• Title, Summary, Keyword: likelihood method

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On Profile Likelihood for Gamma Frailty Models

  • Ha, Il-Do
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.3
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    • pp.999-1007
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    • 2006
  • The semiparametric gamma frailty models have been often used for multivariate survival analysis because they give an explicit marginal likelihood. The commonly used estimation procedure is the profile likelihood method based on marginal likelihood, which provides the same parameter estimates as the EM algorithm. In this paper we show in finite samples the standard profile-likelihood method can lead to an underestimation of parameters, particularly for the frailty parameter. To overcome this problem, we propose an adjusted profile-likelihood method. For the illustration a numerical example and a small-sample simulation study are presented.

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Quasi-Likelihood Approach for Linear Models with Censored Data

  • Ha, Il-Do;Cho, Geon-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.9 no.2
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    • pp.219-225
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    • 1998
  • The parameters in linear models with censored normal responses are usually estimated by the iterative maximum likelihood and least square methods. However, the iterative least square method is simple but hardly has theoretical justification, and the iterative maximum likelihood estimating equations are complicatedly derived. In this paper, we justify these methods via Wedderburn (1974)'s quasi-likelihood approach. This provides an explicit justification for the iterative least square method and also directly the iterative maximum likelihood method for estimating the regression coefficients.

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A correction of SE from penalized partial likelihood in frailty models

  • Ha, Il-Do
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.5
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    • pp.895-903
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    • 2009
  • The penalized partial likelihood based on restricted maximum likelihood method has been widely used for the inference of frailty models. However, the standard-error estimate for frailty parameter estimator can be downwardly biased. In this paper we show that such underestimation can be corrected by using hierarchical likelihood. In particular, the hierarchical likelihood gives a statistically efficient procedure for various random-effect models including frailty models. The proposed method is illustrated via a numerical example and simulation study. The simulation results demonstrate that the corrected standard-error estimate largely improves such bias.

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An Approximation of the Cumulant Generating Functions of Diffusion Models and the Pseudo-likelihood Estimation Method (확산모형에 대한 누율생성함수의 근사와 가우도 추정법)

  • Lee, Yoon-Dong;Lee, Eun-Kyung
    • Journal of the Korean Operations Research and Management Science Society
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    • v.38 no.1
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    • pp.201-216
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    • 2013
  • Diffusion is a basic mathematical tool for modern financial engineering. The theory of the estimation methods for diffusion models is an important topic of the financial engineering. Many researches have been tried to apply the likelihood estimation method for estimating diffusion models. However, the likelihood estimation method for diffusion is complicated and needs much amount of computing. In this paper we develop the estimation methods which are simple enough to be compared to the Euler approximation method, and efficient enough statistically to be compared to the likelihood estimation method. We devise pseudo-likelihood and propose the maximum pseudo-likelihood estimation methods. The pseudo-likelihoods are obtained by approximating the transition density with normal distributions. The means and the variances of the distributions are obtained from the delta expansion suggested by Lee, Song and Lee (2012). We compare the newly suggested estimators with other existing estimators by simulation study. From the simulation study we find the maximum pseudo-likelihood estimator has very similar properties with the maximum likelihood estimator. Also the maximum pseudo-likelihood estimator is easy to apply to general diffusion models, and can be obtained by simple numerical steps.

EXTENSION OF FACTORING LIKELIHOOD APPROACH TO NON-MONOTONE MISSING DATA

  • Kim, Jae-Kwang
    • Journal of the Korean Statistical Society
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    • v.33 no.4
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    • pp.401-410
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    • 2004
  • We address the problem of parameter estimation in multivariate distributions under ignorable non-monotone missing data. The factoring likelihood method for monotone missing data, termed by Rubin (1974), is extended to a more general case of non-monotone missing data. The proposed method is algebraically equivalent to the Newton-Raphson method for the observed likelihood, but avoids the burden of computing the first and the second partial derivatives of the observed likelihood. Instead, the maximum likelihood estimates and their information matrices for each partition of the data set are computed separately and combined naturally using the generalized least squares method.

H-likelihood approach for variable selection in gamma frailty models

  • Ha, Il-Do;Cho, Geon-Ho
    • Journal of the Korean Data and Information Science Society
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    • v.23 no.1
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    • pp.199-207
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    • 2012
  • Recently, variable selection methods using penalized likelihood with a shrink penalty function have been widely studied in various statistical models including generalized linear models and survival models. In particular, they select important variables and estimate coefficients of covariates simultaneously. In this paper, we develop a penalize h-likelihood method for variable selection in gamma frailty models. For this we use the smoothly clipped absolute deviation (SCAD) penalty function, which satisfies a good property in variable selection. The proposed method is illustrated using simulation study and a practical data set.

A Study on Evaluation Method of Fatigue Strength Data Using Likelihood Interval Estimation Method (우도구간 추정법에 의한 피로강도 데이터 평가법에 관한 연구)

  • 최창섭
    • Journal of the Korean Society of Safety
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    • v.10 no.2
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    • pp.10-16
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    • 1995
  • In estimating the fatigue data, only the uniform safety rate has been applied so far However, since more reasonable design concepts such as machine structures or subsidiary materials will be required in the future, the importance of a statistical estimation method for fatigue data is being highlighted. With such basic conception in mind, this study was aimed at critically discussing the interval estimation method which has been applied using the classical statistics thus far It was conceived that this conventional method would result in the estimation of the unstable side from the viewpoint of the likelihood Interval estimation method. In this regard, this study aimed at estimating the fatigue strength through the likelihood interval estimation method comparing it with the conventional interval estimation method would result in the estimation of the unstable side from the viewpoint of the likelihood interval estimation method. One of the methods using the likelihood for estimation data is the Bayes method. Based on this theory, statistical estimations were positivly applied, and thereupon, the fatigue data were estimated.

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A Simplified Blind Decision Method of Modulation Type in impaired AWGN Channel Environment (Impaired AWGN 채널에서의 간단한 Blind 변조 신호 구분 방식)

  • Kim, Young-Wan
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.11 no.1
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    • pp.1-6
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    • 2007
  • In this paper, a simplified new modulation classification method that utilizes likelihood function for received signal in an impaired AWGN channel environment. The proposed method provides the superior to ML method, although the likelihood under the assumption that each modulated signal is sent utilized. On the other hand, the ML method gets the performance characteristics of high computational complexity and weakness to channel impairment such as phase offsets and frequency offsets. The proposed method has lower computational complexity than that of the ML method. Moreover, the proposed method is robust to the channel impairment such as phase offsets and frequency offsets. The correct classification probabilities of the proposed method and the ML method are given for an AWGN channel with phase offsets and frequency offsets, which were simulated with extensive Monte-Carlo simulation. As shown in simulation resole, a more accurate classification performance both in phase offset environment and in frequency offset can be achieved with the low computational complexity of the proposed method.

Automatic Speech Database Verification Method Based on Confidence Measure

  • Kang Jeomja;Jung Hoyoung;Kim Sanghun
    • MALSORI
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    • no.51
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    • pp.71-84
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    • 2004
  • In this paper, we propose the automatic speech database verification method(or called automatic verification) based on confidence measure for a large speech database. This method verifies the consistency between given transcription and speech using the confidence measure. The automatic verification process consists of two stages : the word-level likelihood computation stage and multi-level likelihood ratio computation stage. In the word-level likelihood computation stage, we calculate the word-level likelihood using the viterbi decoding algorithm and make the segment information. In the multi-level likelihood ratio computation stage, we calculate the word-level and the phone-level likelihood ratio based on confidence measure with anti-phone model. By automatic verification, we have achieved about 61% error reduction. And also we can reduce the verification time from 1 month in manual to 1-2 days in automatic.

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Likelihood ratio in estimating gamma distribution parameters

  • Rahman, Mezbahur;Muraduzzaman, S. M.
    • Journal of the Korean Data and Information Science Society
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    • v.21 no.2
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    • pp.345-354
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    • 2010
  • The Gamma Distribution is widely used in Engineering and Industrial applications. Estimation of parameters is revisited in the two-parameter Gamma distribution. The parameters are estimated by minimizing the likelihood ratios. A comparative study between the method of moments, the maximum likelihood method, the method of product spacings, and minimization of three different likelihood ratios is performed using simulation. For the scale parameter, the maximum likelihood estimate performs better and for the shape parameter, the product spacings estimate performs better. Among the three likelihood ratio statistics considered, the Anderson-Darling statistic has inferior performance compared to the Cramer-von-Misses statistic and the Kolmogorov-Smirnov statistic.