• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.363-374
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• 2006

A new bivariate beta distribution based on the Appell function of the third kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix.

• The Korean Journal of Applied Statistics
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• v.9 no.1
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• pp.1-15
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• 1996

This paper discusses the effectiveness of an infection rate under a certain disease on an immunity rate by a protective inoculation. A sequence of dependense models concerning the infection rate is derived by defining conditionally nested binary random variables for the analysis of polytomous data with hierarchical response scale. Maximum likelihood estimates based on the marginal log-likelihood functin are obtained numerically in the Nelder and Mead's(1965) simplex method.

• Journal of the Korean Data and Information Science Society
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• v.27 no.4
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• pp.1083-1090
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• 2016

In clinical studies, different types of outcomes (e.g. repeated measures data and time-to-event data) for the same subject tend to be observed, and these data can be correlated. For example, a response variable of interest can be measured repeatedly over time on the same subject and at the same time, an event time representing a terminating event is also obtained. Joint modelling using a shared random effect is useful for analyzing these data. Inferences based on marginal likelihood may involve the evaluation of analytically intractable integrations over the random-effect distributions. In this paper we propose a joint HGLM approach for analyzing such outcomes using the HGLM (hierarchical generalized linear model) method based on h-likelihood (i.e. hierarchical likelihood), which avoids these integration itself. The proposed method has been demonstrated using various numerical studies.

• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.67-81
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• 2005

Most of the previously proposed methods for the frailty model do not work well when there are many tied observations. This is partly because the empirical likelihood used is not suitable for tied observations. In this paper, we propose a new method for the frailty model with many ties. The proposed method obtains the posterior distribution of the parameters using the binomial form empirical likelihood and Bayesian bootstrap. The proposed method yields stable results and is computationally fast. To compare the proposed method with the maximum marginal likelihood approach, we do simulations.

• Communications for Statistical Applications and Methods
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• v.15 no.2
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• pp.161-171
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• 2008

This study discusses Johnson's $S_U$-normal distribution capturing a wide range of non-normality in various regression models. We provide the likelihood inference using Johnson's $S_U$-normal distribution, and propose a likelihood ratio (LR) test for normality. We also apply the $S_U$-normal distribution to the binary and censored regression models. Monte Carlo simulations are used to show that the LR test using the $S_U$-normal distribution can be served as a model specification test for normal error distribution, and that the $S_U$-normal maximum likelihood (ML) estimators tend to yield more reliable marginal effect estimates in the binary and censored model when the error distributions are non-normal.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.187-200
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• 1992

Samples are often found to be too heterogeneous to be explained by a one-parameter family of models in the sense that the implicit mean-variance relationship in such a family is violated by the data. This phenomenon is often called over-dispersion. The most frequently used method in dealing with over-dispersion is to mix a one-parameter family creating a two parameter marginal mixture family for the data. In this paper, we investigate performance of estimators such as maximum likelihood estimator, method of moment estimator, and maximum quasi-likelihood estimator in negative binomial and beta-binomial distribution. Simulations are done for various mean parameter and dispersion parameter in both distributions, and we conclude that the moment estimators are very superior in the sense of bias and asymptotic relative efficiency.

• Communications for Statistical Applications and Methods
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• v.24 no.3
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• pp.291-301
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• 2017

It is well known in a small sample that the maximum likelihood (ML) approach for variance components in the general linear model yields estimates that are biased downward. The ML estimate of residual variance tends to be downwardly biased. The underestimation of residual variance, which has implications for the estimation of marginal effects and asymptotic standard error of estimates, seems to be more serious in some limited dependent variable models, as shown by some researchers. An alternative frequentist's approach may be restricted or residual maximum likelihood (REML), which accounts for the loss in degrees of freedom and gives an unbiased estimate of residual variance. In this situation, the REML estimator is derived in a censored regression model. A small sample the REML is shown to provide proper inference on regression coefficients.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.193-200
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• 2014

It was recognized by some researchers that the disturbance variance in a censored regression model is frequently underestimated by the maximum likelihood method. This underestimation has implications for the estimation of marginal effects and asymptotic standard errors. For instance, the actual coverage probability of the confidence interval based on a maximum likelihood estimate can be significantly smaller than the nominal confidence level; consequently, a Bayesian estimation is considered to overcome this difficulty. The behaviors of the maximum likelihood and Bayesian estimators of disturbance variance are examined in a fixed effects panel regression model with a limited dependent variable, which is known to have the incidental parameter problem. Behavior under random effect assumption is also investigated.

• The Korean Journal of Applied Statistics
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• v.26 no.3
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• pp.389-399
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• 2013

This article introduces Gaussian process regression and shows its application with time-course microarray gene expression data. Gene screening for yeast cell cycle microarray expression data is accomplished with a ratio of log marginal likelihood that uses Gaussian process regression with a squared exponential covariance kernel function. Gaussian process regression fitting with each gene is done and shown with the nine top ranking genes. With the screened data the Gaussian model-based clustering is done and its silhouette values are calculated for cluster validity.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.507-518
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• 2015

It is not easy to select a linear mixed model since the main interest for model building could be different and the number of parameters in the model could not be clearly defined. In this paper, performance of conditional Akaike Information Criteria and its bias-corrected version are compared with marginal Bayesian and Akaike Information Criteria through a simulation study. The results from the simulation study indicate that bias-corrected conditional Akaike Information Criteria shows promising performance when candidate models exclude large models containing the true model, but bias-corrected one prefers over-parametrized models more intensively when a set of candidate models increases. Marginal Bayesian and Akaike Information Criteria also have some difficulty to select the true model when the design for random effects is nested.