Lack-of-fit Testing for Polynomial Regression Models Without Replications

Maha A. Omair, Abdullah A. Al-Shiha and Ruba A. Alyafi

International Journal of Statistics and Probability, 2019, vol. 8, issue 5, 49-57

Abstract: Parametric and non-parametric approaches are developed to test the adequacy of the polynomial model Y=β_0+∑_(j=1)^p(β_j X^j )+ε when there is no replication in the values of the independent variable. The proposed tests avoid partitioning of the sample space of the continuous covariate. This paper suggests three tests based on the following concept: if the model is appropriate for a selected application, then the error component ε_1,ε_2,…,ε_n is a random sample with zero mean and constant variance. Simulation results are provided to illustrate the power and size of the proposed tests. An example is used to illustrate the methodologies. These tests are also compared with the classical lack-of-fit test to demonstrate their advantage.

Keywords: lack-of-fit test; regression model; replication; non parametric test (search for similar items in EconPapers)
Date: 2019
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