No abstract

Item non‐response in sample surveys is usually addressed by imputation. A bootstrap method that treats the imputed values as if they were observed generally leads to variance estimates that are too small. Shao & Sitter (1996) introduced a bootstrap method in this context, which leads to consistent variance estimators when the sampling fraction is small. In the context of stratified simple random sampling, we introduce the independent bootstrap, which is valid even when the sampling fraction is large. It consists of modifying a bootstrap method for sample surveys, of independently generating the response status of each unit, and of imputing the non‐respondents in the bootstrap sample. We pay special attention to the bootstrap survey weights approach of Rao, Wu, & Yue (1992). The Canadian Journal of Statistics 42: 142–167; 2014 © 2014 Statistical Society of Canada

The most common way to treat item nonresponse in surveys is to replace a missing value by a plausible value constructed on the basis of fully observed variables. Treating the imputed values as if they were observed may lead to invalid inferences. Bootstrap variance estimators for various finite population parameters are obtained using two pseudo-population bootstrap schemes. We establish the asymptotic properties of the resulting bootstrap variance estimators for population totals and population quantiles. A simulation study suggests that the methods perform well in terms of relative bias and coverage probability.

As the volume of online and electronic information increasingly has grown, quickly and accurately access to these important resources is a big challenge. Text analytics can help by transposing words and sentences in unstructured data into high-quality information. Text summarization is one of the applications of text mining, has been of interest to researchers. In addition to text summarization, using optimization algorithms can be influenced results. In this paper, has been presented a hybrid approach for English multi-document summarization. As name suggest, a text summarization system produces summary of original documents. Combination of text mining and optimization algorithms is main ways this research, to improve results and reduce redundancy in summary sentences and simultaneously summary sentences have the most relevant. Similarity measures are cosine and overlap. Using multi-objective particle swarm optimization algorithm improved results. The experimental results of the method on two data sets DUC2005 and DUC2007 show improvements in the three assessment criteria associated. Result of summarization about 3 percent in ROUGE-1, in ROUGE-2 at 2 percent and the benchmark ROUGE-SU for approximately 1.5% compared with the previous methods improves.

Item nonresponse in surveys is usually dealt with through single imputation. It is well known that treating the imputed values as if they were observed values may lead to serious underestimation of the variance of point estimators. In this article, we propose three pseudo-population bootstrap schemes for estimating the variance of imputed estimators obtained after applying a multiply robust imputation procedure. The proposed procedures can handle large sampling fractions and enjoy the multiple robustness property. Results from a simulation study suggest that the proposed methods perform well in terms of relative bias and coverage probability, for both population totals and quantiles.