A Novel Basis Function Approach to Finite Population Parameter Estimation

Abstract

Modeling non-linear data is a common practice in data science and machine learning (ML). It is aberrant to get a natural process whose outcome varies linearly with the values of input variable(s). A robust and easy methodology is needed for accurately and quickly fitting a sampled data set with a set of covariates assuming that the sampled data could be a complicated non-linear function. A novel approach for estimation of finite population parameter τ , a linear combination of the population values is considered, in this article, under superpopulation setting with known basis functions regression (BFR) models. The problems of subsets selection with single predictor under an automatic matrix approach, and ill-conditioned regression models are discussed. Prediction error variance of the proposed estimator is estimated under widely used feature selection criteria in ML. Finally, the expected squared prediction error (ESPE) of the proposed estimator and the expectation of estimated error variance under bootstrapping as well as simulation study with different regularizers are obtained to observe the long-run behavior of the proposed estimator.

Stratum-specific health outcome estimation in Pakistan using double goal CART

“…Similarly [ 11 ], analyzed data in complex surveys by considering the nonparametric estimation methods. Later [ 12 ], proposed a novel method for estimating a finite population parameter, which considers a linear combination of population values in a super-population scenario with a known basis function regression (BFR) model. [ 13 ] discussed applying linear, mixed, nonparametric, and machine learning techniques to estimate finite population parameters using complex survey data and auxiliary information Under commonly used feature selection criteria in machine learning, the suggested estimator’s prediction error variance was computed.…”

Adjustment of model misspecification in estimation of population total under ranked set sampling through balancing

“…Several versions of the model-based estimators have been found utilizing the model relationship between the variable of interest and the predictors [see [22] , [23] , [24] , [25] , [26] and [27] ]. Recently, [28] worked on a general model-based framework for estimation of an unknown population quantity under basis functions regression model (BFRM). The problems of subset selection with one predictor under an automated matrix approach, and ill-conditioning of regression models are also highlighted.…”