Heteroskedasticity-consistent interval estimators

The linear regression model is commonly used in applications. One of the assumptions made is that the error variances are constant across all observations. This assumption, known as homoskedasticity, is frequently violated in practice. A commonly used strategy is to estimate the regression parameters by ordinary least squares and to compute standard errors that deliver asymptotically valid inference under both homoskedasticity and heteroskedasticity of an unknown form. Several consistent standard errors have been proposed in the literature, and evaluated in numerical experiments based on their point estimation performance and on the finite sample behaviour of associated hypothesis tests. We build upon the existing literature by constructing heteroskedasticity-consistent interval estimators and numerically evaluating their finite sample performance. Different bootstrap interval estimators are also considered. The numerical results favour the HC4 interval estimator.     

Interval estimation for misclassification rate parameters in a complementary Poisson model

We investigate three interval estimators for binomial misclassification rates in a complementary Poisson model where the data are possibly misclassified: a Wald-based interval, a score-based interval, and an interval based on the profile log-likelihood statistic. We investigate the coverage and average width properties of these intervals via a simulation study. For small Poisson counts and small misclassification rates, the intervals can perform poorly in terms of coverage. The profile log-likelihood confidence interval (CI) is often proved to outperform the other intervals with good coverage and width properties. Lastly, we apply the CIs to a real data set involving traffic accident data that contain misclassified counts.     

Estimating the propagation rate of a viral infection of potato plants via mixtures of regressions

A problem arising from the study of the spread of a viral infection among potato plants by aphids appears to involve a mixture of two linear regressions on a single predictor variable. The plant scientists studying the problem were particularly interested in obtaining a 95% confidence upper bound for the infection rate. We discuss briefly the procedure for fitting mixtures of regression models by means of maximum likelihood, effected via the EM algorithm. We give general expressions for the implementation of the M-step and then address the issue of conducting statistical inference in this context. A technique due to T. A. Louis may be used to estimate the covariance matrix of the parameter estimates by calculating the observed Fisher information matrix. We develop general expressions for the entries of this information matrix. Having the complete covariance matrix permits the calculation of confidence and prediction bands for the fitted model. We also investigate the testing of hypotheses concerning the number of components in the mixture via parametric and 'semiparametric' bootstrapping. Finally, we develop a method of producing diagnostic plots of the residuals from a mixture of linear regressions.     

A bayesian estimator for the dependence function of a bivariate extreme‐value distribution

Any continuous bivariate distribution can be expressed in terms of its margins and a unique copula. In the case of extreme‐value distributions, the copula is characterized by a dependence function while each margin depends on three parameters. The authors propose a Bayesian approach for the simultaneous estimation of the dependence function and the parameters defining the margins. They describe a nonparametric model for the dependence function and a reversible jump Markov chain Monte Carlo algorithm for the computation of the Bayesian estimator. They show through simulations that their estimator has a smaller mean integrated squared error than classical nonparametric estimators, especially in small samples. They illustrate their approach on a hydrological data set.     

Adaptive interval estimation in one-way random effects models

Two-stage procedures are introduced to control the width and coverage (validity) of confidence intervals for the estimation of the mean, the between groups variance component and certain ratios of the variance components in one-way random effects models. The procedures use the pilot sample data to estimate an “optimal” group size and then proceed to determine the number of groups by a stopping rule. Such sampling plans give rise to unbalanced data, which are consequently analyzed by the harmonic mean method. Several asymptotic results concerning the proposed procedures are given along with simulation results to assess their performance in moderate sample size situations. The proposed procedures were found to effectively control the width and probability of coverage of the resulting confidence intervals in all cases and were also found to be robust in the presence of missing observations. From a practical point of view, the procedures are illustrated using a real data set and it is shown that the resulting unbalanced designs tend to require smaller sample sizes than is needed in a corresponding balanced design where the group size is arbitrarily pre-specified.     

我国房地产价格发展趋势研究

 本文从房地产价格的相关理论出发,主要从房地产需求、房地产供给、房地产金融和房地产宏观调控等角度对影响房价的因素进行了分析,并从实证角度分析了各因素对房价的影响。本研究运用近10年房地产价格季度数据和时间序列模型对房地产价格发展趋势进行预测,最后提出房地产价格发展预警和稳定房价的建议。     

基于局部社团结构平衡的双模符号网络链路预测研究

随着互联网产业的高速发展,双模符号网络已经成为一类常见的复杂网络,然而针对此 类网络的分析较少。本文在传统非符号网络局部社团理论和符号网络结构平衡理论的基础上,首次提出了双模符号网络下的局部社团理论。这一理论不仅考虑了符号网络中共同邻居的信息,还引入了共同邻居间存在的连接。进一步地,本文推导出符号网络中基于局部社团信息的加权平衡回路增益指数,该指标可以表示双模符号网络中用户节点和产品节点间的符号关系。为了将该指标更好地应用于双模 符号网络链路预测问题,本文提出了加权平衡回路增益分类器算法。实验结果表明,相比其他经典链路预测算法,新算法具有更好的预测能力。     

Optimal non-diagonal-type estimators in linear regression under the prediction error sum of squares criterion

This article considers the notion of the non-diagonal-type estimator (NDTE) under the prediction error sum of squares (PRESS) criterion. First, the optimal NDTE in the PRESS sense is derived theoretically and applied to the cosmetics sales data. Second, we make a further study to extend the NDTE to the general case of the covariance matrix of the model and then give a Bayesian explanation for this extension. Third, two remarks concerned with some potential shortcomings of the NDTE are presented and an alternative solution is provided and illustrated by means of simulations.     

Sequential estimation problems for negative exponential populations

The literature on sequential estimation problems for negative exponential populations has been reviewed here, We attempt to bring in all the published and unpublished materials known to us in a fairly coherent fashion. Both the concepts and theoretical findings are discussed.