TITLE:
Estimation of Finite Population Totals in High Dimensional Spaces
AUTHORS:
Festus A. Were, George O. Orwa, Romanus O. Otieno
KEYWORDS:
Neural Networks, Kernel Smoother, Local Polynomial, Nonparametric
JOURNAL NAME:
Open Journal of Statistics,
Vol.12 No.5,
October
11,
2022
ABSTRACT: In this paper, the problem of Nonparametric Estimation of Finite
Population Totals in high dimensional datasets is considered. A robust
estimator of the Finite Population Total based on Feedforward Backpropagation
Neural Network is derived with the aid of a Super-Population Model. This
current study is motivated by the fact that Local Polynomials and Kernel
methods have in preceding related studies, been shown to provide good
estimators for Finite Population Totals but in low dimensions. Even in these
situations however, bias at boundary points presents a big challenge when using
these estimators in estimating Finite Population parameters. The challenge
worsens as the dimension of regressors increase. This is because as the
dimension of the Regressor Vectors grows, the Sparseness of the Regressors’ values
in the design space becomes unfeasible, resulting in a decrease in the fastest
achievable rates of convergence of the Regression Function Estimators towards
the target curve, rendering Kernel Methods and Local Polynomials ineffective to
address these challenges. This study considers the technique of Artificial Neural Networks which
yields robust estimators in high dimensions and reduces the estimation bias
with marginal increase in variance. This is due to its Multi-Layer Structure,
which can approximate a wide range of functions to any required level of
precision. The estimator’s properties are developed, and a comparison with
existing estimators was conducted to evaluate the estimator’s performance using
real data sets acquired from the United Nations Development Programme 2020. The
estimation approach performs well in an example using data from a United
Nations Development Programme 2020 on the study of Human Development Index
against other factors. The theoretical and practical results imply that the
Neural Network estimator is highly recommended for survey sampling estimation
of the finite population total.