A novel basis function approach to finite population parameter estimation

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). Arobust and easy methodology is needed for accurately and quickly fitting a sampled data set witha set of covariates assuming that the sampled data could be a complicated non-linear function. Anovel 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 functionsregression (BFR) models. The problems of subsets selection with single predictor under an automaticmatrix approach, and ill- conditioned regression models are discussed. Prediction error variance ofthe proposed estimator is estimated under widely used feature selection criteria in ML. Finally, theexpected squared prediction error (ESPE) of the proposed estimator and the expectation of estimatederror variance under bootstrapping as well as simulation study with different regularizers are obtainedto observe the long-run behavior of the proposed estimator.