• Communications for Statistical Applications and Methods
• /
• v.26 no.3
• /
• pp.315-323
• /
• 2019

Panel data sets have recently been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Often a dichotomous dependent variable occur in survival analysis, biomedical and epidemiological studies that is analyzed by a generalized linear mixed effects model (GLMM). The most common estimation method for the binary panel data may be the maximum likelihood (ML). Many statistical packages provide ML estimates; however, the estimates are computed from numerically approximated likelihood function. For instance, R packages, pglm (Croissant, 2017) approximate the likelihood function by the Gauss-Hermite quadratures, while Rchoice (Sarrias, Journal of Statistical Software, 74, 1-31, 2016) use a Monte Carlo integration method for the approximation. As a result, it can be observed that different packages give different results because of different numerical computation methods. In this note, we discuss the pros and cons of numerical methods compared with the exact computation method.

• Journal of the Korean Data and Information Science Society
• /
• v.25 no.1
• /
• pp.195-209
• /
• 2014

In this paper, we derive the estimators of the location parameter and the scale parameter in a logistic distribution based on multiply type-II censored samples by the approximate maximum likelihood estimation method. We use four modified empirical distribution function (EDF) types test for the logistic distribution based on multiply type-II censored samples using proposed approximate maximum likelihood estimators. We also propose the modified normalized sample Lorenz curve plot for the logistic distribution based on multiply type-II censored samples. For each test, Monte Carlo techniques are used to generate the critical values. The powers of these tests are also investigated under several alternative distributions.

• Asian-Australasian Journal of Animal Sciences
• /
• v.18 no.12
• /
• pp.1669-1674
• /
• 2005

Maximum likelihood methodology was applied to analyze the efficiency and statistical power of interval mapping by using a threshold model. The factors that affect QTL detection efficiency (e.g. QTL effect, heritability and incidence of categories) were simulated in our study. Daughter design with multiple families was applied, and the size of segregating population is 500. The results showed that the threshold model has a great advantage in parameters estimation and power of QTL mapping, and has nice efficiency and accuracy for discrete traits. In addition, the accuracy and power of QTL mapping depended on the effect of putative quantitative trait loci, the value of heritability and incidence directly. With the increase of QTL effect, heritability and incidence of categories, the accuracy and power of QTL mapping improved correspondingly.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.8
• /
• pp.2053-2061
• /
• 1994

The static and fatigue tensile tests have been conduted to predict the fatigue life of 8-harness satin woven and plain woven carbon/epoxy composite plates containing a circular hole. A fatigue residual strength degradation model, based on the assumption that the residual strength for unnotched specimen decreases monotonically, has been applied to predict statistically the fatigue life of materials used in this study. To determine the parameters(c, b and K) of the residual strength degradation model, the minimization technique and the maximum likelihood method are used. Agreement of the converted ultimate strength by using the minimization technique with the static ultimate strength is reasonably good. Therefore, the minimization technique is more adjustable in the determination of the parameter and the prediction of the fatigue life than the maximum likelihood method.

• Communications for Statistical Applications and Methods
• /
• v.12 no.3
• /
• pp.643-652
• /
• 2005

It has been known that the exponentiated exponential distribution can be used as a possible alternative to the gamma distribution or the Weibull distribution in many situations. But the maximum likelihood method does not admit explicit solutions when the sample is multiply censored. So we derive the approximate maximum likelihood estimators for the location and scale parameters in the exponentiated exponential distribution that are explicit function of order statistics. We also compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Communications for Statistical Applications and Methods
• /
• v.19 no.1
• /
• pp.135-145
• /
• 2012

It is well known that the maximum likelihood estimator(MLE) in normal mixture models with unequal variances does not fall in the interior of the parameter space. Recently, a doubly smoothed maximum likelihood estimator(DS-MLE) (Seo and Lindsay, 2010) was proposed as a general alternative to the ordinary maximum likelihood estimator. Although this method gives a natural modification to the ordinary MLE, its computation is cumbersome due to intractable integrations. In this paper, we derive an EM algorithm for the DS-MLE under normal mixture models and propose a fast computational tool using a local quadratic approximation. The accuracy and speed of the proposed method is then presented via some numerical studies.

• Communications for Statistical Applications and Methods
• /
• v.24 no.3
• /
• 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 the Korean Magnetic Resonance Society
• /
• v.15 no.2
• /
• pp.157-174
• /
• 2011

Although the use of apodization functions in connection with postprocessing of a 2D NMR spectrum proves improved spectral quality, there is usually a trade-off between resolution enhancement and noise suppression due to a classical "uncertainty principle." In this study, therefore, a mathematical deconvolution technique called "Maximum Likelihood Deconvolution (MLD)" was adopted to achieve the spectral resolution and sensitivity enhancement simultaneously. The MLD technique greatly facilitates visualization and restoration of the genuine spectral information from complex 2D NMR spectra that would be problematic with the conventional apodization/FT processing. In particular, application of the MLD to the 2D-NOE spectrum would be very useful to derive the important proton connectivities, which are essential to achieve elucidating the 3D molecular structure.

• International Journal of Reliability and Applications
• /
• v.6 no.1
• /
• pp.41-51
• /
• 2005

The Bayes estimators of the parameters included in the complementary Weibull reliability model are obtained. In the process of deriving Bayes estimators, the scale and shape parameters of the complementary Weibull distribution are considered to be independent random variables having prior exponential distributions. The maximum likelihood estimators of the desired parameters are derived. Further, the least square estimators are obtained in closed forms. Simulation study is made using Monte Carlo method to make a comparison among the obtained estimators. The comparison is made by computing the root mean squared errors associated to each point estimation. Based on the numerical study, the Bayes procedure seems better than the maximum likelihood and least square procedures in the sense of having smaller root mean squared errors.

• 한국데이터정보과학회:학술대회논문집
• /
• 2005.10a
• /
• pp.13-26
• /
• 2005

In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and location parameter of the exponential distribution based on multiply Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples. We also obtain the approximate maximum likelihood estimator (AMLE) of the reliability function by using the proposed estimators. And then we compare the proposed estimators in the sense of the mean squared error.