• Journal of the Korean Data and Information Science Society
• /
• 제23권1호
• /
• pp.199-207
• /
• 2012

Recently, variable selection methods using penalized likelihood with a shrink penalty function have been widely studied in various statistical models including generalized linear models and survival models. In particular, they select important variables and estimate coefficients of covariates simultaneously. In this paper, we develop a penalize h-likelihood method for variable selection in gamma frailty models. For this we use the smoothly clipped absolute deviation (SCAD) penalty function, which satisfies a good property in variable selection. The proposed method is illustrated using simulation study and a practical data set.

• Journal of the Korean Data and Information Science Society
• /
• 제21권2호
• /
• pp.345-354
• /
• 2010

The Gamma Distribution is widely used in Engineering and Industrial applications. Estimation of parameters is revisited in the two-parameter Gamma distribution. The parameters are estimated by minimizing the likelihood ratios. A comparative study between the method of moments, the maximum likelihood method, the method of product spacings, and minimization of three different likelihood ratios is performed using simulation. For the scale parameter, the maximum likelihood estimate performs better and for the shape parameter, the product spacings estimate performs better. Among the three likelihood ratio statistics considered, the Anderson-Darling statistic has inferior performance compared to the Cramer-von-Misses statistic and the Kolmogorov-Smirnov statistic.

• Journal of the Korean Data and Information Science Society
• /
• 제27권5호
• /
• pp.1389-1397
• /
• 2016

Semi-parametric frailty model with nonparametric baseline hazards has been widely used for the analyses of clustered survival-time data. The frailty models can be fitted via an auxiliary Poisson hierarchical generalized linear model (HGLM). For the inferences of the frailty model marginal likelihood, which gives MLE, is often used. The marginal likelihood is usually obtained by integrating out random effects, but it often requires an intractable integration. In this paper, we propose to obtain the MLE via Laplace approximation using a Poisson HGLM approach for semi-parametric frailty model. The proposed HGLM approach uses hierarchical-likelihood (h-likelihood), which avoids integration itself. The proposed method is illustrated using a numerical study.

• Communications for Statistical Applications and Methods
• /
• 제25권1호
• /
• pp.71-78
• /
• 2018

In this study, we consider the likelihood ratio test for the covariance matrix of the multivariate normal data. For this, we propose a method for obtaining null distributions of the likelihood ratio statistics by the Monte-Carlo approach when it is difficult to derive the exact null distributions theoretically. Then we compare the performance and precision of distributions obtained by the asymptotic normality and the Monte-Carlo method for the likelihood ratio test through a simulation study. Finally we discuss some interesting features related to the likelihood ratio test for the covariance matrix and the Monte-Carlo method for obtaining null distributions for the likelihood ratio statistics.

• Communications for Statistical Applications and Methods
• /
• 제25권6호
• /
• pp.647-658
• /
• 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.

• 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
• /
• 제23권1호
• /
• pp.89-98
• /
• 2012

이 논문에서는 두 개의 Maxwell분포의 모수들의 동질성을 모수비에 근거하여 검정하는 근사통계량을 제안한다. Maxwell분포의 모수비에 대한 추정량이 복잡하여 정확한 분포를 유도하기는 매우 어렵다. 이러한 문제를 해결하기 위한 하나의 대안으로 표준정규분포로 근사적으로 수렴하는 통계량을 고려해야 한다. 이 논문에서 제안된 통계량은 표준정규분포로 수렴하며, 표본의 수가 작은 경우에도 사용할 수 있다. 특히, 본 논문에서는 부호화 로그 우도비 통계량과 수정된 부호화 로그 우도비 통계량을 개발한다. 일반적으로, 수정된 부호화 로그 우도비 통계량은 로그 우도비 통계량에 비해 표준정규분포로 수렴하는 속도가 매우 빠르다. 부호화 로그 우도비 통계량은 작은 표본으로도 표준정규분포로 매우 빨리 수렴한다. 제안된 통계량들의 성질들을 모의실험을 통하여 알아보고, 제안된 통계량을 예제를 통하여 연구한다.

• 응용통계연구
• /
• 제13권2호
• /
• pp.407-414
• /
• 2000

Carroll과 Ruppert(1988)는 준가능도(quasi-likelihood)를 이용하여 에스트라제 측정자료를 회귀분석하였다. Jung과 Lee(1997)는 준가능도을 이용한 회귀분석모형의 적합도정통계량을 제안하였으며 검정 별과 기각되지 않아 본 분석모형이 타당하다고 주장하였다. 그러나 Lee와 Nelder(1998)의 잔차그림을 검토한 결과, 상기 모형으로는 평균증가에 따른 분산증가를 충분히 반영할 수 없었다. 본 논문에서는 Lee와 Nelder(1998)의 평균과 분산의 동시모형으로 에스트라제 자료를 재분석하고 잔차그림을 이용하여 모형의 타당성을 재평가하였다. 또한 분산에서 산포모형에 대한 적합도검정에는 Lee와 Nelder(1998)의 제한가능도(restricted likelihood)에 근거한 검정법이 보다 적절함을 제시하였다.

• Communications for Statistical Applications and Methods
• /
• 제16권3호
• /
• pp.479-485
• /
• 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.

• The Journal of Asian Finance, Economics and Business
• /
• 제7권11호
• /
• pp.241-250
• /
• 2020

This study examines the relationship between the attributes of board structure and the likelihood of financial distress for the non-financial sector of an emerging market characterized by concentrated ownership and family-controlled business. The present study utilized panel logistic regression to estimate the relationship between board structure attributes and the likelihood of financial distress. We used Altman Z-Score as a proxy for firm financial distress, as this tool measures the financial distress inversely. The study finds a significant relationship between board size and the likelihood of financial distress. The results show that a one-unit increase in board size would decrease the probability of financial distress by 3.4%. Further, we observe that a greater level of board independence is associated with a lower likelihood of financial distress. A one-unit increase in board independence would decrease the probability of financial distress by 20.4%. We also find a significant positive impact of leverage on the likelihood of financial distress. The present study contributes to the body of literature on board structure attributes and likelihood of financial distress in emerging markets, like Pakistan. Furthermore, the findings would be beneficial for corporate policymakers and investors in formulating corporate financial strategy and predicting business failure.