A Bias Bound for Least Squares Linear Regression

by Naihua Duan, Ker-Chau Li

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Regression analysis is one of the most useful tools in statistical analysis. Usually, regression analysis requires specifying the link function for the model. The popular link functions used widely include the linear link function, the logistic link function, and the probit link function. However, in many applications, the functional form and the link function might not be known precisely. Therefore, the usual regression analysis based on a specific link function might not perform well. In this paper, the authors focus on the least squares linear regression which assumes the linear link function. When the linear link function does not hold, the results based on the least squares regression might be biased. The authors derive bounds for the bias and apply the theory to a special case as an illustration.

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