• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1451-1470
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• 2020

We are concerned with the following elliptic equations: $$\{(-{\Delta})^s_pu={\lambda}f(x,u)\;{\text{in {\Omega}}},\\u=0\;{\text{on {\mathbb{R}}^N{\backslash}{\Omega}},$$ where λ are real parameters, (-∆)^s_p is the fractional p-Laplacian operator, 0 < s < 1 < p < + ∞, sp < N, and f : Ω × ℝ → ℝ satisfies a Carathéodory condition. By applying abstract critical point results, we establish an estimate of the positive interval of the parameters λ for which our problem admits at least one or two nontrivial weak solutions when the nonlinearity f has the subcritical growth condition. In addition, under adequate conditions, we establish an apriori estimate in L^∞(Ω) of any possible weak solution by applying the bootstrap argument.

• Journal of the Korean earth science society
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• v.38 no.5
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• pp.333-344
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• 2017

We present the environmental dependence of the luminosity-size relation of galaxies in the local universe (z < 0.01) along with their dependence on galaxy morphology represented by five broad types (E, dEs, S0, Sp, and Irr). The environmental parameters we consider are the local background density and the group/cluster membership together with the clustercenteric distance for the Virgo cluster galaxies. We derive the regression coefficient (${\beta}$), i.e., the slope of the line representing the least-squares fitting to the data and the Pearson correlation coefficient (c.c.) representing the goodness of the least-squares fit along with the confidence interval from bootstrap resampling. We find no significant dependence of the luminosity-size relation on galaxy morphology. However, there is a weak dependence of the luminosity-size relations on the environment of galaxies, in the sense that galaxies in the low density environment have shallower slopes than galaxies in the high density regions except for elliptical galaxies that show an opposite trend.

• Journal of Korean Society for Quality Management
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• v.35 no.1
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• pp.10-19
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• 2007

ANOVA is widely, used for measurement system analysis. It assumes that the measurement error is normally distributed, which nay not be seen in some industrial cases. In this study the estimates of the measurement system variability and PTR (precision-to-tolerance ratio) are obtained by using weighted standard deviation for the case where the measurement error is non-normally distributed. The Standard Bootstrap method is used foy estimating confidence intervals of measurement system variability and PTR. The point and confidence interval estimates for the cases with normally distributed measurement error are compared to those with non-normally distributed measurement errors through computer simulation.

• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.627-641
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• 2021

An asymmetric least squares estimation method has been employed to estimate linear models for percentile regression. An asymmetric maximum likelihood estimation (AMLE) has been developed for the estimation of Poisson percentile linear models. In this study, we propose generalized nonlinear percentile regression using the AMLE, and the use of the parametric bootstrap method to obtain confidence intervals for the estimates of parameters of interest and smoothing functions of estimates. We consider three conditional distributions of response variables given covariates such as normal, exponential, and Poisson for three mean functions with one linear and two nonlinear models in the simulation studies. The proposed method provides reasonable estimates and confidence interval estimates of parameters, and comparable Monte Carlo asymptotic performance along with the sample size and quantiles. We illustrate applications of the proposed method using real-life data from chemical and radiation epidemiological studies.

• Yonsei Medical Journal
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• v.59 no.9
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• pp.1115-1122
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• 2018

Purpose: To investigate biomechanical properties of the cornea using a dynamic Scheimpflug analyzer according to age. Materials and Methods: In this prospective, cross-sectional, observational study, participants underwent ophthalmic investigations including corneal biomechanical properties, keratometric values, intraocular pressure (IOP), and manifest refraction spherical equivalent (MRSE). We determined the relationship of biomechanical parameters and ocular/systemic variables (participant's age, MRSE, IOP, and mean keratometric values) by piecewise regression analysis, association of biomechanical parameters with variables by Spearman's correlation and stepwise multiple regression analyses, and reference intervals (RI) by the bootstrap method. Results: This study included 217 eyes of 118 participants (20-81 years of age). Piecewise regression analysis between Corvis-central corneal thickness (CCT) and participant's age revealed that the optimal cut-off value of age was 45 years. No clear breakpoints were detected between the corneal biomechanical parameters and MRSE, IOP, and mean keratometric values. Corneal velocity, deformation amplitude, radius, maximal concave power, Corvis-CCT, and Corvis-IOP exhibited correlations with IOP, regardless of age (all ages, 20-44 years, and over 44 years). With smaller deformation amplitude and corneal velocity as well as increased CorvisIOP and Corvis-CCT, IOP became significantly increased. We provided the results of determination of confidence interval from RI data using bootstrap method in three separate age groups (all ages, 20-44 years, and over 44 years). Conclusion: We demonstrated multiple corneal biomechanical parameters according to age, and reported that the corneal biomechanical parameters are influenced by IOP.

• Ocean and Polar Research
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• v.39 no.1
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• pp.13-21
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• 2017

Temporal changes in the number of zooplankton species are important information for understanding basic characteristics and species diversity in marine ecosystems. The aim of the present study was to estimate the optimal monitoring frequency (OMF) to guarantee and predict the minimum number of species occurrences for studies concerning marine ecosystems. The OMF is estimated using the temporal number of zooplankton species through bi-weekly monitoring of zooplankton species data according to operational taxonomic units in the Tongyoung coastal sea. The optimal model comprises two terms, a constant (optimal mean) and a cosine function with a one-year period. The confidence interval (CI) range of the model with monitoring frequency was estimated using a bootstrap method. The CI range was used as a reference to estimate the optimal monitoring frequency. In general, the minimum monitoring frequency (numbers per year) directly depends on the target (acceptable) estimation error. When the acceptable error (range of the CI) increases, the monitoring frequency decreases because the large acceptable error signals a rough estimation. If the acceptable error (unit: number value) of the number of the zooplankton species is set to 3, the minimum monitoring frequency (times per year) is 24. The residual distribution of the model followed a normal distribution. This model can be applied for the estimation of the minimal monitoring frequency that satisfies the target error bounds, as this model provides an estimation of the error of the zooplankton species numbers with monitoring frequencies.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.1-12
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• 2006

The aim of this study is to analyse a survey data on the number of charitable donations using a mixture of two Poisson regression models. The survey was conducted in 2002 by Volunteer 21, an nonprofit organization, based on Koreans, who were older than 20. The mixture of two Poisson distributions is used to model the number of donations based on the empirical distribution of the data. The mixture of two Poisson distributions implies the whole population is subdivided into two groups, one with lesser number of donations and the other with larger number of donations. We fit the mixture of Poisson regression models on the number of donations to identify significant covariates. The expectation-maximization algorithm is employed to estimate the parameters. We computed 95% bootstrap confidence interval based on bias-corrected and accelerated method and used then for selecting significant explanatory variables. As a result, the income variable with four categories and the volunteering variable (1: experience of volunteering, 0: otherwise) turned out to be significant with the positive regression coefficients both in the lesser and the larger donation groups. However, the regression coefficients in the lesser donation group were larger than those in larger donation group.

• Journal of Korea Water Resources Association
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• v.43 no.2
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• pp.187-199
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• 2010

This study evaluated applicability and confidence of probability rainfalls estimated by the non-stationary rainfall frequency analysis which was recently developed. Using rainfall data at 4 sites which have an obvious increasing trend in observations, we estimated 3 type probability rainfalls; probability rainfalls from stationary rainfall frequency analysis using data from 1973-1997, probability rainfalls from stationary rainfall frequency analysis using data from 1973-2006, probability rainfalls from non-stationary rainfall frequency analysis assuming that the current year is 1997 and the target year is 2006. Based on the comparison of residuals from 3 probability rainfalls, the non-stationary rainfall frequency analysis provided more effective and well-directed estimates of probability rainfalls in the target year. Using Bootstrap resampling, this study also evaluated the parameter estimation methods for the non-stationary rainfall frequency analysis based on confidence intervals. The confidence interval length estimated by the maximum likelihood estimation (MLE) is narrower than the probability weighted moments (PWM). The results indicated that MLE provides more proper confidence than PWM for non-stationary probability rainfalls.

• Asian-Australasian Journal of Animal Sciences
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• v.32 no.9
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• pp.1349-1354
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• 2019

Objective: The objective of this study was to determine the best approach for handling missing records of first to successful insemination (FS) in Japanese Black heifers. Methods: Of a total of 2,367 records of heifers born between 2003 and 2015 used, 206 (8.7%) of open heifers were missing. Four penalty methods based on the number of inseminations were set as follows: C1, FS average according to the number of inseminations; C2, constant number of days, 359; C3, maximum number of FS days to each insemination; and C4, average of FS at the last insemination and FS of C2. C5 was generated by adding a constant number (21 d) to the highest number of FS days in each contemporary group. The bootstrap method was used to compare among the 5 methods in terms of bias, mean squared error (MSE) and coefficient of correlation between estimated breeding value (EBV) of non-censored data and censored data. Three percentages (5%, 10%, and 15%) were investigated using the random censoring scheme. The univariate animal model was used to conduct genetic analysis. Results: Heritability of FS in non-censored data was $0.012{\pm}0.016$, slightly lower than the average estimate from the five penalty methods. C1, C2, and C3 showed lower standard errors of estimated heritability but demonstrated inconsistent results for different percentages of missing records. C4 showed moderate standard errors but more stable ones for all percentages of the missing records, whereas C5 showed the highest standard errors compared with noncensored data. The MSE in C4 heritability was $0.633{\times}10^{-4}$, $0.879{\times}10^{-4}$, $0.876{\times}10^{-4}$ and $0.866{\times}10^{-4}$ for 5%, 8.7%, 10%, and 15%, respectively, of the missing records. Thus, C4 showed the lowest and the most stable MSE of heritability; the coefficient of correlation for EBV was 0.88; 0.93 and 0.90 for heifer, sire and dam, respectively. Conclusion: C4 demonstrated the highest positive correlation with the non-censored data set and was consistent within different percentages of the missing records. We concluded that C4 was the best penalty method for missing records due to the stable value of estimated parameters and the highest coefficient of correlation.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.909-916
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• 2010

This study aims to establish storage stability conditions for cook-chilled korean ethenic foods. In order to achieve this aims, we establish a probability model of microbial counts of cook-chilled korean side dishes product-seasoned soybean sprouts. And seasoned soybean sprouts were stored during 1 to 5 days under constant temperature conditions at 0, 5, 10 and $15^{\circ}C$. Next we find confidence intervals for variation in the microbiological quality of seasoned soybean sprouts.