A novel basis function approach to finite population parameter estimation

Document Type : Article


Department of Statistics, Quaid-i-Azam University, Islamabad, 44000, Pakistan


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.


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