On Profile Likelihood for Gamma Frailty Models

하일도 한국데이터정보과학회 2006 한국데이터정보과학회지 Vol.17 No.3

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.

On Profile Likelihood for Gamma Frailty Models

Ha, Il-Do Korean Data and Information Science Society 2006 한국데이터정보과학회지 Vol.17 No.3

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.

Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models

HA, IL DO,NOH, MAENGSEOK,LEE, YOUNGJO Blackwell Publishing Ltd 2010 Scandinavian journal of statistics, theory and app Vol.37 No.2

<P>Abstract. </P><P>Frailty models with a non-parametric baseline hazard are widely used for the analysis of survival data. However, their maximum likelihood estimators can be substantially biased in finite samples, because the number of nuisance parameters associated with the baseline hazard increases with the sample size. The penalized partial likelihood based on a first-order Laplace approximation still has non-negligible bias. However, the second-order Laplace approximation to a modified marginal likelihood for a bias reduction is infeasible because of the presence of too many complicated terms. In this article, we find adequate modifications of these likelihood-based methods by using the hierarchical likelihood.</P>

Profile Likelihood Approach for Cox's Model

Ha, Il-Do,Shin, Yang-Kyu 慶山大學校 基礎科學硏究所 1999 基礎科學 Vol.3 No.1

모수모형에서 장애모수가 존재할 때 흥미모수를 추론하는 문제는 단면우도를 사용함으로써 종종 극복되어진다. Cox(1972)의 준모수 모형에서 주 관심이 되는 고정효과를 추론함에 있어 이러한 단면우도 접근이 또한 적용될 수 있다. 본 논문에서는 Johansen(1983)에 의해 토론된 단면우도를 이용하여 Cox 모형을 추론하는 간단한 방법을 제안한다. The problem of inference for the interest parameters in the presence of the nuisance parameters under parametric models is frequently overcome by using a profile likelihood. The profile likelihood approach can also be applied for inference of fixed effects in Cox's(1972) semiparametric model. In this paper we propose an inferential method of Cox's model, using a profile likelihood discussed by Johansen(1983).

Likelihood-Based Inference on Genetic Variance Component with a Hierarchical Poisson Generalized Linear Mixed Model

Lee, C. Asian Australasian Association of Animal Productio 2000 Animal Bioscience Vol.13 No.8

This study developed a Poisson generalized linear mixed model and a procedure to estimate genetic parameters for count traits. The method derived from a frequentist perspective was based on hierarchical likelihood, and the maximum adjusted profile hierarchical likelihood was employed to estimate dispersion parameters of genetic random effects. Current approach is a generalization of Henderson's method to non-normal data, and was applied to simulated data. Underestimation was observed in the genetic variance component estimates for the data simulated with large heritability by using the Poisson generalized linear mixed model and the corresponding maximum adjusted profile hierarchical likelihood. However, the current method fitted the data generated with small heritability better than those generated with large heritability.

Semiparametric inference with a functional-form empirical likelihood

Sixia Chen,김재광 한국통계학회 2014 Journal of the Korean Statistical Society Vol.43 No.2

A functional-form empirical likelihood method is proposed as an alternative methodto the empirical likelihood method. The proposed method has the same asymptoticproperties as the empirical likelihood method but has more flexibility in choosing theweight construction. Because it enjoys the likelihood-based interpretation, the profilelikelihood ratio test can easily be constructed with a chi-square limiting distribution. Somecomputational details are also discussed, and results from finite-sample simulation studiesare presented.

Empirical likelihood for partially linear varying-coefficient models with missing response variables and error-prone covariates

Chuanhua Wei,Changlin Mei 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.1

In this study, the empirical likelihood method is applied to the partially linear varyingcoefficient model in which some covariates are measured with additive errors and the response variable is sometimes missing. Based on the correction-for-attenuation technique, we define an empirical likelihood-based statistic for the parametric component and show that its limiting distribution is chi-square distribution. The confidence regions of the parameters are constructed accordingly. Furthermore, a simulation study is conducted to evaluate the performance of the proposed method.

The Role of Artificial Observations in Misclassified Binary Data with Common False-Positive Error

Lee, Seung-Chun The Korean Statistical Society 2012 응용통계연구 Vol.25 No.4

An Agresti-Coull type test is considered for the difference of binomial proportions in two doubly sampled data subject to common false-positive error. The performance of the test is compared with likelihood-based tests. The Agresti-Coull test has many desirable properties in that it can approximate the nominal significance level well, and has comparable power performance with a computational advantage.

Adaptive structure inferences on partially linear error-in-functionmodels with error-prone covariates

Ziyi Ye,Zhensheng Huang,Haiying Ding 한국통계학회 2020 Journal of the Korean Statistical Society Vol.49 No.1

Model structural inference on semiparametricmeasurement errormodels have not been well developed in the existing literature, partially due to the difficulties in dealing with unobservable covariates. In this study, a framework for adaptive structure selection is developed in partially linear error-in-function models with error-prone covariates. Firstly, based on the profile-least-square estimators of the current models, we define two test statistics via generalized likelihood ratio (GLR) test method (Fan et al. in Ann Stat 29(1):153–193, 2001). The proposed test statistics are shown to possess the Wilks-type properties, and a class of new Wilks phenomenon is unveiled in the family of semiparametric measurement error models. Then, we demonstrate that the GLR statistics asymptotically follow chi-squared distributions under null hypotheses. Further, we propose efficient algorithms to implement our methodology and assess the finite sample performance by simulated examples. A real example is given to illustrate the performance of the present methodology.

Power t distribution

Zhao, Jun,Kim, Hyoung-Moon The Korean Statistical Society 2016 Communications for statistical applications and me Vol.23 No.4

In this paper, we propose power t distribution based on t distribution. We also study the properties of and inferences for power t model in order to solve the problem of real data showing both skewness and heavy tails. The comparison of skew t and power t distributions is based on density plots, skewness and kurtosis. Note that, at the given degree of freedom, the kurtosis's range of the power t model surpasses that of the skew t model at all times. We draw inferences for two parameters of the power t distribution and four parameters of the location-scale extension of power t distribution via maximum likelihood. The Fisher information matrix derived is nonsingular on the whole parametric space; in addition we obtain the profile log-likelihood functions on two parameters. The response plots for different sample sizes provide strong evidence for the estimators' existence and unicity. An application of the power t distribution suggests that the model can be very useful for real data.