• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1007-1020
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• 2011

Since the research of Black and Scholes (1973), modeling methods using diffusion processes have performed principal roles in financial engineering. In modern financial theories, various types of diffusion processes were suggested and applied in real situations. An estimation of the model parameters is an indispensible step to analyze financial data using diffusion process models. Many estimation methods were suggested and their properties were investigated. This paper reviews the statistical properties of the, Euler approximation method, New Local Linearization(NLL) method, and Generalized Methods of Moment(GMM) that are known as the most practical methods. From the simulation study, we found the NLL and Euler methods performed better than GMM. GMM is frequently used to estimate the parameters because of its simplicity; however this paper shows the performance of GMM is poorer than the Euler approximation method or the NLL method that are even simpler than GMM. This paper shows the performance of the GMM is extremely poor especially when the parameters in diffusion coefficient are to be estimated.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.755-762
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• 2013

In this paper we consider the NHPP software reliability model. And we deal with the maximum likelihood estimation and the Bayesian estimation with conjugate prior for parameter inference in the mean value function of Goel-Okumoto model (1979). The parameter estimates for the proposed model is presented by MLE and Bayes estimator in data set. We compare the predicted number of faults with the actual data set using the proposed mean value function.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.761-769
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• 2018

Simulations are important for survival analyses that deal with censored data. Cox models are widely used in survival analyses, therefore, we investigate how to generate censored data that can simulate the Cox model. Bender et al. (Statistics in Medicine, 24, 1713-1723, 2005) provided a parametric method for generating survival times, but we need to generate censoring times as well as survival times to simulate the censored data. In addition to the parametric method for generating censored data, a nonparametric method is also proposed and applied to a real data set.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.12 no.3
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• pp.211-217
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• 2019

In this study, we compare and analyze the attributes of the software development cost model according to the shape parameters change of the Type-2 Gumbel lifetime distribution using the NHPP model. In order to analyze the software failure phenomena, the parametric estimation is applied to the maximum likelihood estimation method, and the nonlinear equations are calculated using the bisection method. As a result, when the attributes of the cost curves according to the change of shape parameters are compared, it is found that the larger the number of shape parameters, the lower the software development cost and the faster the release time. Through this study, it is expected that it will be helpful for the software developers to search for the development cost according to the software shape parameters change, and also to provide the necessary information for the attributes of the software development cost.

• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.937-944
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• 2021

The problem of selecting variables is addressed in partial linear regression. Model selection for partial linear models is not easy since it involves nonparametric estimation such as smoothing parameter selection and estimation for linear explanatory variables. In this work, several approaches for variable selection are proposed using a fast forward selection algorithm, least angle regression (LARS). The proposed procedures use t-test, all possible regressions comparisons or stepwise selection process with variables selected by LARS. An example based on real data and a simulation study on the performance of the suggested procedures are presented.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1049-1068
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• 2014

Autoregressive models are used to analyze an univariate time series data; however, these methods can be inappropriate when a structural break appears in a time series since they assume that a trend is consistent. Threshold autoregressive models (popular regime-switching models) have been proposed to address this problem. Recently, the models have been extended to two regime-switching models with delay parameter. We discuss two regime-switching threshold autoregressive models from a Bayesian point of view. For a Bayesian analysis, we consider a parametric threshold autoregressive model and a nonparametric threshold autoregressive model using Dirichlet process prior. The posterior distributions are derived and the posterior inferences is performed via Markov chain Monte Carlo method and based on two Bayesian threshold autoregressive models. We present a simulation study to compare the performance of the models. We also apply models to gross domestic product data of U.S.A and South Korea.

• The KIPS Transactions:PartD
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• v.11D no.6
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• pp.1269-1276
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• 2004

The Parameter Estimation for software existing reliability models, Goel-Okumoto, Yamada-Ohba-Osaki model was reviewed and Rayleigh model based on Rayleigh distribution was studied. In this paper, we discusses comparison of parameter estimation using maximum likelihood estimator and Bayesian estimation based on Gibbs sampling to analysis of the estimator' pattern. Model selection based on sum of the squared errors and Braun statistic, for the sake of efficient model, was employed. A numerical example was illustrated using real data. The current areas and models of Superposition, mixture for future development are also employed.

• The Korean Journal of Applied Statistics
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• v.21 no.6
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• pp.923-932
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• 2008

We are likely to face complex multivariate data which can be characterized by having a non-trivial correlation structure. For instance, omitted covariates may simultaneously affect more than one count in clustered data; hence, the modeling of the correlation structure is important for the efficiency of the estimator and the computation of correct standard errors, i.e., valid inference. A standard way to insert dependence among counts is to assume that they share some common unobservable variables. For this assumption, we fitted correlated random effect models considering multilevel model. Estimation was carried out by adopting the semiparametric approach through a finite mixture EM algorithm without parametric assumptions upon the random coefficients distribution.

• The Korean Journal of Applied Statistics
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• v.26 no.5
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• pp.767-783
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• 2013

Generalized Method of Moment(GMM) is a popular estimation method to estimate model parameters in empirical financial studies. GMM is frequently applied to estimate diffusion models that are basic techniques of modern financial engineering. However, recent research showed that GMM had poor properties to estimate the parameters that pertain to the diffusion coefficient in diffusion models. This research corrects the weakness of GMM and suggests alternatives to improve the statistical properties of GMM estimators. In this study, a simulation method is adopted to compare estimation methods. Out of compared alternatives, NGMM-Y, a version of improved GMM that adopts the NLL idea of Shoji and Ozaki (1998), showed the best properties. Especially NGMM-Y estimator is superior to other versions of GMM estimators for the estimation of diffusion coefficient parameters.

• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.115-125
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• 2009

Simultaneous equation models, which are widely used in business and economic areas, generally consist of endogenous variables determined within models and exogenous variables externally determined and in the simultaneous equations model framework there are rank and order conditions for the model identification and the existence of unique solutions. By contrast, their estimating results have less efficiencies and furthermore do not exist, since the most estimating procedures are performed under the assumptions for rank and order conditions. We propose the new statistical test for sufficiency of the rank condition under the order condition, and show the asymptotic properties for the test. The Monte Carlo simulation studies are achieved in order to evaluate its power and to suggest the baseline for satisfying the rank conditions.