Seung-Chun Lee

A measure of association for complex data

A measure of association for complex data types is proposed based on the measure of departure from independence using the p-value of a statistical independence test. The measure is numerically shown to be comparable to Silveys general measure of association. It is demonstrated with real data sets of complex data types that the measure works efficiently for the decision tree and the logistic regression at the initial stage of variable selection.

Interval estimation of binomial proportions based on weighted Polya posterior

Recently the interval estimation of binomial proportions is revisited in various literatures. This is mainly due to the erratic behavior of the coverage probability of the well-known Wald confidence interval. Various alternatives have been proposed. Among them, Agresti-Coull confidence interval has been recommended by Brown et al. [2001. Interval estimation for a binomial proportion. Statist. Sci. 16, 101-133] with other confidence intervals such as the Wilson interval and the equal tailed interval resulting from the natural noninformative Jefferys prior for a binomial proportion. However, it seems that Agresti-Coull interval is little bit wider than necessary when sample size is small, say n=<40. In this note, an interval estimator is developed using weighted Polya posterior. It is shown that the confidence interval based on the weighted Polya posterior is essentially the Agresti-Coull interval with some improved features.

Bayesian Interval Estimation of Tobit Regression Model

Abstract The Bayesian method can be applied successfully to the estimation of the censored regression model intro-duced by Tobin (1958). The Bayes estimates show improvements over the maximum likelihood estimate;however, the performance of the Bayesian interval estimation is questionable. In Bayesian paradigm, theprior distribution usually reects personal beliefs about the parameters. Such subjective priors will typi-cally yield interval estimators with poor frequentist properties; however, an objective noninformative oftenyields a Bayesian procedure with good frequentist properties. We examine the performance of frequentistproperties of noninformative priors for the Tobit regression model.Keywords: Gibbs sampling, noninformative prior, censored regression model, coverage probability. 1. 서론 임상실험의생존분석데이터에는 중도절단된관측값이포함되어 있는 경우가 흔히 있다. 일반적으로 선형모형의모수는 최소제곱법에 의해 추정되고 있으나 이와 같이중도절단된데이터에 의한 최소제곱추정량은편의추정량(biased estimator)이라는 것이잘알려져 있으며 특히, 중도절단된데이터의비중이클 경우, 편의의정도가 커지기 때문에 설명변수의영향을과소, 또는 과대 추정하게 된다. 그러므로 최소제곱법의의한 분석은오류를 피할 수없다. 이러한 이유로 Amemiya (1984), Green (1990) 등많은학자들이반응변수가 중도절단된토빗모형(Tobit model)에서모수추정방법을연구하였다.토빗회귀모형에 대한 빈도학파의추정방법은최대가능도추정법(maximum likelihood estimation)으로귀결되며, censReg 패캐지의censReg 함수, VGAM 패키지의Tobit 함수, survival 패키지의survreg등다양한 패키지에 구현되어 있다. 한편, Chib (1992)은베이지안 추정에서모수의사후분포 기대값을몬테칼로 적분, 라플라스근사법 (Tierney와 Kadane, 1986) 및 깁스샘플링(Gibbs sampling)으로구하는 방법에 대해 모의실험을하였다. 이모의실험에서그는 표본크기가 큰 경우는 베이지안 추정과최대가능도추정은큰 차이를 보이지 않지만, 표본크기가 작은경우에는 베이지안 추정값이최대가능도추정값보다 실제값에 가까운 것으로 결론지었다. 그러나 베이지안 추정값의표준오차가 최대가능도 추정의표준오차보다 모든표본크기에서대체로 큰 값을갖는다고 하였다. 이는 두추정방법 중 어느 하

Bayesian Inference for Censored Panel Regression Model

Abstract It was recognized by some researchers that the disturbance variance in a censored regression model is fre-quently underestimated by the maximum likelihood method. This underestimation has implications for the es-timation of marginal effects and asymptotic standard errors. For instance, the actual coverage probability of theconfidence interval based on a maximum likelihood estimate can be significantly smaller than the nominal con-fidence level; consequently, a Bayesian estimation is considered to overcome this difficulty. The behaviors ofthe maximum likelihood and Bayesian estimators of disturbance variance are examined in a fixed effects panelregression model with a limited dependent variable, which is known to have the incidental parameter problem. Behavior under random effect assumption is also investigated.Keywords: Censored panel regression, Gibbs sampling, incidental parameter problem. 1. Introduction In many statistical data analysis, a dependent variable could be subject to censoring due to a varietyof reasons. In particular, the censored data is common in survival analysis. The ordinary least squaresmethod fails to provide consistent estimates for a conventional regression model, if the fraction ofcensored data is significant. This leads to discuss the estimation methods in a censored regressionmodel (see,

Confidence Intervals for the Difference of Binomial Proportions in Two Doubly Sampled Data

The construction of asymptotic confidence intervals is considered for the difference of binomial proportions in two doubly sampled data subject to false-positive error. The coverage behaviors of several likelihood based confidence intervals and a Bayesian confidence interval are examined. It is shown that a hierarchical Bayesian approach gives a confidence interval with good frequentist properties. Confidence interval based on the Rao score is also shown to have good performance in terms of coverage probability. However, the Wald confidence interval covers true value less often than nominal level.

Interval Estimation of Population Proportion in a Double Sampling Scheme

The double sampling scheme is effective in reducing the sampling cost. However, the doubly sampled data is contaminated by two types of error, namely false-positive and false-negative errors. These would make the statistical analysis more difficult, and it would require more sophisticate analysis tools. For instance, the Wald method for the interval estimation of a proportion would not work well. In fact, it is well known that the Wald confidence interval behaves very poorly in many sampling schemes. In this note, the property of the Wald interval is investigated in terms of the coverage probability and the expected width. An alternative confidence interval based on the Agresti-Coulls approach is recommended.

A Comparison of Bayesian and Maximum Likelihood Estimations in a SUR Tobit Regression Model

Both Bayesian and maximum likelihood methods are efficient for the estimation of regression coefficients of various Tobit regression models (see. e.g. Chib, 1992; Greene, 1990; Lee and Choi, 2013); however, some researchers recognized that the maximum likelihood method tends to underestimate the disturbance variance, which has implications for the estimation of marginal effects and the asymptotic standard error of estimates. The underestimation of the maximum likelihood estimate in a seemingly unrelated Tobit regression model is examined. A Bayesian method based on an objective noninformative prior is shown to provide proper estimates of the disturbance variance as well as other regression parameters

The Role of Artificial Observations in Testing for the Difference of Proportions in Misclassified Binary Data

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

Theoretical Considerations for the Agresti-Coull Type Confidence Interval in Misclassified Binary Data

Although misclassified binary data occur frequently in practice, the statistical methodology available for the data is rather limited. In particular, the interval estimation of population proportion has relied on the classical Wald method. Recently, Lee and Choi (2009) developed a new confidence interval by applying the Agresti-Coulls approach and showed the efficiency of their proposed confidence interval numerically, but a theoretical justification has not been explored yet. Therefore, a Bayesian model for the misclassified binary data is developed to consider the Agresti-Coull confidence interval from a theoretical point of view. It is shown that the Agresti-Coull confidence interval is essentially a Bayesian confidence interval.

Likelihood Based Confidence Intervals for the Difference of Proportions in Two Doubly Sampled Data with a Common False-Positive Error Rate

Lee (2010) developed a confidence interval for the difference of binomial proportions in two doubly sampled data subject to false-positive errors. The confidence interval seems to be adequate for a general double sampling model subject to false-positive misclassification. However, in many applications, the false-positive error rates could be the same. On this note, the construction of asymptotic confidence interval is considered when the false-positive error rates are common. The coverage behaviors of nine likelihood based confidence intervals are examined. It is shown that the confidence interval based Rao score with the expected information has good performance in terms of coverage probability and expected width.