• Journal of the Korean Statistical Society
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• 제32권3호
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• pp.261-270
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• 2003

This paper introduces a new density estimator which is Hellinger consistent under a simple condition. A number of issues are discussed, such as extension to Kullback-Leibler consistency, robustness, the Bayes version of the estimator and the maximum likelihood case. An illustration is presented.

• Journal of the Korean Data and Information Science Society
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• 제15권1호
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• pp.273-284
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• 2004

Bayes estimation of parameters is considered for two independent exponential distributions with ordered means. Order restricted Bayes estimators for means are obtained with respect to inverted gamma, noninformative prior and uniform prior distributions, and their asymptotic properties are established. It is shown that the maximum likelihood estimator, restricted maximum likelihood estimator, unrestricted Bayes estimator, and restricted Bayes estimator of the mean are all consistent and have the same limiting distribution. These estimators are compared with the corresponding unrestricted Bayes estimators by Monte Carlo simulation.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.229-239
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• 2007

We present a diagnostic method for the quasi-likelihood estimators in generalized linear models. Since these estimators can be usually obtained by iteratively reweighted least squares which are well known to be very sensitive to unusual data, a diagnostic step is indispensable to analysis of data. We extend the local influence approach based on the maximum likelihood function to that on the quasi-likelihood function. Under several perturbation schemes local influence diagnostics are derived. An illustrative example is given and we compare the results provided by local influence and deletion.

• 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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• 제9권3호
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• pp.639-647
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• 2002

Efforts to obtain more power for unit root tests have continued. Pantula at el.(1994) compared empirical powers of several unit root test statistics and addressed that the weighted symmetric estimator(WSE) and the unconditional maximum likelihood estimator(UMLE) are the best among them. One can easily see that the powers of these two statistics are almost the same. In this paper we explain a connection between WSE and UMLE and suggest a unit root test statistic which may explain the connection between them.

• Communications for Statistical Applications and Methods
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• 제20권4호
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• pp.311-319
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• 2013

Cooray and Ananda (2005) proposed a composite lognormal-Pareto model to analyze loss payment data in the actuarial and insurance industries. Their model is based on a lognormal density up to an unknown threshold value and a two-parameter Pareto density. In this paper, we implement the minimum density power divergence estimation for the composite lognormal-Pareto density. We compare the performances of the minimum density power divergence estimator (MDPDE) and the maximum likelihood estimator (MLE) by simulations and an example. The minimum density power divergence estimator performs reasonably well against various violations in the distribution. The minimum density power divergence estimator better fits small observations and better resists against extraordinary large observations than the maximum likelihood estimator.

• 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.

• Communications for Statistical Applications and Methods
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• 제23권6호
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• pp.479-496
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• 2016

In this survey, we present a modified inverse moment estimation of parameters and its applications. We use a specific model to demonstrate its principle and how to apply this method in practice. The estimation of unknown parameters is considered. A necessary and sufficient condition for the existence and uniqueness of maximum-likelihood estimates of the parameters is obtained for the classical maximum likelihood estimation. Inverse moment and modified inverse moment estimators are proposed and their properties are studied. Monte Carlo simulations are conducted to compare the performances of these estimators. As far as the biases and mean squared errors are concerned, modified inverse moment estimator works the best in all cases considered for estimating the unknown parameters. Its performance is followed by inverse moment estimator and maximum likelihood estimator, especially for small sample sizes.

• Journal of the Korean Data and Information Science Society
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• 제22권4호
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• pp.811-817
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• 2011

We shall introduce a general probability mass function which includes several discrete probability mass functions. Especially, when the random variable X is Poisson, binomial, and negative binomial random variables as some special cases of the introduced distribution, the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the probability P(X ${\leq}$ t) are considered. And the efficiencies of the MLE and the UMVUE of the reliability ar compared each other.

• Communications for Statistical Applications and Methods
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• 제10권2호
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• pp.619-626
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• 2003

Given a prior guess for the unknown value of P(Y