• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.167-178
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• 1994

To estimate coefficient matrix in autoregressive model, usually ordinary least squares estimator or unconditional maximum likelihood estimator is used. It is unknown that for univariate AR(p) model, unconditional maximum likelihood estimator gives better power property that ordinary least squares estimator in testing for unit root with mean estimated. When autoregressive model contains multiple unit roots and unconditional likelihood function is used to estimate coefficient matrix, the seperation of nonstationary part and stationary part of the eigen-values in the estimated coefficient matrix in the limit is developed. This asymptotic property may give an idea to test for multiple unit roots.

• 품질경영학회지
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• 제38권4호
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• pp.480-490
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• 2010

In this paper, two estimation methods(least square estimation and maximum likelihood estimation) were compared for Weibull distribution and Type I censoring. Data obtained by Monte Carlo simulation were analyzed using two estimation methods and analysis results were compared by MSE(Mean Squared Error). Comparison results show that maximum likelihood estimator is better for censored data and complete data with more than 30 samples and least square estimator is better for small size complete data(less than and equal to 20 samples).

• Communications for Statistical Applications and Methods
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• 제18권5호
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• pp.625-636
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• 2011

본 논문에서는 로그정규분포의 엔트로피에 대한 모수적 추정량으로 최소분산비편향추정량과 최대가능도추정량을 제시하고 성질을 비교한다. 각 추정량의 분산을 유도해서 일치성을 밝히고 최대가능도 추정량의 편향이 추정에 미치는 영향을 분석한다. 델타근사방법을 이용해서 얻은 추정량의 분포를 제시하고 적합도 평가를 통한 유도한 분포의 확증을 위해서 모의실험을 수행한다. 평균제곱오차에 의한 상대적 효율성에 대한 조사를 통해 두 추정량의 성능을 비교한다. 모의실험의 결과에서 최소분산비편향추정량은 최대가능도 추정량보다 더 좋은 효율을 보이는 것으로 나타나며, 특히 표본크기와 분산이 동시에 작아짐에 따라 효율이 점점 높아지게 되어 월등히 나은 성능을 발휘함을 볼 수 있다.

• Journal of the Korean Statistical Society
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• 제33권3호
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• pp.313-321
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• 2004

We consider the problem of testing cell probabilities in sparse multinomial data. Aerts et al. (2000) presented T=${{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2$ as a test statistic with the local least square polynomial estimator ${{p}_{i}}^{*}$, and derived its asymptotic distribution. The local least square estimator may produce negative estimates for cell probabilities. The local maximum likelihood polynomial estimator ${{\hat{p}}_{i}}$, however, guarantees positive estimates for cell probabilities and has the same asymptotic performance as the local least square estimator (Baek and Park, 2003). When there are cell probabilities with relatively much different sizes, the same contribution of the difference between the estimator and the hypothetical probability at each cell in their test statistic would not be proper to measure the total goodness-of-fit. We consider a Pearson type of goodness-of-fit test statistic, $T_1={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ instead, and show it follows an asymptotic normal distribution. Also we investigate the asymptotic normality of $T_2={{\Sigma}_{i=1}}^{k}{[{p_i}^{*}-E{(p_{i}}^{*})]^2/p_{i}$ where the minimum expected cell frequency is very small.

• Journal of the Korean Statistical Society
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• 제22권1호
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• pp.133-138
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• 1993

We consider two estimators of the infection rate in the simple stochastic epidemic model. It is shown that the maximum likelihood estimator of teh infection rate under the discrete time observation does not have the moment of any positive order. Some properties of the Choi-Severo estimator, an approximation to the maximum likelihood estimator, are also investigated.

• The Journal of Asian Finance, Economics and Business
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• 제5권1호
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• pp.11-16
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• 2018

This research examines the alternative ways of estimating the coefficient of non-diversifiable risk, namely beta coefficient, in Capital Asset Pricing Model (CAPM) introduced by Sharpe (1964) that is an essential element of assessing the value of diverse assets. The non-parametric methods used in this research are the robust Least Trimmed Square (LTS) and Maximum likelihood type of M-estimator (MM-estimator). The Jackknife, the resampling technique, is also employed to validate the results. According to finance literature and common practices, these coecients have often been estimated using Ordinary Least Square (LS) regression method and monthly return data set. The empirical results of this research pointed out that the robust Least Trimmed Square (LTS) and Maximum likelihood type of M-estimator (MM-estimator) performed much better than Ordinary Least Square (LS) in terms of eciency for large-cap stocks trading actively in the United States markets. Interestingly, the empirical results also showed that daily return data would give more accurate estimation than monthly return data in both Ordinary Least Square (LS) and robust Least Trimmed Square (LTS) and Maximum likelihood type of M-estimator (MM-estimator) regressions.

• Journal of the Korean Data and Information Science Society
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• 제6권2호
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• pp.1-7
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• 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 Statistical Society
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• 제26권1호
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• pp.117-130
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• 1997

We study the asymptotic behavior of the maximum partial likelihood estimator in the Cox proportional hazards model in the presence of nuisance parameters when the entry of patients is staggered. When entry of patients is simultaneous and there is only one regression parameter in the Cox model, the efficient score process of the partial likelihood is martingale and converges weakly to a time-chnaged Brownian motion. Our problem is to get a similar result in the presence of nuisance parameters when entry of patient is staggered.

• 한국신뢰성학회지:신뢰성응용연구
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• 제13권3호
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• pp.191-206
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• 2013

Application areas for Lifetime Performance Index(LPI), a kind of process capability index to be frequently used as a means of measuring process performance are illustrated with examples. Statistical properties for maximum likelihood and unbiased estimators of LPI are evaluated and discussed under Weibull distribution with known shape parameter. Furthermore, guidelines for selecting an estimator of LPI are also presented.

• 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.