Publisher: Cambridge University Press | 1992 | ISBN: 0521429501 |
434 pages
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 condence bands in practice. Various smoothing methods among them splines and orthogonal polynomials are presented and discussed in their qualitative aspects. To simplify the exposition keel smoothers are investigated in greater detail. It is argued that all smoothing methods are in an asymptotic sense essentially equivalent to keel smoothing. So it seems legitimate to expose the deeper problems of smoothing parameter selection and condence bands for that method that is mathematically convenient and can be most easily understood on an intuitive level.
Most of the results are stated in a rather compact form and proved only in the simplest situations. On purpose I have tried to avoid being as general and precise as possible since I believe that the essential ideas which are relevant to practical data analysis can be understood without too much mathematical background. Generalizations and specializations, as well as additional results are deferred to an Exercises and Problems part at the end of each section. I am aware that this decision might discourage most theoretical and some practical statisticians. However, I am sure that for the average reader this is a convenient presentation of a collection of tools and mathematical concepts for the application of smoothing methods.
Professor H?rdle has provided us with an important book, one that will be appreciated both by applied statisticians who want to implement nonparametric regression techniques and by theoreticians interested in becoming knowledgeable in this growing field. Applied Nonparametric Regression is a very welcome addition to the literature." Joual of the American Statistical Association
"Nonparametric regression analysis has become central to economic theory. H?rdle, by writing the first comprehensive and accessible book on the subject, has contributed enormously to making nonparametric regression equally central to econometric practice." Charles F. Manski, University of Wisconsin, Madison
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 condence bands in practice. Various smoothing methods among them splines and orthogonal polynomials are presented and discussed in their qualitative aspects. To simplify the exposition keel smoothers are investigated in greater detail. It is argued that all smoothing methods are in an asymptotic sense essentially equivalent to keel smoothing. So it seems legitimate to expose the deeper problems of smoothing parameter selection and condence bands for that method that is mathematically convenient and can be most easily understood on an intuitive level.
Most of the results are stated in a rather compact form and proved only in the simplest situations. On purpose I have tried to avoid being as general and precise as possible since I believe that the essential ideas which are relevant to practical data analysis can be understood without too much mathematical background. Generalizations and specializations, as well as additional results are deferred to an Exercises and Problems part at the end of each section. I am aware that this decision might discourage most theoretical and some practical statisticians. However, I am sure that for the average reader this is a convenient presentation of a collection of tools and mathematical concepts for the application of smoothing methods.
Professor H?rdle has provided us with an important book, one that will be appreciated both by applied statisticians who want to implement nonparametric regression techniques and by theoreticians interested in becoming knowledgeable in this growing field. Applied Nonparametric Regression is a very welcome addition to the literature." Joual of the American Statistical Association
"Nonparametric regression analysis has become central to economic theory. H?rdle, by writing the first comprehensive and accessible book on the subject, has contributed enormously to making nonparametric regression equally central to econometric practice." Charles F. Manski, University of Wisconsin, Madison