Another look at Huber's estimator: A new minimax estimator in regression with stochastically bounded noise

Huber's estimator has had a long lasting impact, particularly on robust statistics. It is well known that under certain conditions, Huber's estimator is asymptotically minimax. A moderate generalization in rederiving Huber's estimator shows that Huber's estimator is not the only choice. We develop an alternative asymptotic minimax estimator and name it regression with stochastically bounded noise (RSBN). Simulations demonstrate that RSBN is slightly better in performance, although it is unclear how to justify such an improvement theoretically. We propose two numerical solutions: an iterative numerical solution, which is extremely easy to implement and is based on the proximal point method; and a solution by applying state-of-the-art nonlinear optimization software packages, e.g., SNOPT. Contribution: the generalization of the variational approach is interesting and should be useful in deriving other asymptotic minimax estimators in other problems.     

基于多变量动态模型的产出缺口估算

 本文运用多变量动态模型系统下的Beveridge-Nelson分解方法和贝叶斯Gibbs抽样估计,估算了1985年1季度至2008年2季度期间中国的产出缺口,并且与传统的单变量估计方法测算的结果在统计属性和对货币政策调节的预测效果方面进行了比较。实证结果表明,不同产出缺口的统计属性存在差别,并且只有基于多变量系统测算的产出缺口对货币政策具有显著预测效果。这说明多变量模型估计出的产出缺口更全面地考虑了经济产出与其他相关变量的互动效应,含有的信息更为丰富,从而对宏观政策调整具有更重要的参考价值。     

Copula-based regression models: A survey

In this review paper we collect several results about copula-based models, especially concerning regression models, by focusing on some insurance applications.     

Forecasting obesity trends in England

Summary.  Forecasts of trends in obesity in England for 2010 are produced by treating the available data, which contain the proportions of the population, categorized by age and sex, falling into different body mass index ranges, as compositional data sets, so that the implicit simplex restrictions are automatically satisfied. Forecasts are calculated by using linear trend models for the log-ratio transformations and are accompanied by prediction regions. The advantages of treating data on proportions compositionally are emphasized and compared with forecasts that have been obtained by ignoring this restriction.     

Modified inference about the mean of the exponential distribution using moving extreme ranked set sampling

The maximum likelihood estimator (MLE) and the likelihood ratio test (LRT) will be considered for making inference about the scale parameter of the exponential distribution in case of moving extreme ranked set sampling (MERSS). The MLE and LRT can not be written in closed form. Therefore, a modification of the MLE using the technique suggested by Maharota and Nanda (Biometrika 61:601–606, 1974) will be considered and this modified estimator will be used to modify the LRT to get a test in closed form for testing a simple hypothesis against one sided alternatives. The same idea will be used to modify the most powerful test (MPT) for testing a simple hypothesis versus a simple hypothesis to get a test in closed form for testing a simple hypothesis against one sided alternatives. Then it appears that the modified estimator is a good competitor of the MLE and the modified tests are good competitors of the LRT using MERSS and simple random sampling (SRS).     

Estimating a sensitive proportion through randomized response procedures based on auxiliary information

Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of people, π _A , bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π _A , for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons’ model.     

ESTIMATING A PARAMETER WHEN IT IS KNOWN THAT THE PARAMETER EXCEEDS A GIVEN VALUE

In some statistical problems a degree of explicit, prior information is available about the value taken by the parameter of interest, θ say, although the information is much less than would be needed to place a prior density on the parameter's distribution. Often the prior information takes the form of a simple bound, ‘θ > θ₁ ’ or ‘θ < θ₁ ’, where θ₁ is determined by physical considerations or mathematical theory, such as positivity of a variance. A conventional approach to accommodating the requirement that θ > θ₁ is to replace an estimator, , of θ by the maximum of and θ₁. However, this technique is generally inadequate. For one thing, it does not respect the strictness of the inequality θ > θ₁ , which can be critical in interpreting results. For another, it produces an estimator that does not respond in a natural way to perturbations of the data. In this paper we suggest an alternative approach, in which bootstrap aggregation, or bagging, is used to overcome these difficulties. Bagging gives estimators that, when subjected to the constraint θ > θ₁ , strictly exceed θ₁ except in extreme settings in which the empirical evidence strongly contradicts the constraint. Bagging also reduces estimator variability in the important case for which is close to θ₁, and more generally produces estimators that respect the constraint in a smooth, realistic fashion.     

论少数民族地区非物质文化遗产的保护性旅游开发——以柳州融水苗族系列坡会群为例

非物质文化遗产主要指的是流传民间文化艺术的表现形式或文化空间,存在于居民的日常生产生活中.是他们习以为常的民间活动.但现代化快速发展的社会环境,既对非物质文化遗产造成了一定的冲击,同时也让人们看到了它的另一种价值,作为一类具有旅游价值的文化资源而存在,故而对其进行旅游开发意义重大.本文在详细论述了融水苗族系列坡会群的发展沿革及其文化内涵的基础上.针对当前其发展现状问题,提出了进一步推动融水苗族系列坡会群保护性旅游开发的对策建议.