Sharif University of Technology Scientia Iranica 1026-3098 30 3 2023 06 01 A novel basis function approach to finite population parameter estimation 1224 1244 22251 10.24200/sci.2021.56353.4682 EN Sh. Ahmed Department of Statistics, Quaid-i-Azam University, Islamabad, 44000, Pakistan J. Shabbir Department of Statistics, Quaid-i-Azam University, Islamabad, 44000, Pakistan Journal Article 2020 07 06 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<br />robust and easy methodology is needed for accurately and quickly fitting a sampled data set with<br />a set of covariates assuming that the sampled data could be a complicated non-linear function. A<br />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<br />regression (BFR) models. The problems of subsets selection with single predictor under an automatic<br />matrix approach, and ill-conditioned regression models are discussed. Prediction error variance of<br />the proposed estimator is estimated under widely used feature selection criteria in ML. Finally, the<br />expected squared prediction error (ESPE) of the proposed estimator and the expectation of estimated<br />error variance under bootstrapping as well as simulation study with different regularizers are obtained<br />to observe the long-run behavior of the proposed estimator. https://scientiairanica.sharif.edu/article_22251_3d7ce1a976af6a646c9e95a83c33f191.pdf