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Difference-based nonparametric regression models are based on assumptions about the unknown nonparametric function and are appropriate for large sample problems. However, most of the difference-based estimators and residual-based estimators previously used do not balance between bias and variance, 𝜎2, which depends on the bandwidth, b, a phenomenon commonly referred to as bias-variance trade-off. As such, it is necessary to perform modification at boundary point as a measure to counter this drawback. Another drawback to these estimators is that they are generally biased due to the problem of boundary and therefore require modification at the boundary points. This study adopts a simple and explicit bias corrected estimator 𝜎̂𝑣𝑜 2 of a finite population error variance in the setting where the variance is a constant (homoscedastic) using a model-based technique under simple random sampling without replacement (SRSWOR). [ABSTRACT FROM AUTHOR]