In sample surveys, it is usual to increase the efficiency of the estimators by the use of the auxiliary information. We propose a class of ratio estimators of a finite population mean using two auxiliary variables and obtain mean square error (MSE) equations for the class of proposed estimators. We find theoretical conditions that make proposed family estimators more efficient than the traditional ratio estimator and the estimators proposed by Abu-Dayeh et al. using two auxiliary variables. In addition, we support these theoretical results with the aid of a numerical example.

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The researches and applications of sentiment analysis become increasingly important with the rapid growth of online reviews. But traditional sentiment analysis models have been lacking in concern on the modifying relationship between words for sentiment analysis of Chinese reviews, and limit the development of opinion mining. This paper proposes a feature-based vector model and a novel weighting algorithm for sentiment analysis of Chinese product reviews. It considers both modifying relationships between words and punctuations in review texts. Specifically, it can classify reviews into two categories, i.e., positive and negative, and can also represent the sentiment strength by adverb of degree. Moreover, a novel feature extraction method based on dependency parsing is presented to identify the corresponding aspects that opinions words modify. We conduct some experiments to evaluate our algorithms, and demonstrate that the proposed approaches are efficient and promising. Index Terms-sentiment analysis, dependency parsing, polarity classification * Supported by the Beijing Natural Science Foundation (No. 4133084) and the Beijing Key Disciplines of Computer Application Technology.

To improve the efficiency of an estimator with two auxiliary variables, we propose a new estimator of a finite population mean under simple random sampling. The bias and mean square error expressions of the proposed estimator have been obtained. In a comparison study, we found that the new estimator was consistently better than those of Abu-Dayyeh et al., Kadilar and Cingi, and Malik and Singh, as well as the regression estimator using two auxiliary variables, and that the minimum MSE values of the previous three above reported estimators were equal. We used four numerical examples in agricultural, biomedical, and power engineering to support these theoretical results, thus enriching the theory of survey samples by the development of new estimators with two auxiliary variables.

In sample surveys, it is usual to make use of auxiliary information to increase the precision of the estimators. We propose a new chain ratio estimator and regression estimator of a finite population mean using linear combination of two auxiliary variables and obtain the mean squared error (MSE) equations for the proposed estimators. We find theoretical conditions that make proposed estimators more efficient than the traditional multivariate ratio estimator and the regression estimator using information of two auxiliary variables.

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In sample surveys, it is usual to make use of auxiliary information to increase the precision of estimators. We propose a new exponential ratio-type estimator of a finite population mean using linear combination of two auxiliary variables and obtain mean square error (MSE) equation for proposed estimator. We find theoretical conditions that make proposed estimator more efficient than traditional multivariate ratio estimator using information of two auxiliary variables, the estimator of Bahl and Tuteja and the estimator proposed by Abu-Dayeh et al. In addition, we support these theoretical results with the aid of two numerical examples.