Power and Sample Size for Approximate Chi-Square Tests

Approximate chi-square tests for hypotheses concerning multinomial probabilities are considered in many textbooks. In this article power calculations and sample size based on power are discussed and illustrated for the three most frequently used tests of this type. Available noncentrality parameters and existing tables permit a relatively easy solution of these kinds of problems.     

Inferences on the reliability in balanced and unbalanced one-way random models

In this article, the hypothesis testing and interval estimation for the reliability parameter are considered in balanced and unbalanced one-way random models. The tests and confidence intervals for the reliability parameter are developed using the concepts of generalized p-value and generalized confidence interval. Furthermore, some simulation results are presented to compare the performances between the proposed approach and the existing approach. For balanced models, the simulation results indicate that the proposed approach can provide satisfactory coverage probabilities and performs better than the existing approaches across the wide array of scenarios, especially for small sample sizes. For unbalanced models, the simulation results show that the two proposed approaches perform more satisfactorily than the existing approach in most cases. Finally, the proposed approaches are illustrated using two real examples.     

Liu estimator in partly linear regression models with correlated errors

This article is concerned with the parameter estimation in partly linear regression models when the errors are dependent. To overcome the multicollinearity problem, a generalized Liu estimator is proposed. The theoretical properties of the proposed estimator and its relationship with some existing methods designed for partly linear models are investigated. Finally, a hypothetical data is conducted to illustrate some of the theoretical results.     

On several estimates to the precision parameter of Dirichlet process prior

The article presents careful comparisons among several empirical Bayes estimates to the precision parameter of Dirichlet process prior, with the setup of univariate observations and multigroup data. Specifically, the data are equipped with a two-stage compound sampling model, where the prior is assumed as a Dirichlet process that follows within a Bayesian nonparametric framework. The precision parameter α measures the strength of the prior belief and kinds of estimates are generated on the basis of observations, including the naive estimate, two calibrated naive estimates, and two different types of maximum likelihood estimates stemming from distinct distributions. We explore some theoretical properties and provide explicitly detailed comparisons among these estimates, in the perspectives of bias, variance, and mean squared error. Besides, we further present the corresponding calculation algorithms and numerical simulations to illustrate our theoretical achievements.     

Testing equality of two beta binomial proportions in the presence of unequal extra-dispersion parameters

Data in the form of proportions with extra-dispersion (over/under) arise in many biomedical, epidemiological, and toxicological applications. In some situations, two samples of data in the form of proportions with extra-dispersion arise in which the problem is to test the equality of the proportions in the two groups with unspecified and possibly unequal extra-dispersion parameters. This problem is analogous to the traditional Behrens-Fisher problem in which two normal population means with possibly unequal variances are compared. To deal with this problem we develop eight tests and compare them in terms of empirical size and power, using a simulation study. Simulations show that a C(α) test based on extended quasi-likelihood estimates of the nuisance parameters holds nominal level most effectively (close to the nominal level) and it is at least as powerful as any other statistic that is not liberal. It has the simplest formula, is based on estimates of the nuisance parameters only under the null hypothesis, and is easiest to calculate. Also, it is robust in the sense that no distributional assumption is required to develop this statistic.     

Linearly admissible estimators of the common mean parameter under balanced loss function

Admissibility of linear estimators of the common mean parameter is investigated in the context of a linear model under balanced loss function. Sufficient and necessary conditions for linear estimators to be admissible in classes of homogeneous and non homogeneous linear estimators are obtained, respectively.     

Lower Risk Bounds and Properties of Confidence Sets for Ill‐Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation,Unit Roots,and Estimation of Long Memory Parameters

Important estimation problems in econometrics like estimating the value of a spectral density at frequency zero, which appears in the econometrics literature in the guises of heteroskedasticity and autocorrelation consistent variance estimation and long run variance estimation, are shown to be “ill‐posed” estimation problems. A prototypical result obtained in the paper is that the minimax risk for estimating the value of the spectral density at frequency zero is infinite regardless of sample size, and that confidence sets are close to being uninformative. In this result the maximum risk is over commonly used specifications for the set of feasible data generating processes. The consequences for inference on unit roots and cointegration are discussed. Similar results for persistence estimation and estimation of the long memory parameter are given. All these results are obtained as special cases of a more general theory developed for abstract estimation problems, which readily also allows for the treatment of other ill‐posed estimation problems such as, e.g., nonparametric regression or density estimation.     

基于二元Logistic模型的农村劳动力转移培训需求意愿研究

通过对农村劳动力转移培训需求进行二元Logistic模型检验,发现女性、已婚、群众、转移时间长、目前工作状况不好,以及能对未来家庭生活有所改善等因素可以促进农村劳动力进行转移培训。对此,政府应加大对农村劳动力的培训力度,切实提高培训质量,推行培训与职业资格认证制度的结合。     

Long-range dependence analysis of Internet traffic

Long-range-dependent time series are endemic in the statistical analysis of Internet traffic. The Hurst parameter provides a good summary of important self-similar scaling properties. We compare a number of different Hurst parameter estimation methods and some important variations. This is done in the context of a wide range of simulated, laboratory-generated, and real data sets. Important differences between the methods are highlighted. Deep insights are revealed on how well the laboratory data mimic the real data. Non-stationarities, which are local in time, are seen to be central issues and lead to both conceptual and practical recommendations.