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

• Communications for Statistical Applications and Methods
• /
• 제26권4호
• /
• pp.371-383
• /
• 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.

• Journal of the Korean Data and Information Science Society
• /
• 제15권1호
• /
• pp.273-284
• /
• 2004

Bayes estimation of parameters is considered for two independent exponential distributions with ordered means. Order restricted Bayes estimators for means are obtained with respect to inverted gamma, noninformative prior and uniform prior distributions, and their asymptotic properties are established. It is shown that the maximum likelihood estimator, restricted maximum likelihood estimator, unrestricted Bayes estimator, and restricted Bayes estimator of the mean are all consistent and have the same limiting distribution. These estimators are compared with the corresponding unrestricted Bayes estimators by Monte Carlo simulation.

• Journal of the Korean Data and Information Science Society
• /
• 제12권1호
• /
• pp.19-25
• /
• 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 Data and Information Science Society
• /
• 제6권2호
• /
• pp.1-7
• /
• 1995

This paper considers the reliability estimation of a two-component shared-load system based on Freund model. Maximum likelihood estimator, order restricted maximum likelihood estimator and uniformly minimum variance unbiased estimator of the reliability function for the system are obtained. Performance of three estimators for moderate sample sizes is studied by simulation.

• Journal of the Korean Data and Information Science Society
• /
• 제21권5호
• /
• pp.951-958
• /
• 2010

In this paper, we obtain the restricted maximum likelihood estimators (RMLE's) for means in normal distributions with the ordered mean constraints. The biases and mean squared errors (MSE's) of these RMLE's are approximated by Mote Carlo methods. In every case a substantial savings in MSE is obtained at the expense of a small loss in bias when using RMLE's instead of the unrestricted MLE's.

• Communications for Statistical Applications and Methods
• /
• 제24권3호
• /
• pp.291-301
• /
• 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.

• Journal of applied mathematics & informatics
• /
• 제13권1_2호
• /
• pp.457-470
• /
• 2003

The comparison of two or more Lorenz curves of Pareto distributions of first kind under arbitrary order restriction is studied. The problem is turned out to be a statistical inference problem concerning scale parameters under order restriction. We assume that the location parameters of Palate distributions are completely unknown. In this paper the maximum likelihood estimation and likelihood ratio tests for and against order restriction are proposed.

• Journal of the Korean Statistical Society
• /
• 제36권3호
• /
• pp.335-347
• /
• 2007

Two new types of positive biasedness, which are closely related to Type III positive biasedness (Yanagimoto and Sibuya, 1972), are proposed. We call these near Type III positive biasedness. Though no implication between Type II and near Type III biasedness exists, near Type III seems to be less restrictive than Type II biasedness. Constrained maximum likelihood estimates of distribution functions under near Type III positive bisedness are obtained. The likelihood ratio tests of symmetry against new positive biasedness restrictions are proposed. A small simulation study is conducted to compare the performance of the tests.

• 응용통계연구
• /
• 제19권2호
• /
• pp.349-360
• /
• 2006

SAS의 PROC MIXED를 사용하면 일반적인 ANOVA 추정량뿐만 아니라 더 많은 장점을 갖는 제한최대우도추정법 또는 최대우도추정법으로 모수들을 추론할 수 있다. 혼합모형에 속하는 불균형중첩오차구조를 갖는 선형회귀모형에서 랜덤효과와 관련된 그룹간 분산의 신뢰 구간과 고정효과에 해당되는 회귀 계수들에 대 한 신뢰구간을 구하기 위하여 세 가지 크기를 갖는 표본에 대하여 PROC MIXED를 사용하였다. 모의실험을 실행한 결과, 대표본인 경우에는 모수들의 신뢰 구간을 구하기 위하여 PROC MIXED를 활용할 수 있지만, 소표본인 경우에는 PROC MIXED를 사용할 경우, 그룹간 분산의 신뢰 구간과 회귀계수 가운데 절편항의 신뢰구간은 주어진 신뢰계수를 지키지 못하는 것을 보인다.