Abstract:
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Least Squares (LS) regression is a frequently used method for estimating a linear association between an independent variable and a dependent variable. However, homoscedastic errors and a correctly specified mean model are conditions for the optimality of LS regression, and these conditions are not always valid. The goal of this research was to develop a new method that outperforms LS regression in situations where the LS optimality conditions are invalid. This new method is closer in interpretation to a linear association, that is, an average change in a dependent variable given a change in an independent variable, than the LS estimator. We have developed a new nonparametric method that estimates the linear association using localized smoother estimates. In some situations, we have found that the new method performs comparably to LS regression when LS is optimal, and in other situations, the new method performs better than LS regression.
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