个人教育投资的风险收益测度

将教育资本分解成受教育程度和职业的各种组合,借鉴Markowiz的有效投资组合理论,计算Mincer收入方程中扰动项的均值—标准差来衡量投资风险收益,以此建立中国教育投资风险和收益之间的平衡关系,并且利用F检验衡量投资组合的均值方差张成。结果表明,有效的教育资本组合不仅与所接受教育程度有关,还与未来职业选择有关。在以受教育程度为高中和中等职业的基础上,高中(06)可以张成其他全部14个投资组合的均值方差边界。因此,个体和政府在进行教育投资时,都需要全面衡量投资组合的风险收益平衡问题。     

Modified maximum likelihood estimator under the Jones and Faddy's skew t-error distribution for censored regression model

It is well-known that classical Tobit estimator of the parameters of the censored regression (CR) model is inefficient in case of non-normal error terms. In this paper, we propose to use the modified maximum likelihood (MML) estimator under the Jones and Faddy''s skew t-error distribution, which covers a wide range of skew and symmetric distributions, for the CR model. The MML estimators, providing an alternative to the Tobit estimator, are explicitly expressed and they are asymptotically equivalent to the maximum likelihood estimator. A simulation study is conducted to compare the efficiencies of the MML estimators with the classical estimators such as the ordinary least squares, Tobit, censored least absolute deviations and symmetrically trimmed least squares estimators. The results of the simulation study show that the MML estimators work well among the others with respect to the root mean square error criterion for the CR model. A real life example is also provided to show the suitability of the MML methodology.     

Double and group acceptance sampling plan for truncated life test based on inverse log-logistic distribution

This paper introduces a double and group acceptance sampling plans based on time truncated lifetimes when the lifetime of an item follows the inverse log-logistic (ILL) distribution with known shape parameter. The operating characteristic function and average sample number (ASN) values of the double acceptance sampling inspection plan are provided. The values of the minimum number of groups and operating characteristic function for various quality levels are obtained for a group acceptance sampling inspection plan. A comparative study between single acceptance sampling inspection plan and double acceptance sampling inspection plan is carried out in terms of sample size. One simulated example and four real-life examples are discussed to show the applicability of the proposed double and group acceptance sampling inspection plans for ILL distributed quality parameters.     

Robust inference for group sequential trials

For ethical reasons, group sequential trials were introduced to allow trials to stop early in the event of extreme results. Endpoints in such trials are usually mortality or irreversible morbidity. For a given endpoint, the norm is to use a single test statistic and to use that same statistic for each analysis. This approach is risky because the test statistic has to be specified before the study is unblinded, and there is loss in power if the assumptions that ensure optimality for each analysis are not met. To minimize the risk of moderate to substantial loss in power due to a suboptimal choice of a statistic, a robust method was developed for nonsequential trials. The concept is analogous to diversification of financial investments to minimize risk. The method is based on combining P values from multiple test statistics for formal inference while controlling the type I error rate at its designated value.This article evaluates the performance of 2 P value combining methods for group sequential trials. The emphasis is on time to event trials although results from less complex trials are also included. The gain or loss in power with the combination method relative to a single statistic is asymmetric in its favor. Depending on the power of each individual test, the combination method can give more power than any single test or give power that is closer to the test with the most power. The versatility of the method is that it can combine P values from different test statistics for analysis at different times. The robustness of results suggests that inference from group sequential trials can be strengthened with the use of combined tests.     

Testing independence based on Bernstein empirical copula and copula density

In this paper we provide three nonparametric tests of independence between continuous random variables based on the Bernstein copula distribution function and the Bernstein copula density function. The first test is constructed based on a Cramér-von Mises divergence-type functional based on the empirical Bernstein copula process. The two other tests are based on the Bernstein copula density and use Cramér-von Mises and Kullback–Leibler divergence-type functionals, respectively. Furthermore, we study the asymptotic null distribution of each of these test statistics. Finally, we consider a Monte Carlo experiment to investigate the performance of our tests. In particular we examine their size and power which we compare with those of the classical nonparametric tests that are based on the empirical distribution function.     

Robust tests for the common principal components model

When dealing with several populations, the common principal components (CPC) model assumes equal principal axes but different variances along them. In this paper, a robust log-likelihood ratio statistic allowing to test the null hypothesis of a CPC model versus no restrictions on the scatter matrices is introduced. The proposal plugs into the classical log-likelihood ratio statistic robust scatter estimators. Using the same idea, a robust log-likelihood ratio and a robust Wald-type statistic for testing proportionality against a CPC model are considered. Their asymptotic distributions under the null hypothesis and their partial influence functions are derived. A small simulation study allows to compare the behavior of the classical and robust tests, under normal and contaminated data.     

中国制造业集聚：度量与显著性检验 ——基于集聚测量新方法

 根据集聚分布的自身特点,本文提出了可以进行显著性检验的普适性产业集聚指数,并对我国28制造业1994年的860个样本和2004年800个样本进行测量和检验,我们的计算结果表明,中国制造业的集聚强度总体上呈上升趋势,同时具有集聚和扩散双重现象。     

Modelling udder infection data using copula models for quadruples

We study copula models for correlated infection times in the four udder quarters of dairy cows. Both a semi-parametric and a nonparametric approach are considered to estimate the marginal survival functions, taking into account the effect of a binary udder quarter level covariate. We use a two-stage estimation approach and we briefly discuss the asymptotic behaviour of the estimators obtained in the first and the second stage of the estimation. A pseudo-likelihood ratio test is used to select an appropriate copula from the power variance copula family that describes the association between the outcomes in a cluster. We propose a new bootstrap algorithm to obtain the p-value for this test. This bootstrap algorithm also provides estimates for the standard errors of the estimated parameters in the copula. The proposed methods are applied to the udder infection data. A small simulation study for a setting similar to the setting of the udder infection data gives evidence that the proposed method provides a valid approach to select an appropriate copula within the power variance copula family.