /
• v.61 no.3
• /
• pp.427-444
• /
• 2024

The matrix completion problem is to predict missing entries of a data matrix using the low-rank approximation of the observed entries. Typical approaches to matrix completion problem often rely on thresholding the singular values of the data matrix. However, these approaches have some limitations. In particular, a discontinuity is present near the thresholding value, and the thresholding value must be manually selected. To overcome these difficulties, we propose a shrinkage and thresholding function that smoothly thresholds the singular values to obtain more accurate and robust estimation of the data matrix. Furthermore, the proposed function is differentiable so that the thresholding values can be adaptively calculated during the iterations using Stein unbiased risk estimate. The experimental results demonstrate that the proposed algorithm yields a more accurate estimation with a faster execution than other matrix completion algorithms in image inpainting problems.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1993.04a
• /
• pp.438-438
• /
• 1993

• Journal of the Korea Society for Simulation
• /
• v.2 no.1
• /
• pp.125-133
• /
• 1993

A statistical method is described for estimation of the unknown constants in a theory using both of the computer simulation data and the real experimental data, The best linear unbiased predictor based on a spatial linear model is fitted from the computer simulation data alone. Then nonlinear least squares estimation method is applied to the real experimental data using the fitted prediction model as if it were the true simulation model. An application to the computational nuclear fusion devices is presented, where the nonlinear least squares estimates of four transport coefficients of the theoretical nuclear fusion model are obtained.

• The Korean Journal of Applied Statistics
• /
• v.14 no.1
• /
• pp.13-24
• /
• 2001

In this paper, we investigated mean estimation methods in two-phase sampling. Under the fixed expected cost we reviewed the optimal sample sizes, minimum variances and approximate unbiased variance estimators for usual ratio estimator, stratified sample mean with proportional allocation and Rao's allocation of the second phase sample. Also we proposed combined ratio estimator, which uses both ratio estimation and stratification and derived optimal sample size, minimum variance and unbiased variance estimator. Through a limited simulation study, we compared estimators by design effects and came to know that ratio estimator is more efficient than stratified sample mean in some cases and inefficient in the other cases, but combined ratio estimator is more efficient than others in most cases.

• Journal of Institute of Control, Robotics and Systems
• /
• v.20 no.1
• /
• pp.1-5
• /
• 2014

In this paper, we propose an optimal fixed-lag FIR (Finite-Impulse-Response) smoother for a class of discrete time-varying state-space signal models. The proposed fixed-lag FIR smoother is linear with respect to inputs and outputs on the recent finite horizon and estimates the delayed state so that the variance of the estimation error is minimized with the unbiased constraint. Since the proposed smoother is derived with system inputs, it can be adapted to feedback control system. Additionally, the proposed smoother can give more general solution than the optimal FIR filter, because it reduced to the optimal FIR filter by setting the fixed-lag size as zero. A numerical example is presented to illustrate the performance of the proposed smoother by comparing with an optimal FIR filter and a conventional fixed-lag Kalman smoother.

• Journal of the Korean Statistical Society
• /
• v.15 no.2
• /
• pp.87-96
• /
• 1986

Sequential estimation of parameters in a compound Poisson process whose jump sizes are one-parameter exponential class random variables is discussed. Cramer-Rao type information inequality is used as an efficiency cirterion. Unbiased estimators for certain parametric functions whose variance attain the lower bound are all characterized with the corresponding sampling plans.

• Journal of the Korean Data and Information Science Society
• /
• v.6 no.2
• /
• pp.1-7
• /
• 1995

This paper considers the reliability estimation of a two-component shared-load system based on Freund model. Maximum likelihood estimator, order restricted maximum likelihood estimator and uniformly minimum variance unbiased estimator of the reliability function for the system are obtained. Performance of three estimators for moderate sample sizes is studied by simulation.

• Journal of Korean Society for Quality Management
• /
• v.8 no.2
• /
• pp.3-14
• /
• 1980

This paper is concerned with the design of an appropriate sampling plan or stopping rule and the construction of estimate for the estimation of process or lot fraction defective. Various sampling plans which are well known or have potential applications are unified into a generalized sampling plan. Under this sampling plan sufficient statistic, probability distribution, moment, and minimum variance unbiased estimate are obtained. Results for various sampling plans can be derived as special cases. Then, under given parameter values, the relative efficiencies of the various sampling plans are compared with respect to expected sample sizes and variances of estimates.

• Proceedings of the Korea Society for Simulation Conference
• /
• 1992.10a
• /
• pp.6-6
• /
• 1992

This work deals with nonlinear least squares method for estimating unknown universial constants C in a computer simulation code real experimental data(or database) and computer simulation data. The best linear unbiased predictor based on a spatial statistical model is fitted from the computer simulation data. Then nonlinear least squares estimation method is applied to the real data using the fitted prediction model(or simulation predictor) as if it were the true simulation model. An application to the computational nuclear fusion device is presented.

• Journal of Embryo Transfer
• /
• v.23 no.3
• /
• pp.203-209
• /
• 2008

To estimate the genetic characteristics and cumulative power of discrimination (CPD) existing among Hanwoo (Korean cattle) and exotic foreign population (Angus, Herford, Charolais, Holstein) we used a total of 414 genomic DNAs from five breeds population (Hanwoo, Angus, Hereford, Charolais, Holstein). Genetic characteristics indices including mean allele number among loci, unbiased heterozygosity ($h_i$) within locus and polymorphic information content (PIC) and unbiased average heterozygosity (H) among loci in four breeds were calculated using the generated allele frequencies by each marker. The mean allele numbers for all loci ranged between 5 and 7 while heterozygosity (H) ranged from 0.75 (HW) to 0.64 (HF) among loci and across breeds heterozygosity (H) was 0.69. The generated unbiased average heterozygosity among loci in each breed was integrated to the global formula of CPD resulting in 99.71 % within the populations. The genetic variation of HW (Hanwoo) showed highest estimates among the analyzed breeds.