• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.371-383
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• 2019

Panel data sets have been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Maximum likelihood (ML) may be the most common statistical method for analyzing panel data models; however, the inference based on the ML estimate will have an inflated Type I error because the ML method tends to give a downwardly biased estimate of variance components when the sample size is small. The under estimation could be severe when data is incomplete. This paper proposes the restricted maximum likelihood (REML) method for a random effects panel data model with a censored dependent variable. Note that the likelihood function of the model is complex in that it includes a multidimensional integral. Many authors proposed to use integral approximation methods for the computation of likelihood function; however, it is well known that integral approximation methods are inadequate for high dimensional integrals in practice. This paper introduces to use the moments of truncated multivariate normal random vector for the calculation of multidimensional integral. In addition, a proper asymptotic standard error of REML estimate is given.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1309-1317
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• 2013

There are various parameter estimation methods for the generalized exponential distribution under progressive type I interval censoring. Chen and Lio (2010) studied the parameter estimation method by the maximum likelihood estimation method, mid-point approximation method, expectation maximization algorithm and methods of moments. Among those, mid-point approximation method has the smallest mean square error in the generalized exponential distribution under progressive type I interval censoring. However, this method is difficult to derive closed form of solution for the parameter estimation using by maximum likelihood estimation method. In this paper, we propose two type of approximate maximum likelihood estimate to solve that problem. The simulation results show the obtained estimators have good performance in the sense of the mean square error. And proposed method derive closed form of solution for the parameter estimation from the generalized exponential distribution under progressive type I interval censoring.

• Communications for Statistical Applications and Methods
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• v.25 no.6
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• pp.647-658
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• 2018

In this paper, we study statistical inferences on the maximum likelihood estimation of a normal distribution when data are randomly censored. Likelihood equations are derived assuming that the censoring distribution does not involve any parameters of interest. The maximum likelihood estimators (MLEs) of the censored normal distribution do not have an explicit form, and it should be solved in an iterative way. We consider a simple method to derive an explicit form of the approximate MLEs with no iterations by expanding the nonlinear parts of the likelihood equations in Taylor series around some suitable points. The points are closely related to Kaplan-Meier estimators. By using the same method, the observed Fisher information is also approximated to obtain asymptotic variances of the estimators. An illustrative example is presented, and a simulation study is conducted to compare the performances of the estimators. In addition to their explicit form, the approximate MLEs are as efficient as the MLEs in terms of variances.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2000.04a
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• pp.21-27
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• 2000

For earthquake hazard estimation the data containing large historical events and recent complete observations with various uncertainty should be used together. The traditional maximum likelihood method is not adequate for this kind work. The maximum probable earthquakes in the Korean Peninsula are estimated by the method of an extended maximum likelihood estimation. The method can handle data with various uncertainty. The maximum probable earthquake in the Korean Peninsula is appeared to be 7.14$\pm$0.34 in magnitude.

• Communications for Statistical Applications and Methods
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• v.25 no.4
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• pp.355-371
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• 2018

The two parameter negative exponential distribution has many practical applications in queuing theory such as the service times of agents in system, the time it takes before your next telephone call, the time until a radioactive practical decays, the distance between mutations on a DNA strand, and the extreme values of annual snowfall or rainfall; consequently, has many applications in reliability systems. This paper considers an estimation problem of stress-strength model with two parameter negative parameter exponential distribution. We introduce a maximum penalized likelihood method, Bayes estimator using Lindley approximation to estimate stress-strength model and compare the proposed estimators with regular maximum likelihood estimator for complete data. We also introduce a maximum penalized likelihood method, Bayes estimator using a Markov chain Mote Carlo technique for incomplete data. A Monte Carlo simulation study is performed to compare stress-strength model estimates. Real data is used as a practical application of the proposed model.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• Journal of Korea Water Resources Association
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• v.45 no.2
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• pp.191-201
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• 2012

This study reviewed the parameter estimation procedure of the Freund bivariate exponential distribution for the decision of the annual maximum rainfall event. The method of moments was reviewed first, whose results were compared with those from the method of maximum likelihood. Both methods were applied to the hourly rainfall data of the Seoul rain gauge station measured from 1961 to 2010 to select the annual maximum rainfall events, which were also compared each other. The results derived are as follows. First, when applying the method of moments for the parameter estimation, it was found necessary to consider the correlation coefficient between the two variables as well as the mean and variance. Second, the method of maximum likelihood was better to reproduce the mean, but the method of moments was better to reproduce the annual variation of the variance. Third, The annual maximum rainfall events derived were very similar in both cases. Among differently selected annual maximum rainfall events, those with the higher rainfall amount were selected by the method of maximum likelihood, but those with the higher rainfall intensity by the method of moments.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.479-496
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• 2016

In this survey, we present a modified inverse moment estimation of parameters and its applications. We use a specific model to demonstrate its principle and how to apply this method in practice. The estimation of unknown parameters is considered. A necessary and sufficient condition for the existence and uniqueness of maximum-likelihood estimates of the parameters is obtained for the classical maximum likelihood estimation. Inverse moment and modified inverse moment estimators are proposed and their properties are studied. Monte Carlo simulations are conducted to compare the performances of these estimators. As far as the biases and mean squared errors are concerned, modified inverse moment estimator works the best in all cases considered for estimating the unknown parameters. Its performance is followed by inverse moment estimator and maximum likelihood estimator, especially for small sample sizes.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.1
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• pp.38-44
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• 1998

The modified maximum likelihood estimation method is used to estimate the nondimensional aerodynamic derivatives of a single turbo-prop aircraft at a specified flight condition for the best deduction of the dynamic characteristics. In wind axes the six degree of freedom equations are algebraically linearized so that the linear state equation contains aerodynamic derivatives in a state-space form and is used in the maximum likelihood method. The simulated data added with the measurement noise is used as a flight test data which is necessary to the estimation of nondimensional aerodynamic derivatives. It is obtained by implementing the 6-DOF nonlinear flight simulation. In the flight simulation, the effects of several control input types, control deflection amplitudes, and the turbulence intensities on the statistical convergence criteria are also examined and quantitative analysis of the results is discussed.