Abstract
This study introduces a general framework on inference for a general parameter using nonprobability survey data when a probability sample with auxiliary variables, common to both samples, is available. The proposed framework covers parameters from inequality measures and distribution function estimates but the scope of the paper is broader. We develop a rigorous framework for general parameter estimation by solving survey weighted estimating equations which involve propensity score estimation for units in the non-probability sample. This development includes the expression of the variance estimator, as well as some alternatives which are discussed under the proposed framework. We carried a simulation study using data from a real-world survey, on which the application of the estimation methods showed the effectiveness of the proposed design-based inference on several general parameters.
Highlights
IntroductionThe rise of online and smartphone surveys, along with the decrease of response rates in traditional survey modes, have contributed to the popularization of volunteer surveys where sampling is non-probabilistic
Nonprobability samples are increasingly common in empirical sciences
We aim to develop a framework for statistical inference on a general parameter with non probability survey samples when a reference probability sample is available
Summary
The rise of online and smartphone surveys, along with the decrease of response rates in traditional survey modes, have contributed to the popularization of volunteer surveys where sampling is non-probabilistic. The development of Big Data involves the analysis of large scale datasets whose obtention is conditioned by data availability and not by a probabilistic selection, and they can be considered large nonprobability samples of a population [1]. The lack of a probability sampling scheme can be responsible for selection bias. Differences between individuals in UT and individuals in U pc are caused by a lack of coverage induced by the survey administration mode (for example, an online questionnaire cannot be administered to the population without internet access), while differences between U pc and
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