• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.371-383
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• 2019

Panel data sets have been developed in various areas, and many recent studies have analyzed panel, or longitudinal data sets. Maximum likelihood (ML) may be the most common statistical method for analyzing panel data models; however, the inference based on the ML estimate will have an inflated Type I error because the ML method tends to give a downwardly biased estimate of variance components when the sample size is small. The under estimation could be severe when data is incomplete. This paper proposes the restricted maximum likelihood (REML) method for a random effects panel data model with a censored dependent variable. Note that the likelihood function of the model is complex in that it includes a multidimensional integral. Many authors proposed to use integral approximation methods for the computation of likelihood function; however, it is well known that integral approximation methods are inadequate for high dimensional integrals in practice. This paper introduces to use the moments of truncated multivariate normal random vector for the calculation of multidimensional integral. In addition, a proper asymptotic standard error of REML estimate is given.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.209-217
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• 2001

We obtain the approximate maximum likelihood estimators (AMLEs) for the scale and location parameters $\theta$ and $\mu$ in the three-parameter Weibull distribution based on Type-II censored samples. We also compare the AMLEs with the modified maximum likelihood estimators (MMLEs) in the sense of the mean squared error (MSE) based on complete sample.

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.263-272
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• 1996

In this parer, under random censorship model, an estimation of scale and shape parameters in Weibull lifetime model is considered. Based on nonparametric estimator of survival function, the least square method is proposed. The proposed estimation method is simple and the performance of the proposed estimator is as efficient as maximum likelihood estimators. An example is presented, using field winding data. Simulation studies are performed to compare the performaces of the proposed estimator and maximum likelihood estimator.

• Communications for Statistical Applications and Methods
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• v.25 no.4
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• pp.355-371
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• 2018

The two parameter negative exponential distribution has many practical applications in queuing theory such as the service times of agents in system, the time it takes before your next telephone call, the time until a radioactive practical decays, the distance between mutations on a DNA strand, and the extreme values of annual snowfall or rainfall; consequently, has many applications in reliability systems. This paper considers an estimation problem of stress-strength model with two parameter negative parameter exponential distribution. We introduce a maximum penalized likelihood method, Bayes estimator using Lindley approximation to estimate stress-strength model and compare the proposed estimators with regular maximum likelihood estimator for complete data. We also introduce a maximum penalized likelihood method, Bayes estimator using a Markov chain Mote Carlo technique for incomplete data. A Monte Carlo simulation study is performed to compare stress-strength model estimates. Real data is used as a practical application of the proposed model.

• International Journal of Reliability and Applications
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• v.3 no.1
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• pp.51-60
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• 2002

This paper presents the methodology for obtaining point and interval estimating of the parameters of a new two-parameter distribution with multiple-censored and singly censored data (Type-I censoring or Type-II censoring) as well as complete data, using the maximum likelihood method. The basis is the likelihood expression for multiple-censored data. Furthermore, this model can be extended to a three-parameter distribution that is added a scale parameter. Then, the parameter estimation can be obtained by the graphical estimation on probability plot.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.111-119
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• 2007

In this paper, we develop a nonparametric Bayesian methodology of estimating an unknown distribution function F at the given survival time with current status data under the assumption of Dirichlet process prior on F. We compare our algorithm with the nonparametric maximum likelihood estimator through application to simulated data and real data.

• Water Engineering Research
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• v.4 no.3
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• pp.155-173
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• 2003

Parameters and quantiles of the 2-parameter generalized Pareto distribution were estimated using the methods of regular moments, modified moments, probability weighted moments, linear moments, maximum likelihood, and entropy for Monte Carlo-generated samples. The performance of these seven estimators was statistically compared, with the objective of identifying the most robust estimator. It was found that in general the methods of probability-weighted moments and L-moments performed better than the methods of maximum likelihood estimation, moments and entropy, especially for smaller values of the coefficient of variation and probability of exceedance.

• The Korean Journal of Applied Statistics
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• v.7 no.1
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• pp.121-129
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• 1994

Using the software named MATHEMATICA which can evaluate symbolic operation, it is demonstrated to obtain the maximum likelihood estimation form. A sample from Multivariate Normal distribution is adopted to show the process of obtaining the maximum likelihood estimator.

• Journal of the Korean Statistical Society
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• v.25 no.2
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• pp.161-173
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• 1996

When we deal with a Hilbert space-valued Stochastic Differential Equation (SDE) (or Stochastic Partial Differential Equation (SPDE)), depending on some unknown parameters, the solution usually has a Fourier series expansion. In this situation we consider the maximum likelihood method for the statistical estimation problem and derive the asymptotic properties (consistency and normality) of the Maximum Likelihood Estimator (MLE).

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.185-191
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• 2013

Kiefer (1961) studied asymptotic behavior of empirical distribution using the law of the iterated logarithm. Robertson and Wright (1974a) discussed whether this type of result would hold for a maximum likelihood estimator of a stochastically ordered distribution function; however, we show that this cannot be achieved. We provide only a partial answer to this problem. The result is applicable to both estimation and testing problems under the restriction of stochastic ordering.