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Local polynomial modelling and its applications. (English) Zbl 0873.62037
Monographs on Statistics and Applied Probability. 66. London: Chapman & Hall. xvi, 341 p. (1996).
Local polynomial fitting provides a powerful methodology for nonparametric estimation of a regression function. Under appropriate smoothness assumptions the least-squares principle is applied to fit a polynomial to data contained in a small window. The present monograph nicely reviews the current state of art. Topics which are dealt with in greater details are: adaptive choice of the smoothing parameter, bias and variance considerations, applications to survival and time series data. The authors spend much time on motivation. Proofs are given only for some selected mathematical statements.
Reviewer: W.Stute (Gießen)

MSC:
62G07 Density estimation
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P99 Applications of statistics
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