Double sampling for Non-Response: A study on combined log-type estimators with an application of solar radiation spectrum

The validity and accuracy of parameter estimation are undermined with the involvement of non-response, which is considered as a major challenge in survey sampling, particularly when auxiliary data is only partially available. A unique class of six combined log-type estimators is developed in this paper to fill this gap. It is used to estimate the finite population mean under a stratified double sampling design that is impacted by non-response. Because it lowers bias, stabilizes variance, and improves estimator resilience in the presence of missing values, the estimators use bivariate auxiliary information in a log-linear framework, which works especially well for skewed data. The expressions for the bias and mean squared error (MSE) of each proposed estimator are derived in order to provide a solid theoretical basis. The Hansen-Hurwitz estimator, ratio and product estimators, and other log-type forms are among the classical estimators are considered and are compared analytically with the proposed estimators. Empirical investigation of three real-world datasets on apple production, supply chain greenhouse gas emission variables and solar radiation spectrum data which are environment related datasets to support the theoretical derivations. Every dataset was meticulously stratified, and by establishing suitable first-phase and second-phase sample sizes under specified stratum sizes, double sampling was replicated. Additionally, a thorough simulation analysis with 25,000 iterations was carried out under six various scenarios, combining different degrees of auxiliary information availability with varying percentages of non-response (10 %, 20 %, and 30 %). In comparison to traditional and existing estimators considered here, the proposed estimators performed well in all the analytical, empirical and simulation analysis using the metrics MSE and Percent Relative Efficiency (PRE). These findings highlight the suggested log-type estimators' resilience, adaptability, and effectiveness in practical settings where non-response and partial auxiliary data are frequent. The study offers a methodological framework that can be used in a variety of industrial, socioeconomic, and environmental studies. 62D05, 62D10.