• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.385-395
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• 2020

We present a new maximum likelihood approach to estimate demographic history using genomic data sampled from two populations. A demographic model such as an isolation-with-migration (IM) model explains the genetic divergence of two populations split away from their common ancestral population. The standard probability model for an IM model contains a latent variable called genealogy that represents gene-specific evolutionary paths and links the genetic data to the IM model. Under an IM model, a genealogy consists of two kinds of evolutionary paths of genetic data: vertical inheritance paths (coalescent events) through generations and horizontal paths (migration events) between populations. The computational complexity of the IM model inference is one of the major limitations to analyze genomic data. We propose a fast maximum likelihood approach to estimate IM models from genomic data. The first step analyzes genomic data and maximizes the likelihood of a coalescent tree that contains vertical paths of genealogy. The second step analyzes the estimated coalescent trees and finds the parameter values of an IM model, which maximizes the distribution of the coalescent trees after taking account of possible migration events. We evaluate the performance of the new method by analyses of simulated data and genomic data from two subspecies of common chimpanzees in Africa.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.573-578
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• 2009

We prove the consistency of a penalized maximum likelihood estimate proposed by Ahn (2001). The PMLE not only avoids the well-known problem that the ordinary likelihood of the normal mixture model is unbounded for any given sample size, but also removes redundant components.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.991-1002
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• 2014

Both Bayesian and maximum likelihood methods are efficient for the estimation of regression coefficients of various Tobit regression models (see. e.g. Chib, 1992; Greene, 1990; Lee and Choi, 2013); however, some researchers recognized that the maximum likelihood method tends to underestimate the disturbance variance, which has implications for the estimation of marginal effects and the asymptotic standard error of estimates. The underestimation of the maximum likelihood estimate in a seemingly unrelated Tobit regression model is examined. A Bayesian method based on an objective noninformative prior is shown to provide proper estimates of the disturbance variance as well as other regression parameters

• Journal of Korea Water Resources Association
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• v.42 no.4
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• pp.331-341
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• 2009

In this study, we compared the observed information matrix with the Fisher information matrix to estimate the uncertainty of maximum likelihood estimators of the generalized logistic (GL) distribution. The previous literatures recommended the use of the observed information matrix because this is convenient since this matrix is determined as the part of the parameter estimation procedure and there is little difference in accuracy between the observed information matrix and the Fisher information matrix for large sample size. The observed information matrix has been applied for the generalized logistic distribution based on the previous study without verification. For this purpose, a simulation experiment was performed to verify which matrix gave the better accuracy for the GL model. The simulation results showed that the variance-covariance of the ML parameters for the GL distribution came up with similar results to those of previous literature, but it is preferable to use of the Fisher information matrix to estimate the uncertainty of quantile of ML estimators.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.885-897
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• 2000

The use of an unweighted mean and of separate tests is part of the current practice for analyzing interlaboratory studies, and we hope to improve on this method. We fit, using maximum likelihood(ML), a rather intricate, multi-parameter measurement model with the material's true value as a latent variable in a situation where quite serviceable regression and ANOVA calculations have already been developed. The model fit leads to both a weighted estimate of he overall mean, and to tests for equality of means, slopes and variances. Maximum likelihood tests for difference among variances poses a challenge in that the likelihood can easily becoem unbounded. Thus the major objective become to provide a useful test of variance equality.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.479-485
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• 2009

When a part of data is unobserved the marginal likelihood of parameters given the observed data often involves analytically intractable high dimensional integral and hence it is hard to find the maximum likelihood estimate of the parameters. Simulated maximum likelihood(SML) method which estimates the marginal likelihood via Monte Carlo importance sampling and optimize the estimated marginal likelihood has been used in many applications. A key issue in SML is to find a good proposal density from which Monte Carlo samples are generated. The optimal proposal density is the conditional density of the unobserved data given the parameters and the observed data, and attempts have been given to find a good approximation to the optimal proposal density. Algorithms which adaptively improve the proposal density have been widely used due to its simplicity and efficiency. In this paper, we describe a fully adaptive algorithm which has been used by some practitioners but has not been well recognized in statistical literature, and evaluate its estimation performance and robustness via a simulation study. The simulation study shows a great improvement in the order of magnitudes in the mean squared error, compared to non-adaptive or partially adaptive SML methods. Also, it is shown that the fully adaptive SML is robust in a sense that it is insensitive to the starting points in the optimization routine.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.257-262
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• 1996

When we are estimate the smoothing parameter in spline regression model, we deal the diagnostic of influence observations as posteriori analysis. When we use Generalized Maximum Likelihood Function as the estimation method of smoothing parameter, we propose the diagnostic measure for influencial observations in the obtained estimate, and we introduce the finding method of the proper smoothing parameter estimate.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.3
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• pp.26-35
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• 2005

This paper is intended to compare the hazard rate estimations from Bayesian approach and maximum likelihood estimate(MLE) method. Hazard rate frequently involves unknown parameters and it is common that those parameters are estimated from observed data by using MLE method. Such estimated parameters are appropriate as long as there are sufficient data. Due to various reasons, however, we frequently cannot obtain sufficient data so that the result of MLE method may be unreliable. In order to resolve such a problem we need to rely on the judgement about the unknown parameters. We do this by adopting the Bayesian approach. The first one is to use a predictive distribution and the second one is a method called Bayesian estimate. In addition, in the Bayesian approach, the prior distribution has a critical effect on the result of analysis, so we introduce the method using computerized-simulation to elicit an effective prior distribution. For the simplicity, we use exponential and gamma distributions as a likelihood distribution and its natural conjugate prior distribution, respectively. Finally, numerical examples are given to illustrate the potential benefits of the Bayesian approach.

• International Journal of Reliability and Applications
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• v.8 no.2
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• pp.199-210
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• 2007

This paper presents estimations of the generalized Rayleigh distribution model based on grouped and censored data. The maximum likelihood method is used to derive point and asymptotic confidence estimates of the unknown parameters. The results obtained in this paper generalize some of those available in the literature. Finally, we test whether the current model fits a set of real data better than other models.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.255-261
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• 2014

Many studies have estimated a mixture of binomial distributions. This paper considers an extension, a mixture of shifted binomial distributions, and the estimation of the distribution. The range of each component binomial distribution is rst evaluated and then for each possible value of shifted parameters, the EM algorithm is employed to estimate those parameters. From a set of possible value of shifted parameters and corresponding estimated parameters of the distribution, the likelihood of given data is determined. The simulation results verify the performance of the proposed method.