上市公司初始股权结构分析

上市公司发起人对初始股权结构的设计是筹资者与投资者之间的第一次也是非常重要的一次“契约安排”。在价格管制与额度发行背景下,发起人必须在发股收入最大化与持股比例最大化之间有所取舍,不能两者兼得。本文建立了指导发起人在实现自身利益最大化目标下壬响设计初始股权结构的模型,并以此模型计算结果为最优初始股权结构。对上市公司初始股权结构设计现状进行的实证研究,发现实际发起人持股比例远高于最优持股比例,并对“65％现象”进行了新的解释。     

Bayesian inference for the proportion of true null hypotheses using minimum Hellinger distance

It is important that the proportion of true null hypotheses be estimated accurately in a multiple hypothesis context. Current estimation methods, however, are not suitable for high-dimensional data such as microarray data. First, they do not consider the (strong) dependence between hypotheses (or genes), thereby resulting in inaccurate estimation. Second, the unknown distribution of false null hypotheses cannot be estimated properly by these methods. Third, the estimation is affected strongly by outliers. In this paper, we find out the optimal procedure for estimating the proportion of true null hypotheses under a (strong) dependence based on the Dirichlet process prior. In addition, by using the minimum Hellinger distance, the estimation should be robust to any model misspecification as well as to any outliers while maintaining efficiency. The results are confirmed by a simulation study, and the newly developed methodology is illustrated by a real microarray data.     

Design of a rotation scheme for a stratified multi-stage sample

A rotation scheme for a stratified multi-stage sample, discussed in this paper, was designed to statisfy the following conditions: (i) there is a constraint on the number of units that can be replaced in each round, and (ii) it is relatively inexpensive to increase the sample size gradually. An example of these conditions was observed in the development of a plan for measuring the accuracy of the billing process of a telephone company. Estimators of the population proportion of elements that possess a specified characteristic are also derived. Each estimator is a weighted average of the corresponding estimates based on the retained units from the original sample and on the new units, where the weight of the estimate based on the new units increases over time. While this rotation scheme is discussed in connection with the billing accuracy of a telephone company, the methodology can be applied to other similar problems.     

Estimation of proportion ratio in non-compliance randomized trials with repeated measurements in binary data

It is not uncommon to encounter a randomized clinical trial (RCT) in which each patient is treated with several courses of therapies and his/her response is taken after treatment with each course because of the nature of a treatment design for a disease. On the basis of a simple multiplicative risk model proposed elsewhere for repeated binary measurements, we derive the maximum likelihood estimator (MLE) for the proportion ratio (PR) of responses between two treatments in closed form without the need of modeling the complicated relationship between patient’s compliance and patient’s response. We further derive the asymptotic variance of the MLE and propose an asymptotic interval estimator for the PR using the logarithmic transformation. We also consider two other asymptotic interval estimators. One is derived from the principle of Fieller’s Theorem and the other is derived by using the randomization-based approach suggested elsewhere. To evaluate and compare the finite-sample performance of these interval estimators, we apply the Monte Carlo simulation. We find that the interval estimator using the logarithmic transformation of the MLE consistently outperforms the other two estimators with respect to efficiency. This gain in efficiency can be substantial especially when there are patients not complying with their assigned treatments. Finally, we employ the data regarding the trial of using macrophage colony stimulating factor (M-CSF) over three courses of intensive chemotherapies to reduce febrile neutropenia incidence for acute myeloid leukemia patients to illustrate the use of these estimators.     

Improved Empirical Bayes Estimation in Group Testing Procedure for Small Proportions

Group testing has been long recognized as an efficient method to classify all the experimental units into two mutually exclusive categories: defective or not defective. In recent years, more attention has been brought to the estimation of the population prevalence rate p of a disease, or of some property, using group testing. In this article, we propose two scaled squared-error loss functions, which improve the Bayesian approach to estimating p in terms of minimizing the mean squared error (MSE) of the Bayes estimators of p for small p. We show that the new estimators are preferred over the estimator from the usual squared-error loss function and the maximum likelihood estimator (MLE) for small p.