Dual-type quantile regression approach for mean estimation incorporating sampled and non-sampled data

Abstract

Drawing inspiration from recent advancements in robust mean estimation within finite sampling theory, we introduce a novel dual-type class of mean estimators in a design-based framework. The dual-type class is based on quantile regression and is specifically designed to be effective in the presence of extreme observations. Significantly, it integrates the averages of both sampled observations and non-sampled observations of auxiliary variable. In the initial discussion of this class, it is presumed that the target variable is non-sensitive, signifying its relevance to subjects that respondents do not consider embarrassing when queried directly. In this standard setting, we present specific estimators within the class and determine their theoretical properties. The class's scope broadens to include scenarios where the target variable incorporates sensitive topics, giving rise to nonresponse rates and inaccurate reporting. To alleviate these errors, one can promote respondent cooperation by employing scrambled response methods that obscure the actual value of the sensitive variable. Accordingly, the article delves into discussions on additive methods. Subsequently, a numerical study is conducted using asymmetric data to evaluate the effectiveness of the dual-type class by comparing it with several existing estimators, both in the absence and presence of scrambled responses.