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

• 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.18 no.5
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• pp.667-674
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• 2011

A recent trend in software reliability engineering accounts for the coverage growth behavior during testing. The coverage growth function (representing the coverage growth behavior) has become an essential component of software reliability models. Application of a coverage growth function requires the estimation of the coverage growth function. This paper considers the problem of estimating the coverage growth function. The existing maximum likelihood method is reviewed and corrected. A method of minimizing the sum of squares of the standardized prediction error is proposed for situations where the maximum likelihood method is not applicable.

• Journal of Communications and Networks
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• v.16 no.6
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• pp.583-591
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• 2014

In wireless communications, knowledge of the signal-to-noise ratio is required in diverse communication applications. In this paper, we derive the variance of the maximum likelihood estimator in the data-aided and non-data-aided schemes for determining the optimal shrinkage factor. The shrinkage factor is usually the constant that is multiplied by the unbiased estimate and it increases the bias slightly while considerably decreasing the variance so that the overall mean squared error decreases. The closed-form biased estimators for binary-phase-shift-keying and quadrature phase-shift-keying systems are then obtained. Simulation results show that the mean squared error of the proposed method is lower than that of the maximum likelihood method for low and moderate signal-to-noise ratio conditions.

• 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.

• Communications for Statistical Applications and Methods
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• v.20 no.1
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• pp.63-75
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• 2013

In this paper, we derive maximum likelihood estimators (MLEs) and approximate maximum likelihood estimators (AMLEs) of unknown parameters in a generalized half logistic distribution under Type-II hybrid censoring. We also obtain approximate confidence intervals using asymptotic variance and covariance matrices based on the MLEs and the AMLEs. As an illustration, we examine the validity of the proposed estimation using real data. Finally, we compare the proposed estimators in the sense of the mean squared error (MSE), bias, and length of the approximate confidence interval through a Monte Carlo simulation for various censoring schemes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.1C
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• pp.110-116
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• 2008

Maximum likelihood(ML) diretion-of-arrival(DOA) estimation is essentially optimization of multivariable nonlinear cost function. Since the final estimate is highly dependent on the initial estimate, an initialization is critical in nonlinear optimization. We propose a multi-dimensional(M-D) search scheme of uniform exhaustive search and improved exhaustive search. Improved exhaustive search is superior to uniform exhaustive search in terms of the computational complexity and the accuracy of the estimates.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.633-641
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• 2014

The exponential distibution is one of the most popular distributions in analyzing the lifetime data. In this paper, we propose multiply Type I hybrid censoring. And this paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply Type I hybrid censoring. The scale parameter is estimated by approximate maximum likelihood estimation methods using two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator (MLE) of the scale parameter ${\sigma}$ under the proposed multiply Type I hybrid censored samples. We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 10,000 times for the sample size n=20 and 40 and various censored schemes. The $AMLE_{II}$ is better than $AMLE_I$ in the sense of the RMSE.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1581-1589
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• 2014

In this paper, we consider maximum likelihood estimators of the location and scale parameters for the half-logistic distribution when samples are multiply Type I hybrid censored. The scale parameter is estimated by approximate maximum likelihood estimation methods using two different Taylor series expansion types ($\hat{\sigma}_I$, $\hat{\sigma}_{II}$). We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 10,000 times for the sample size n=20 and 40 and various censored schemes. The approximate MLE of the second type is better than that of the first type in the sense of the RMSE. Further an illustrative example with the real data is presented.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.443-451
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• 2005

The studied in this paper is a new algorithm for searching the maximum likelihood estimate(MLE) in which probability density function is not explicitly expressed. Newton-Raphson's root-finding routine and a nonlinear numerical optimization algorithm with constraint (so-called feasible sequential quadratic programming) are used. This algorithm is applied to the Wakeby distribution which is importantly used in hydrology and water resource research for analysis of extreme rainfall. The performance comparison between maximum likelihood estimates and method of L-moment estimates (L-ME) is studied by Monte-carlo simulation. The recommended methods are L-ME for up to 300 observations and MLE for over the sample size, respectively. Methods for speeding up the algorithm and for computing variances of estimates are discussed.