• Communications for Statistical Applications and Methods
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• 제16권3호
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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.

• Communications for Statistical Applications and Methods
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• 제16권6호
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• pp.971-978
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• 2009

Poisson generalized linear mixed models(GLMMs) have been widely used for the analysis of clustered or correlated count data. For the inference marginal likelihood, which is obtained by integrating out random effects is often used. It gives maximum likelihood(ML) estimator, but the integration is usually intractable. In this paper, we propose how to obtain the ML estimator via Laplace approximation based on hierarchical-likelihood (h-likelihood) approach under the Poisson GLMMs. In particular, the h-likelihood avoids the integration itself and gives a statistically efficient procedure for various random-effect models including GLMMs. The proposed method is illustrated using two practical examples and simulation studies.

• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.895-903
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• 2009

The penalized partial likelihood based on restricted maximum likelihood method has been widely used for the inference of frailty models. However, the standard-error estimate for frailty parameter estimator can be downwardly biased. In this paper we show that such underestimation can be corrected by using hierarchical likelihood. In particular, the hierarchical likelihood gives a statistically efficient procedure for various random-effect models including frailty models. The proposed method is illustrated via a numerical example and simulation study. The simulation results demonstrate that the corrected standard-error estimate largely improves such bias.

• Journal of the Korean Data and Information Science Society
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• 제12권1호
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• pp.19-25
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• 2001

Random effects models which describe the dependence via random effects in various correlated data have recently received considerable attention in the biomedical literature. They include mixed linear models (MLMs), generatized linear mixed models (GLMMS) and hierarchical generalized linear models (HGLMs). For the inference Lee and Nelder (2000) proposed the first-and second-order REML (restricted maximum likelihood) methods based on hierarchical-likelihood of tee and Welder (1996). In this paper, for Poisson-gamma HGLMs the new methods are theoretically compared with marginal likelihood methods and both methods are illustrated by two practical examples.

• Journal of the Korean Statistical Society
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• 제36권1호
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• pp.1-29
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• 2007

Suppose one is trying to estimate a high dimensional vector of parameters from a series of one observation per parameter. Often, it is possible to take advantage of sparsity in the parameters by thresholding the data in an appropriate way. A marginal maximum likelihood approach, within a suitable Bayesian structure, has excellent properties. For very sparse signals, the procedure chooses a large threshold and takes advantage of the sparsity, while for signals where there are many non-zero values, the method does not perform excessive smoothing. The scope of the method is reviewed and demonstrated, and various theoretical, practical and computational issues are discussed, in particularly exploring the wide potential and applicability of the general approach, and the way it can be used within more complex thresholding problems such as curve estimation using wavelets.

• Communications for Statistical Applications and Methods
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• 제24권3호
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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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• 제21권2호
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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.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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• pp.193-200
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• 2000

Modelling the dependence via random effects in censored multivariate survival data has recently received considerable attention in the biomedical literature. The random effects models model not only the conditional survival times but also the conditional hazard rate. Systematic likelihood inference for the models with random effects is possible using Lee and Nelder's (1996) hierarchical-likelihood (h-likelihood). The purpose of this presentation is to introduce Ha et al.'s (2000a,b) inferential methods for the random effects models via the h-likelihood, which provide a conceptually simple, numerically efficient and reliable inferential procedures.

• 대한수학회논문집
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• 제21권2호
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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.

• 응용통계연구
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• 제9권1호
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• pp.1-15
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• 1996

본 논문은 질병발생집단의 감염율이 질병발생집단내 감염되지 않은 개체들에 대한 어떤 처치효과가 감염율에 어떻게 영향을 받는가를 알아보기 위한 통계적 분석모형으로 연속적 분석모형을 제시하고, 모형내 미지모수들을 추정하기 위한 방법을 논의하고 있다.