This book concentrates on the statistical aspects of nonparametric regression smoothing from an applied point of view. The methods covered in this text can be used in biometry, econometrics, engineering and mathematics. The two central problems discussed are the choice of smoothing parameter and the construction of con dence bands in practice. Various smoothing methods among them splines and orthogonal polynomials are presented and discussed in their qualitative aspects. To simplify the exposition kernel smoothers areinvestigated in greater detail. It is argued that all smoothing methods are in an asymptotic sense essentially equivalent to kernel smoothing. So it seems legitimate to expose the deeper problems of smoothing parameter selection and con dence bands for that method that is mathematically convenient and can be most easily understood on an intuitive level.

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