Non-parametric calibration estimation of distribution function under stratified random sampling

We introduced an innovative kernel-based nonparametric estimator for the cumulative distribution function (CDF) in finite populations, addressing the critical need to evaluate the proportion of values in a target variable that are less than or equal to specific thresholds. By leveraging auxiliary information under a stratified random sampling (StRS) framework, the proposed methodology employs multiple calibration constraints with a chi-square distance measure to derive calibrated weights, enhancing estimation efficiency. The estimators incorporate key descriptive measures of auxiliary variable, including the CDF and coefficient of variation, and tackle the challenge of bandwidth selection using advanced techniques such as plug-in selectors and cross-validation approaches. Simulation studies using datasets on apple production in Turkey and wheat production in Pakistan were conducted to assess the performance of the proposed estimators.