Estimation of Finite Population Totals Based on a Robust Nonparametric Feedforward Backpropagation Neural Network

Abstract

Estimation procedure of Population Parameters in Model Based framework has employed Nonparametric techniques widely. This has become more interesting when complete Auxiliary information is available allowing use of more flexible methods in predicting the value taken by the survey variable in nonsampled units ensuring more efficient Estimators of Finite Population Totals are build. In this context, estimators such as Local Polynomial and Kernel Smoothers have dom- inantly been used and shown to provides good estimators for Finite Population Total in low dimension. Even in these scenarios however, bias at boundary points presents a big problem when using these estimators in estimating Finite Popula- tion Parameters. The problem worsens as the dimension of the regressors vectors increases. This leads to sparseness of regressors values in the design space making these methods unfeasible due to the decrease in the fastest achievable rates of con- vergence of the regression function estimator towards the target curve. To address this challenges, this study considers estimation of Finite Population Totals in high dimension using a Feedforward Backpropagation Neural Network. The technique of Neural Network ensures Robust Estimator in high dimensions and reduces estimation bias with marginal increase in variance. The estimators properties are developed, and a comparison with existing estimators such as Generalized Additive Models, Multivariate Adaptive Regression Spline and Local Polynomial was conducted to evaluate the estimators performance using simulated data and data acquired from the United Nations Development Programme 2020. When certain conditions are met, the estimator was found to have an asymptotic Mean Square Error and asymptotically consistent. Simulation results showed that, the Feedforward Backpropagation Neural Network estimator is efficient and outper- formed the existing estimators in estimating Finite Population Totals as it had smaller values of biases, and mean square errors compared to other Estimators. The estimation approach performs well in an example using data from a United Nations Development Programme 2020 on the study of Human Development In- dex against other factors. The theoretical and practical results imply that the Feedforward Backpropagation Neural Network Estimator is highly recommended for Survey Sampling in the Estimation of Finite Population Totals. xiii