• 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.

• Journal of environmental and Sanitary engineering
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• v.23 no.4
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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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• v.16 no.6
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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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.10 no.11
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• pp.5365-5380
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• 2016

Estimation of signal-to-noise ratio (SNR) is an important problem in wireless communication systems. It has been studied for various constellation types and channels using different estimation techniques. Maximum likelihood estimation is a technique which provides efficient and in most cases unbiased estimators. In this paper, we have applied maximum likelihood estimation for systems employing square or cross QAM signals which are undergoing slow flat Rayleigh fading. The problem has been considered under various scenarios like data-aided (DA), non-data-aided (NDA) and partially data-aided (PDA) and the performance of each type of estimator has been evaluated and compared. It has been observed that the performance of DA estimator is best due to usage of pilot symbols, with the drawback of greater bandwidth consumption. However, this can be catered for by using partially data-aided estimators whose performance is better than NDA systems with some extra bandwidth requirement.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.11C
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• pp.1025-1028
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• 2009

This paper presents upper bounds of Maximum Likelihood (ML) decoding performance of a few irregular LDPC codes using the simple bound and ML input output weight distributions and it is shown that contrary to general opinion that as block length becomes longer, BP decoding performance becomes simply closer to ML decoding performance, before peak degradation, as block length becomes longer, BP decoding performance falls behind ML decoding performance more and after peak degradation, general opinion holds.

• Computational Structural Engineering
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• v.2 no.4
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• pp.111-116
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• 1989

Methods for the estimation of the coefficient matrices in the equation of motion for a linear multi-degree-of-freedom structure are studied. For this purpose, the equation of motion is transformed into an auto-regressive and moving average with auxiliary input(ARMAX) model. The ARMAX parameters are evaluated using several methods of parameter estimation : such as the least squares, the instrumental variable, the maximum likelihood and the limited information maximum likelihood methods. Then the parameters of the equation of motion are recovered therefrom. Numerical example is given for a 3-story building model subjected to an earthquake exitation.

• Communications for Statistical Applications and Methods
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• v.23 no.3
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• pp.241-250
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• 2016

In this paper, we consider statistical inferences on the estimation of the parameters of a Weibull distribution when data are randomly censored. Maximum likelihood estimators (MLEs) and approximate MLEs are derived to estimate the parameters. We consider two cases for the censoring model: the assumption that the censoring distribution does not involve any parameters of interest and a censoring distribution that follows a Weibull distribution. A simulation study is conducted to compare the performances of the estimators. The result shows that the MLEs and the approximate MLEs are similar in terms of biases and mean square errors; in addition, the assumption of the censoring model has a strong influence on the estimation of scale parameter.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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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.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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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 Statistical Society
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• v.26 no.3
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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.