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The bias of least squares polynomial interpolants. (English) Zbl 0743.62055
Summary: The fitting of a straight line — or more generally of a low degree polynomial — to a point cloud in the plane is a commonly performed statistical technique. This paper discusses the bias of such a procedure and in particular generalizes the well-known remainder formula for polynomial interpolation to the regression setting. Designs minimizing the maximum bias are discussed as well.
MSC:
62J02 General nonlinear regression
62K05 Optimal statistical designs
65D05 Numerical interpolation
65D10 Numerical smoothing, curve fitting
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References:
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