Comparison of relative efficiency of the mean estimator with different DGCART models for different sample sizes under Case 1.

Comparison of relative efficiency of the mean estimator with different DGCART models for different sample sizes under Case 1.</p

Flow diagram of DGCART.

Post-stratification is applied when the subpopulation membership is observed only for sampled values and the goal is to estimate stratum-specific parameters which leads the survey statisticians towards primary goals i.e., classification of non-sampled units into different strata and prediction of the values of the study variables. Regression models, on one side, optimize the prediction of the study variable’s non-sampled values while the classification algorithms, on the other side, look for the classification of non-sampled cases into different strata. Hence, it is crucial to deal with these two goals simultaneously for the estimation of stratum-specific parameters. This study introduces the idea of a double-objective classification and regression trees (CARTs) approach for estimating stratum-specific parameters. Theoretical properties of the total estimator are derived. An application on the estimation of health outcomes in different domains is given to delineate the practical significance as well as the efficiency of the proposed CART-based method. The proposed estimator of population total performs better than the existing stratum-specific estimator in terms of relative efficiency for all choices of parameters. As an ensemble model, the random forest CART outperforms the other competing tree-based models and homogenous population model without using any auxiliary variable.</div

Bootstrap results for Case 1.

Post-stratification is applied when the subpopulation membership is observed only for sampled values and the goal is to estimate stratum-specific parameters which leads the survey statisticians towards primary goals i.e., classification of non-sampled units into different strata and prediction of the values of the study variables. Regression models, on one side, optimize the prediction of the study variable’s non-sampled values while the classification algorithms, on the other side, look for the classification of non-sampled cases into different strata. Hence, it is crucial to deal with these two goals simultaneously for the estimation of stratum-specific parameters. This study introduces the idea of a double-objective classification and regression trees (CARTs) approach for estimating stratum-specific parameters. Theoretical properties of the total estimator are derived. An application on the estimation of health outcomes in different domains is given to delineate the practical significance as well as the efficiency of the proposed CART-based method. The proposed estimator of population total performs better than the existing stratum-specific estimator in terms of relative efficiency for all choices of parameters. As an ensemble model, the random forest CART outperforms the other competing tree-based models and homogenous population model without using any auxiliary variable.</div

Details of DGCART Models used in the study (hyper-parameters).

Details of DGCART Models used in the study (hyper-parameters).</p

Comparison of relative efficiency of the mean estimator with different DGCART models for different sample sizes under Case 1.

Comparison of relative efficiency of the mean estimator with different DGCART models for different sample sizes under Case 1.</p

Comparison of relative efficiency of the mean estimator with different DGCART models for different sample sizes under Case 2.

Comparison of relative efficiency of the mean estimator with different DGCART models for different sample sizes under Case 2.</p

Bootstrap results Case 2.

Post-stratification is applied when the subpopulation membership is observed only for sampled values and the goal is to estimate stratum-specific parameters which leads the survey statisticians towards primary goals i.e., classification of non-sampled units into different strata and prediction of the values of the study variables. Regression models, on one side, optimize the prediction of the study variable’s non-sampled values while the classification algorithms, on the other side, look for the classification of non-sampled cases into different strata. Hence, it is crucial to deal with these two goals simultaneously for the estimation of stratum-specific parameters. This study introduces the idea of a double-objective classification and regression trees (CARTs) approach for estimating stratum-specific parameters. Theoretical properties of the total estimator are derived. An application on the estimation of health outcomes in different domains is given to delineate the practical significance as well as the efficiency of the proposed CART-based method. The proposed estimator of population total performs better than the existing stratum-specific estimator in terms of relative efficiency for all choices of parameters. As an ensemble model, the random forest CART outperforms the other competing tree-based models and homogenous population model without using any auxiliary variable.</div

Comparison of relative efficiency of the mean estimator with different DGCART models for different sample sizes under Case 2.

Comparison of relative efficiency of the mean estimator with different DGCART models for different sample sizes under Case 2.</p

Illustration of DGCART for estimation of finite population total.

Illustration of DGCART for estimation of finite population total.</p

Mesoporous Cu-Doped Manganese Oxide Nano Straws for Photocatalytic Degradation of Hazardous Alizarin Red Dye

The present work reports the photocatalytic degradation of alizarin red (AR) using Cu-doped manganese oxide (MH16–MH20) nanomaterials as catalysts under UV light irradiation. Cu-doped manganese oxides were synthesized by a very facile hydrothermal approach and characterized by energy dispersive X-ray spectroscopy, powder X-ray diffraction, scanning electron microscopy, Brunauer–Emmett–Teller analysis, UV–vis spectroscopy, and photoluminescence techniques. The structural, morphological, and optical characterization revealed that the synthesized compounds are nanoparticles (38.20–54.10 nm), grown in high mesoporous density (constant C > 100), possessing a tetragonal phase, and exhibiting 2.98–3.02 eV band gap energies. Synthesized materials were utilized for photocatalytic AR dye degradation under UV light which was monitored by UV–visible spectroscopy and % AR degradation was calculated at various time intervals from absorption spectra. More than 60% AR degradation at various time intervals was obtained for MH16–MH20 indicating their good catalytic efficiencies for AR removal. However, MH20 was found to be the most efficient catalyst showing more than 84% degradation, hence MH20 was used to investigate the effect of various catalytic doses, AR concentrations, and pH of the medium on degradation. More than 50% AR degradation was obtained for all studied parameters with MH20 whereas the pseudo-first-order kinetic model was found to be the best-fitted kinetic model for AR degradation with k = 0.0015 and R2 = 0.99 indicating a significant correlation between experimental data