A novel basis function approach to finite population parameter estimation

Modeling nonlinear data is a common practice in data science and Machine Learning (ML). It is aberrant for the outcome of a natural process to vary linearly with the values of input variable(s). A robust and easy methodology is needed for accurately and quickly fitting a sampled dataset with a set of covariates, assuming that the sampled data can be a complicated nonlinear function. A novel approach to the estimation of finite population parameter tau, which is 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 a single predictor using an automatic matrix approach and ill-conditioned regression models are discussed. Prediction error variance of the proposed estimator is estimated based on 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. (c) 2023 Sharif University of Technology. All rights reserved.