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Smoothing and regression : approaches, computation, and application / edited by Michael G. Schimek.

Contributor(s): Schimek, Michael G.
Material type: materialTypeLabelBookSeries: Wiley series in probability and statisticsedited by Noel A. Cressie ... [et al.].Publisher: New York ; Chichester : Wiley, 2000Description: xix, 607 p. : ill. ; 25 cm.ISBN: 0471179469.Subject(s): Smoothing (Statistics) | Nonparametric statistics | Regression analysisDDC classification: 519.536
Contents:
Spline regression -- Variance estimation and smoothing-parameter selection for spline regression -- Kernel regression -- Variance estimation and bandwidth selection for kernel regression -- Spline and kernel regression under shape restrictions -- Spline and kernel regression for dependent data -- Wavelets for regression and other statistical problems -- Smoothing methods for discrete data -- Local polynomial fitting -- Additive and generalized additive models -- Multivariate spline regression -- Multivariate and semiparametric kernel regression -- Spatial-process estimates as smoothers -- Resampling methods, for non parametric regression -- Multidimensional smoothing and visualization -- Project pursuit regression -- Sliced inverse regression -- Dynamic and semiparametric models -- Nonparametric Bayesian bivariate surface estimation.
Holdings
Item type Current library Call number Copy number Status Barcode
General lending MTU Bishopstown Library Lending 519.536 (Browse shelf(Opens below)) 1 Available 00075272
Total holds: 0

Enhanced descriptions from Syndetics:

A comprehensive introduction to a wide variety of univariate and multivariate smoothing techniques for regression

Smoothing and Regression: Approaches, Computation, and Application bridges the many gaps that exist among competing univariate and multivariate smoothing techniques. It introduces, describes, and in some cases compares a large number of the latest and most advanced techniques for regression modeling. Unlike many other volumes on this topic, which are highly technical and specialized, this book discusses all methods in light of both computational efficiency and their applicability for real data analysis.

Using examples of applications from the biosciences, environmental sciences, engineering, and economics, as well as medical research and marketing, this volume addresses the theory, computation, and application of each approach. A number of the techniques discussed, such as smoothing under shape restrictions or of dependent data, are presented for the first time in book form. Special features of this book include:
* Comprehensive coverage of smoothing and regression with software hints and applications from a wide variety of disciplines
* A unified, easy-to-follow format
* Contributions from more than 25 leading researchers from around the world
* More than 150 illustrations also covering new graphical techniques important for exploratory data analysis and visualization of high-dimensional problems
* Extensive end-of-chapter references

For professionals and aspiring professionals in statistics, applied mathematics, computer science, and econometrics, as well as for researchers in the applied and social sciences, Smoothing and Regression is a unique and important new resource destined to become one the most frequently consulted references in the field.

"A Wiley-Interscience Publication.".

Includes bibliographical references and index.

Spline regression -- Variance estimation and smoothing-parameter selection for spline regression -- Kernel regression -- Variance estimation and bandwidth selection for kernel regression -- Spline and kernel regression under shape restrictions -- Spline and kernel regression for dependent data -- Wavelets for regression and other statistical problems -- Smoothing methods for discrete data -- Local polynomial fitting -- Additive and generalized additive models -- Multivariate spline regression -- Multivariate and semiparametric kernel regression -- Spatial-process estimates as smoothers -- Resampling methods, for non parametric regression -- Multidimensional smoothing and visualization -- Project pursuit regression -- Sliced inverse regression -- Dynamic and semiparametric models -- Nonparametric Bayesian bivariate surface estimation.

Table of contents provided by Syndetics

  • Foreword (p. xv)
  • Preface (p. xvii)
  • 1. Spline Regression (p. 1)
  • 1.1 Introduction (p. 1)
  • 1.2 General Form of the Estimator (p. 5)
  • 1.3 The Linear Smoothing Spline (p. 7)
  • 1.4 Large-Sample Efficiency (p. 9)
  • 1.5 Bayesian Motivation (p. 11)
  • 1.6 Extensions and Implementations (p. 15)
  • References (p. 16)
  • 2. Variance Estimation and Smoothing-Parameter Selection for Spline Regression (p. 19)
  • 2.1 Introduction and Some Definitions (p. 19)
  • 2.2 Interpretation of the Smoothing Parameter (p. 22)
  • 2.3 Quantifying the Complexity of a Smoothing Spline (p. 24)
  • 2.4 Estimation of [sigma superscript 2] (p. 29)
  • 2.5 Determination of [lambda] (p. 32)
  • 2.6 Estimation of [tau superscript 2] (p. 38)
  • 2.7 Final Remarks (p. 38)
  • References (p. 38)
  • 3. Kernel Regression (p. 43)
  • 3.1 Introduction (p. 43)
  • 3.2 The Nadaraya--Watson Kernal Regression Estimate (p. 44)
  • 3.3 Pointwise Bias Properties of the Nadaraya--Watson Estimate (p. 48)
  • 3.4 Pointwise Variance Properties of the Nadaraya--Watson Estimate (p. 51)
  • 3.5 Trade-off Between Bias and Variance: The Mean Squared Error (p. 53)
  • 3.6 Global Results: Mean Integrated Squared Error Properties (p. 56)
  • 3.7 L[subscript infinity] Convergence Properties of the Nadaraya--Watson Estimate (p. 58)
  • 3.8 Complementary Bibliography (p. 63)
  • References (p. 67)
  • 4. Variance Estimation and Bandwidth Selection for Kernel Regression (p. 71)
  • 4.1 Introduction (p. 71)
  • 4.2 Nonparametric Variance Estimators (p. 74)
  • 4.3 Bandwidth Choice for Kernel Regression Estimators (p. 88)
  • References (p. 103)
  • 5. Spline and Kernel Regression under Shape Restrictions (p. 109)
  • 5.1 Introduction (p. 109)
  • 5.2 Description of the Main Methods (p. 110)
  • 5.3 A Comparative View (p. 119)
  • 5.4 Examples (p. 122)
  • 5.5 Software Hints (p. 128)
  • References (p. 130)
  • 6. Spline and Kernel Regression for Dependent Data (p. 135)
  • 6.1 Introduction (p. 135)
  • 6.2 Approaches for a Known Autocorrelation Function (p. 138)
  • 6.3 Approaches for an Unknown Autocorrelation Function (p. 144)
  • 6.4 A Bayesian Approach to Smoothing Dependent Data (p. 148)
  • 6.5 Applications of Smoothing Dependent Data (p. 151)
  • References (p. 156)
  • 7. Wavelets for Regression and Other Statistical Problems (p. 159)
  • 7.1 Introduction (p. 159)
  • 7.2 Wavelet Expansions (p. 160)
  • 7.3 The Discrete Wavelet Transform in S (p. 163)
  • 7.4 Wavelet Shrinkage (p. 170)
  • 7.5 Estimators for Data With Correlated Noise (p. 177)
  • 7.6 Implementation of the Wavelet Transform (p. 181)
  • 7.7 How to Obtain and Install the Wavelet Software (p. 187)
  • References (p. 189)
  • 8. Smoothing Methods for Discrete Data (p. 193)
  • 8.1 Introduction (p. 193)
  • 8.2 Smoothing Contingency Tables (p. 194)
  • 8.3 Smoothing Approaches to Categorical Regression (p. 207)
  • 8.4 Conclusion (p. 224)
  • References (p. 225)
  • 9. Local Polynomial Fitting (p. 229)
  • 9.1 Introduction (p. 229)
  • 9.2 Properties of Local Polynomial Fitting (p. 237)
  • 9.3 Choice of Bandwidth (p. 247)
  • 9.4 Choice of the Degree (p. 257)
  • 9.5 Local Modeling (p. 259)
  • 9.6 Some More Applications (p. 268)
  • References (p. 273)
  • 10. Additive and Generalized Additive Models (p. 277)
  • 10.1 Introduction (p. 277)
  • 10.2 The Additive Model (p. 279)
  • 10.3 Generalized Additive Models (p. 297)
  • 10.4 Alternating Conditional Expectations, Additivity, and Variance Stabilization (p. 315)
  • 10.5 Smoothing Parameter and Bandwidth Determination (p. 321)
  • 10.6 Model Diagnostics (p. 322)
  • 10.7 New Developments (p. 323)
  • References (p. 324)
  • 11. Multivariate Spline Regression (p. 329)
  • 11.1 Introduction (p. 329)
  • 11.2 Smoothing Splines as Bayes Estimates (p. 330)
  • 11.3 ANOVA Decomposition on Product Domains (p. 332)
  • 11.4 Tensor Product Splines (p. 333)
  • 11.5 Computation (p. 336)
  • 11.6 Bayesian Confidence Intervals (p. 338)
  • 11.7 Software (p. 340)
  • 11.8 Cosine Diagnostics (p. 344)
  • 11.9 Partial Splines (p. 348)
  • 11.10 Thin-Plate Splines (p. 350)
  • 11.11 Non-Gaussian Regression (p. 352)
  • References (p. 354)
  • 12. Multivariate and Semiparametric Kernel Regression (p. 357)
  • 12.1 Introduction (p. 357)
  • 12.2 Multidimensional Smoothing with Kernels (p. 357)
  • 12.3 Semiparametric Generalized Regression Models (p. 377)
  • 12.4 Practical Application and Software Hints (p. 386)
  • References (p. 389)
  • 13. Spatial-Process Estimates as Smoothers (p. 393)
  • 13.1 Introduction (p. 393)
  • 13.2 Thin-Plate Splines (p. 397)
  • 13.3 Spatial-Process Estimates (p. 401)
  • 13.4 Ridge-Regression Estimates and Shrinkage (p. 407)
  • 13.5 A Response-Surface Example (p. 411)
  • 13.6 Predicting Ambient Ozone (p. 419)
  • 13.7 Future Directions (p. 421)
  • References (p. 423)
  • 14. Resampling Methods for Nonparametric Regression (p. 425)
  • 14.1 Introduction (p. 425)
  • 14.2 The Idea of Bootstrap (p. 426)
  • 14.3 Bootstrap in Nonparametric Regression (p. 430)
  • 14.4 Bootstrap Confidence Intervals and Bands (p. 434)
  • 14.5 Bootstrap-Bandwidth Choice (p. 437)
  • 14.6 Bootstrap Tests in Nonparametrics (p. 439)
  • 14.7 Bootstrap Inference on the Shape of a Curve (p. 442)
  • 14.8 Extensions (p. 445)
  • References (p. 446)
  • 15. Multidimensional Smoothing and Visualization (p. 451)
  • 15.1 Introduction (p. 451)
  • 15.2 Data-Point Visualization (p. 452)
  • 15.3 Functional Visualization in One and Two Variables (p. 456)
  • 15.4 Averaged Shifted Histograms (p. 458)
  • 15.5 Functional Visualization in Three Variables and Beyond (p. 462)
  • 15.6 Visualization of Regression Functions (p. 467)
  • 15.7 Summary (p. 468)
  • References (p. 468)
  • 16. Projection Pursuit Regression (p. 471)
  • 16.1 Introduction (p. 471)
  • 16.2 The Basic PPR Algorithm (p. 473)
  • 16.3 Quality of Approximation (p. 474)
  • 16.4 Number of Terms to Choose (p. 475)
  • 16.5 Interpretable PPR (p. 476)
  • 16.6 Convergence Rates (p. 477)
  • 16.7 Modifications (p. 478)
  • 16.8 PPR and Neural Networks (p. 484)
  • 16.9 Optimization Methods for PPR and Neural Networks (p. 487)
  • 16.10 The Implementation of PPR in S-PLUS, R, and Xplore (p. 488)
  • 16.11 An Example (p. 490)
  • 16.12 Conclusion (p. 493)
  • References (p. 493)
  • 17. Sliced Inverse Regression (p. 497)
  • 17.1 Introduction (p. 497)
  • 17.2 The Idea (p. 499)
  • 17.3 Statistical Properties (p. 501)
  • 17.4 The Unknown Dimensionality (p. 502)
  • 17.5 Slicing Strategies (p. 503)
  • 17.6 Implementation (p. 504)
  • 17.7 Modifications (p. 507)
  • 17.8 An Example (p. 508)
  • References (p. 511)
  • 18. Dynamic and Semiparametric Models (p. 513)
  • 18.1 Introduction (p. 513)
  • 18.2 Linear Dynamic Models and Optimal Smoothing for Time Series Data (p. 514)
  • 18.3 Non-Gaussian Observation Models (p. 520)
  • 18.4 Generalized Additive and Varying Coefficient Models (p. 536)
  • 18.5 Conclusions (p. 540)
  • References (p. 542)
  • 19. Nonparametric Bayesian Bivariate Surface Estimation (p. 545)
  • 19.1 Introduction (p. 545)
  • 19.2 Bayesian Model and Subset Selection (p. 547)
  • 19.3 Bivariate Surface Estimation (p. 554)
  • 19.4 Robust Surface Estimation (p. 568)
  • 19.5 Surface Estimation for Time Series Data (p. 575)
  • 19.6 Alternative Bases and Model Mixing (p. 576)
  • References (p. 578)
  • Index (p. 581)

Author notes provided by Syndetics

Michel Delecroix, ENSAI, Rennes, France
Randall L. Eubank, Texas AandM University, College Station, Texas, USA
Ludwig Fahrmeir, Ludwig-Maximilians-Universitat Munchen, Munich, Germany
Jianqing Fan, University of North Carolina, Chapel Hill, North Carolina, USA and The Chinese University of Hong Kong, Hong Kong, PRC
Irene Gijbels, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium
Janet Grassmann, SONEM, Wurzburg, Germany
Chong Gu, Purdue University, West Lafayette, Indiana, USA
Wolfgang Hardle, Humboldt-Universitat zu Berlin, Berlin, Germany
Eva Herrmann, Technische Universitat Darmstadt, Darmstadt, Germany
Sigbert Klinke, Humboldt-Universitat zu Berlin, Berlin, Germany
Leonhard Knorr-Held, Ludwig-Maximilians-Universitat Munchen, Munich, Germany
Robert Kohn, Australian Graduate School of Management, Sydney, Australia
Thomas T. Kotter, SAP AG, Walldorf, Germany
Angelka van der Linde, Edinburgh University, Edinburgh, UK
Enno Mammen, Ruprecht-Karls-Universitat Heidelberg, Heidelberg, Germany
Marlene Muller, Humboldt-Universitat zu Berlin, Berlin, Germany
Guy P. Nason. University of Bristol, Bristol, UK
Douglas W. Nychka, National Center for Atmospheric Research, Boulder, Colorado, USA
Pascal Sarda, Universite Paul Sabatier, Toulouse, France
Michael G. Schimek, Karl-Franzens-Universitat Graz, Graz and Universitat Wien, Vienna, Austria
David W. Scott, Rice University, Houston, Texas, USA
Bernard W. Silverman, University of Bristol, Bristol, UK
Jeffrey S. Simonoff, New York University, New York, USA
Michael Smith, University of Sydney, Sydney, Australia
Christine Thomas-Agnan, Universite de Toulouse I, Toulouse, France
Berwin A. Turlach, The University of Western Australia, Perth, Australia
Gerhard Tutz, Ludwig-Maximilians-Universitat Munchen, Munich, Germany
Philippe Vieu, Universite Paul Sabatier, Toulouse, France
Paul Yau, Australian Graduate School of Management, Sydney, Australia