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Title: Nonparametric Smoothing and Lack-Of-Fit Tests (Springer Series in Statistics) by Jeffrey D. Hart ISBN: 0-387-94980-1 Publisher: Springer-Verlag Pub. Date: 01 August, 1997 Format: Hardcover Volumes: 1 List Price(USD): $79.95

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Average Customer Rating: 4.5 (2 reviews)

Rating: 4
Summary: God Bless nonparametric estimation....
Comment: I read this book for the lecture. The writer does a nice job on the second moment locally Taylor expasion....The nonparametric smoothing is the one which could be used as the statistic inference but not the prediction...I know people who knows it better perhaps would have different of thinking about this... But the prediction should be based on the structure-remained assumption....This is a good one and contains a lot of new researches...Especially Fan's local linear fit....That is a

great part in this field....

Rating: 5
Summary: excellent coverage of classical and new smoothing methods
Comment: The editors review of the contents of the book and the brief biography of the author give the reader a proper view and so I will not repeat that information here. Rather I would like to stress that the book deals with nonparametric regression. This differs from linear and nonlinear regression in that a specific form of the regression equation is not specified in advance. We only assume that the function is smooth. This allows us to estimate a variety of shapes based on local averaging or kernel methods.

Hart covers all the classical approaches. Assessment of the accuracy of the regression function is a much more difficult problem but reasonable approaches are now available thanks to the incredible speed of modern computers. This has opened the door to a wide variety of new techniques for the estimation and accuracy assessment of nonparametric regression functions. This is perhaps the reason for its recent surge in popularity and the flood on the market of a number of excellent texts including this one by Hart, one by Simonoff, one by Eubank and a few by Hardle.

The editors say that it is intended for those with a modest knowledge of calculus. So it could be used for a junior or senior level undergraduate course. However, I think it would be more common and more advisable to use it for a graduate level course.

Chapter 8 covers data-driven lack of fit tests and includes a bootstrap procedure. Chapter 9 is very interesting as it extends the scope of application by dealing with thorny issues such as uncertainty in the predictors (i.e. the x's). This is often called the error-in-variables regression problem. Chapter 9 tests other assumptions including additivity and homoscedasticity. It also covers comparison of two regression curves and some interesting time series problems such as trend detection and white noise tests.

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