• 환경위생공학
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• 제23권4호
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• pp.83-93
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• 2008

The non-linear least squares model(NLSM) has long been the standard technique used by hydrologists for constructing rating curves. The reasons for its adaptation are vague, and its appropriateness as a method of describing discharge measurement uncertainty has not been well investigated. It is shown in this paper that the classical method of NLSM can model only a very limited class of variance heterogeneity. Furthermore, this lack of flexibility often leads to unaccounted heteroscedasticity, resulting in dubious values for the rating curve parameters and estimated discharge. By introducing a heteroscedastic maximum likelihood model(HMLM), the variance heterogeneity is treated more generally. The maximum likelihood model stabilises the variance better than the NLSM approach, and thus is a more robust and appropriate way to fit a rating curve to a set of discharge measurements.

• Communications for Statistical Applications and Methods
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• 제16권6호
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• pp.1055-1066
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• 2009

Many articles have considered a hybrid censoring scheme, which is a mixture of Type-I and Type-II censoring schemes. We introduce a double hybrid censoring scheme and derive some approximate maximum likelihood estimators(AMLEs) of the scale parameter for the half logistic distribution under the proposed double hybrid censored samples. The scale parameter is estimated by approximate maximum likelihood estimation method using two different Taylor series expansion types. We also obtain the maximum likelihood estimator(MLE) and the least square estimator(LSE) of the scale parameter under the proposed double hybrid censored samples. We compare the proposed estimators in the sense of the mean squared error. The simulation procedure is repeated 10,000 times for the sample size n = 20(10)40 and various censored samples. The performances of the AMLEs and MLE are very similar in all aspects but the MLE and LSE have not a closed-form expression, some numerical method must be employed.

• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.397-405
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• 1997

Recently maximum likelihood estimators using unconditional likelihood function are used for testing unit roots. When one wants to use this method the determinant term of initial values in the multivariate unconditional likelihood function produces a complicated function of the elements in the coefficient matrix and variance matrix. In this paper an approximation of the determinant term is calculated and based on this aproximation an approximated unconditional likelihood function is calculated. The approximated unconditional maximum likelihood estimators can be used to test for unit roots. When multivariate process has one unit root the limiting distribution obtained by this method and the limiting distribution using exact unconditional likelihood function are the same.

• 응용통계연구
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• 제6권2호
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• pp.393-399
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• 1993

반응이 두 가지로 나타나는 자료에서 설명변수와 반응변수와의 관계를 연구할 때 많이 사용되는 로지스틱 회귀모형에 대하여 그 모수들을 최우추정법으로 구할 때 추정량의 표준오차는 보통 로그우도함수의 2차도함수에 바탕을 두어 계산하게 된다. 한편 피셔정보량이 로그우도함수의 1차도함수를 제곱한 통계량의 기대값으로도 계산된다는 점에 착안하여 얻어지는 피셔정보량의 추정량도 이와 거의 비슷한 대표본 성질을 갖는 것으로 알려져 있다. 이러한 피셔정보량의 추정량들은 최우추정량을 구할 때의 반복 알고리즘과 깊은 관련을 갖고 있다. 어느 방법이 더 효과적으로 최우추정량을 계산하는 지 평균반복횟수를 비교하고 대표본분산의 추정량으로서 각 방법에서 계산되는 분산의 추정량들을 비교하였다.

• Communications for Statistical Applications and Methods
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• 제20권3호
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• pp.217-223
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• 2013

Two influence diagnostic methods for the common mean model are proposed. First, an investigation of the influence of observations according to minor perturbations of the common mean model is made by adapting the local influence method which is based on the likelihood displacement. It is well known that the maximum likelihood estimates are in general sensitive to influential observations. Case-deletions can be a candidate for detecting influential observations. However, the maximum likelihood estimators are iteratively computed and therefore case-deletions involve an enormous amount of computations. An approximation by Newton's method to the maximum likelihood estimator obtained after a single observation was deleted can reduce much of computational burden, which will be treated in this work. A numerical example is given for illustration and it shows that the proposed diagnostic methods can be useful tools.

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

• Journal of the Korean Data and Information Science Society
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• 제26권2호
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• pp.313-322
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• 2015

본 연구에서는 하나의 균일분포 또는 퇴화분포와 두 개의 이항분포의 혼합분포 모형에 대하여 최우추정법을 소개하며, 제시된 모형에 대하여 시뮬레이션을 통해 최우추정량의 성질을 밝히며, 실험을 통해 얻은 강의 평가 자료에 대하여 퇴화분포를 가지는 혼합분포에 대하여 적용하여 보았다. 특히 퇴화분포는 한국의 문화 특성상 가운데 값을 선호하는 현상을 모형화하는데 유용하게 사용될 수 있음을 보였다.

• Communications for Statistical Applications and Methods
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• 제20권5호
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• pp.417-425
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• 2013

We consider an extended version of a logarithmic series distribution and discuss the estimation of its parameters by the method of moments and the method of maximum likelihood. Test procedures are suggested to test the significance of the additional parameter of this distribution and all procedures are illustrated with the help of real life data sets. In addition, a simulation study is conducted to assess the performance of the estimators.

• Journal of the Korean Data and Information Science Society
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• 제17권4호
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• pp.1319-1328
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• 2006

For multiply Type-II censored samples from two-parameter Rayleigh distribution, the maximum likelihood method does not admit explicit solutions. In this case, we propose some explicit estimators of the location and scale parameters in the Rayleigh distribution by the approximate maximum likelihood methods. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Journal of the Korean Data and Information Science Society
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• 제11권1호
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• pp.57-64
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• 2000

By assuming a Type-I censored sample, we propose the approximate maximum likelihood estimators(AMLE) of the scale and location parameters of the gamma distribution. We compare the proposed estimators with the maximum likelihood estimators(MLE) in the sense of the mean squared errors(MSE) through Monte Carlo method.