民族共生理论:散杂居民族关系及目标范示研究

本文以生物学中的共生理论为参照,基于生物共生理论的理念范畴和分析方法,结合生物共生理论在其他领域的研究成果,重点考察了我国散杂居民族的共生关系,并提供了民族共生目标范式以及实现途径.     

Two new estimators for the proportion of true null hypotheses in multiple test

In multiple hypothesis test, an important problem is estimating the proportion of true null hypotheses. Existing methods are mainly based on the p-values of the single tests. In this paper, we propose two new estimations for this proportion. One is a natural extension of the commonly used methods based on p-values and the other is based on a mixed distribution. Simulations show that the first method is comparable with existing methods and performs better under some cases. And the method based on a mixed distribution can get accurate estimators even if the variance of data is large or the difference between the null hypothesis and alternative hypothesis is very small.     

Improved likelihood inferences for Weibull regression model

A general procedure is developed for bias-correcting the maximum likelihood estimators (MLEs) of the parameters of Weibull regression model with either complete or right-censored data. Following the bias correction, variance corrections and hence improved t-ratios for model parameters are presented. Potentially improved t-ratios for other reliability-related quantities are also discussed. Simulation results show that the proposed method is effective in correcting the bias of the MLEs, and the resulted t-ratios generally improve over the regular t-ratios.     

Analysis of Type-II hybrid censored competing risks data

Kundu and Gupta [Analysis of hybrid life-tests in presence of competing risks. Metrica. 2007;65:159–170] provided the analysis of Type-I hybrid censored competing risks data, when the lifetime distributions of the competing cause of failures follows exponential distribution. In this paper, we consider the analysis of Type-II hybrid censored competing risks data. It is assumed that latent lifetime distributions of the competing causes of failures follow independent exponential distributions with different scale parameters. It is observed that the maximum likelihood estimators of the unknown parameters do not always exist. We propose the modified estimators of the scale parameters, which coincide with the corresponding maximum likelihood estimators when they exist, and asymptotically they are equivalent. We obtain the exact distribution of the proposed estimators. Using the exact distributions of the proposed estimators, associated confidence intervals are obtained. The asymptotic and bootstrap confidence intervals of the unknown parameters are also provided. Further, Bayesian inference of some unknown parametric functions under a very flexible Beta-Gamma prior is considered. Bayes estimators and associated credible intervals of the unknown parameters are obtained using the Monte Carlo method. Extensive Monte Carlo simulations are performed to see the effectiveness of the proposed estimators and one real data set has been analysed for the illustrative purposes. It is observed that the proposed model and the method work quite well for this data set.     

Estimation of flood frequencies from data sets with outliers using mixed distribution functions

In this paper the estimation of high return period quantiles of the flood peak and volume in the Kolubara River basin are carried out. Estimation of flood frequencies is carried out on a data set containing high outliers which are identified by the Rosner’s test. Simultaneously, low outliers are determined by the multiple Grubbs–Beck. The next step involved the usage of the mixed distribution functions applied to a data set from three populations: floods with low outliers, normal floods and floods with high outliers. The contribution of the data set with low outliers is neglected, since it should underestimate the flood quantiles with large return periods. Consequently, the best fitted mixed distribution from the applied types (EV1, GEV, P3 and LP3) was determined by using the minimum standard error of fit.     

Empirical Uncertain Bayes Methods in Area‐level Models

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area‐level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an estimation error. Thus, it is desirable to consider the uncertain prior distribution, which is expressed as the mixture of a one‐point distribution and a proper prior distribution. In this paper, we develop an empirical Bayes approach for estimating area‐level means, using the uncertain prior distribution in the context of a natural exponential family, which we call the empirical uncertain Bayes (EUB) method. The regression model considered in this paper includes the Poisson‐gamma and the binomial‐beta, and the normal‐normal (Fay–Herriot) model, which are typically used in small area estimation. We obtain the estimators of hyperparameters based on the marginal likelihood by using a well‐known expectation‐maximization algorithm and propose the EUB estimators of area means. For risk evaluation of the EUB estimator, we derive a second‐order unbiased estimator of a conditional mean squared error by using some techniques of numerical calculation. Through simulation studies and real data applications, we evaluate a performance of the EUB estimator and compare it with the usual empirical Bayes estimator.     

Score test for homogeneity of dispersion in generalized Poisson mixed models with excess zeros

In many applications, the clustered count data often contain excess zeros and the zero-inflated generalized Poisson mixed (ZIGPM) regression model may be suitable. However, dispersion in ZIGPM is often treated as fixed unknown parameter, and this assumption may be not appropriate in some situations. In this article, a score test for homogeneity of dispersion parameter in ZIGPM regression model is developed and corresponding test statistic is obtained. Sampling distribution and power of the score test statistic are investigated through Monte Carlo simulation. Finally, results from a biological example illustrate the usefulness of the diagnostic statistic.     

Computational approach test for inference about several correlation coefficients: Equality and common

In this article, we consider inference about the correlation coefficients of several bivariate normal distributions. We first propose computational approach tests for testing the equality of the correlation coefficients. In fact, these approaches are parametric bootstrap tests, and simulation studies show that they perform very satisfactory, and the actual sizes of these tests are better than other existing approaches. We also present a computational approach test and a parametric bootstrap confidence interval for inference about the parameter of common correlation coefficient. At the end, all the approaches are illustrated using two real examples.     

Bootstrap methods for multivariate hypothesis testing

The nonparametric and parametric bootstrap methods for multivariate hypothesis testing are developed. They are used to approximate the null distribution of the test statistics proposed by Duchesne and Francq (2015 Duchesne, P., Francq, C. (2015). Multivariate hypothesis testing using generalized and {2}-inverses—with applications. Statistics 49:475–496.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), resulting in bootstrap testing procedures. In the problem of testing for the mean vector of a multivariate distribution, the asymptotic validity of the bootstrap methods is proved. The finite sample performance of the new solutions is demonstrated by means of Monte Carlo simulation studies. They indicate that for small-sample size, the bootstrap tests provide a better finite sample properties than the asymptotic tests considered by Duchesne and Francq (2015 Duchesne, P., Francq, C. (2015). Multivariate hypothesis testing using generalized and {2}-inverses—with applications. Statistics 49:475–496.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]).