Confidence bands for the bias of linear estimators of a function of one variable

The choice of a parametric family of curves used in fitting a response in dependence of an exploratory variable is always debatable, since the fitted curve is merely an approximation of the true response curve. The present paper discusses the computation of (simultaneous) confidence bands for the bias of a fitted curve. Our development is based on integral expressions for the bias using derivatives of the unknown response curve. Such formulas can be used to convert confidence bands on the derivative(s) into confidence band(s) for the bias.