Research on Superpopulation Local Polynomial Regression Model Inference of Web Survey Samples Under the Background of Big Data

With the rapid development of big data and Internet technology, web surveys are be- coming increasingly popular. However, most web survey samples are essentially non-probability samples. Thus, it is difficult to make inference from web survey samples using traditional sampling inference theory. Taking into account the few assumptions of nonparametric models, the superpopulation local polynomial regression model inference approach of web survey samples is proposed. The nonparametric superpopula- tion local polynomial regression model is firstly established to predict the target variable of the population based on web survey samples. Then the propensity score method is adopted to estimate the prediction error based on web survey samples. The population mean estimator of local polynomial regression is lastly obtained. Simulation and empirical analysis show that compared with the inverse weighted esti- mator of propensity scores and the population mean estimator based on the parametric superpopulation linear regression model, the population mean estimator based on the nonparametric superpopulation local polynomial regression model has smaller bias, standard deviation and mean square error. The proposed method has good performance.