A new class of ratio-type estimators for improving mean estimation of nonsensitive and sensitive variables by using supplementary information

Motivated by some recent improvements for mean estimation in finite sampling theory, we propose, in a design-based approach, a new class of ratio-type estimators. The class is initially discussed on the assumption that the study variable has a nonsensitive nature, meaning that it deals with topics that do not generate embarrassment when respondents are directly questioned about them. Under this standard setting, some estimators belonging to the class are shown and the bias, mean square error and minimum mean square error are determined up to the first-order of approximation. The class is subsequently extended to the case where the study variable refers to sensitive issues which produce measurement errors due to nonresponses and/or untruthful reporting. These errors may be reduced by enhancing respondent cooperation through scrambled response methods that mask the true value of the sensitive variable. Hence, four methods (say the additive, multiplicative, mixed and combined additive-multiplicative methods) are discussed for the purposes of the article. Finally, a simulation study is carried out to assess the performance of the proposed class by comparing a number of competing estimators, both in the sensitive and the nonsensitive setting.