• Journal of the Korean Statistical Society
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• v.35 no.4
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• pp.409-417
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• 2006

This article is concerned with threshold modeling of the bifurcating autoregressive model (BAR) originally suggested by Cowan and Staudte (1986) for tree structured data of cell lineage study where each individual $(X_t)$ gives rise to two off-spring $(X_{2t},\;X_{2t+1})$ in the next generation. The triplet $(X_t,\;X_{2t},\;X_{2t+1})$ refers to mother-daughter relationship. In this paper we propose a threshold model incorporating the difference of 'fertility' of the mother for the first and second off-springs, and thereby extending BAR to threshold-BAR (TBAR, for short). We derive a sufficient condition of stationarity for the suggested TBAR model. Also various inferential methods such as least squares (LS), maximum likelihood (ML) and quasi-likelihood (QL) methods are discussed and relevant limiting distributions are obtained.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.723-730
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• 2009

Missing values in time series can be treated as unknown parameters and estimated by maximum likelihood or as random variables and predicted by the expectation of the unknown values given the data. The purpose of this study is to impute missing values which are regarded as the maximum likelihood estimator and random variable in incomplete data and to compare with two methods using ARMA model. For illustration, the Mumps data reported from the national capital region monthly over the years 2001 ${\sim}$ 2006 are used, and results from two methods are compared with using SSF(Sum of square for forecasting error).

• The Journal of Asian Finance, Economics and Business
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• v.5 no.1
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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.

• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.67-81
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• 2005

Most of the previously proposed methods for the frailty model do not work well when there are many tied observations. This is partly because the empirical likelihood used is not suitable for tied observations. In this paper, we propose a new method for the frailty model with many ties. The proposed method obtains the posterior distribution of the parameters using the binomial form empirical likelihood and Bayesian bootstrap. The proposed method yields stable results and is computationally fast. To compare the proposed method with the maximum marginal likelihood approach, we do simulations.

• Journal of Advanced Navigation Technology
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• v.27 no.1
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• pp.43-49
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• 2023

Object tracking is being studied with various techniques such as Kalman filter and Luenberger tracker. Even in situations, such as the one in which the system model is not well specified, to which existing signal processing techniques are not successfully applicable, it is possible to design artificial neural networks to track objects. In this paper, we propose an artificial neural network, which we call 'maximum-likelihood weighted-average neural network', to continuously track unpredictably moving objects. This neural network does not directly estimate the locations of an object but obtains location estimates by making weighted average combining various results of maximum likelihood tracking with different data lengths. We compare the performance of the proposed system with those of Kalman filter and maximum likelihood object trackers and show that the proposed scheme exhibits excellent performance well adapting the change of object moving characteristics.

• MALSORI
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• no.67
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• pp.79-102
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• 2008

In this paper, we investigate the relation between Bayes factor and likelihood ratio test (LRT) approaches and apply the neighborhood information of Bayes factor to building an alternate hypothesis model of the LRT system. To consider the neighborhood approaches, we contemplate a distance measure between models and algorithms to be applied. We also evaluate several methods to improve performance of utterance verification using neighborhood information. Among these methods, the system which adopts anti-models built by collecting mixtures of neighborhood models obtains maximum error rate reduction of 17% compared to the baseline, linear and weighted combination of neighborhood models.

• Journal of the Korean Statistical Society
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• v.2 no.1
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• pp.9-15
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• 1973

In the first-order moving average model, we present the exact likelihood equations as function of variance, correlation and parameters of coefficients in the orthogonally transformed model. Existence of maximum likelihood estimates for these unknowns are studied and a computational method is provided. (Because of the limited space Ive do not present the computer program which is written in FORTRAN.) 40 sets of generated data and economic data are used to demonstrate, and few of them are presented in the Appendix. A numerical comparison of MLE with the efficient estimate proposed by Durbin is presented in the particular case.

• The Korean Journal of Applied Statistics
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• v.27 no.5
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• pp.755-771
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• 2014

Isotropy is one of the main assumptions for the ease of spatial prediction (named kriging) based on some covariance models. A lack of isotropy (or anisotropy) in a spatial process necessitates that some additional parameters (angle and ratio) for anisotropic covariance model be obtained in order to produce a more reliable prediction. In this paper, we propose a new class of geometrically extended anisotropic covariance models expressed as a weighted average of some geometrically anisotropic models. The maximum likelihood estimation method is taken into account to estimate the parameters of our interest. We evaluate the performances of our proposal and compare it with an isotropic covariance model and a geometrically anisotropic model in simulation studies. We also employ extended geometric anisotropy to the analysis of real data.

• Journal of the Korean Data and Information Science Society
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• v.20 no.6
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• pp.1169-1175
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• 2009

In this paper, the inferences of data obtained from periodic inspection and type I censoring for the step-stress accelerated life test are studied. The exponential distribution with a failure rate function that a log-linear function of stress and the tampered failure rate model are considered. The maximum likelihood estimators of the model parameters are estimated and also the optimal stress change time which minimize the asymptotic variance of maximum likelihood estimators of parameters is determined. A numerical example will be given to illustrate the proposed inferential procedures and the sensitivity of the asymptotic variance of the estimated mean by the guessed parameters is investigated.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1375-1386
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• 2006

In life testing, the lifetimes of test units under the usual conditions are so long that life testing at usual conditions is impractical. Testing units are subjected to conditions of high stress to yield informations quickly. In this paper, the inferences of parameters on the three step-stress accelerated life testing are studied. The two-parameter exponential distribution with a failure rate function that a log-quadratic function of stress and the tempered failure rate model are considered. We obtain the maximum likelihood estimators of the model parameters and their confidence regions. A numerical example will be given to illustrate the proposed inferential procedures.