Recent Advances and Trends in Nonparametric Statistics
- M.G. Akritas, Penn State University, Department of Statistics, PA, USA
- D.N. Politis, The University of California, Department of Mathematics, La Jolla, USA
The advent of high-speed, affordable computers in the last two decades has given a new boost to the nonparametric way of thinking. Classical nonparametric procedures, such as function smoothing, suddenly lost their abstract flavour as they became practically implementable. In addition, many previously unthinkable possibilities became mainstream; prime examples include the bootstrap and resampling methods, wavelets and nonlinear smoothers, graphical methods, data mining, bioinformatics, as well as the more recent algorithmic approaches such as bagging and boosting. This volume is a collection of short articles - most of which having a review component - describing the state-of-the art of Nonparametric Statistics at the beginning of a new millennium.
• algorithic approaches
• wavelets and nonlinear smoothers
• graphical methods and data mining
• biostatistics and bioinformatics
• bagging and boosting
• support vector machines
• resampling methods
Researchers in statistics; researchers in machine learning.
- Published: October 2003
- Imprint: JAI Press (Elsevier)
- ISBN: 978-0-444-51378-6
"The book provides current literature in many areas." Tapabrata Maiti (Iowa State University), in: Journal of American Statistical Association, 2005
Table of Contents
1. Algorithmic Approaches to Statistics
An introduction to support vector machines(B. Schölkopf).
Bagging, subagging and bragging for improving some prediction algorithms(P. Bühlmann).
Data compression by geometric quantization(Nkem-Amin Khumbah , E. J. Wegman).
2. Functional Data AnalysisFunctional data analysis in evolutionary biology(N. E. Heckman).
Functional nonparametric statistics: a double infinite dimensional framework(F. Ferraty, P. Vieu).
3. Nonparametric Model BuildingNonparametric models for ANOVA and ANCOVA: a review(M. G. Akritas, E. Brunner).
Isotonic additive interaction models(I. Gluhovsky).
A nonparametric alternative to analysis of covariance(A. Bathke, E. Brunner).
4. Goodness Of FitAssessing structural relationships between distributions - a quantileprocess approach based on Mallows distance(G. Freitag, A. Munk, M. Vogt).
Almost sure representations in survival analysis under censoring and truncation:applications to goodness-of-fit tests(R. Cao, W. González Manteiga, C. Iglesias Pérez)
5. High-Dimensional Data And VisualizationData depth: center-outward ordering of multivariate data and nonparametric multivariate statistics(R. Y. Liu).
Visual exploration of data through their graph representations(G. Michailidis).
6. Nonparametric RegressionInference for nonsmooth regression curves and surfaces using kernel-based methods(I. Gijbels).
Nonparametric smoothing methods for a class of non-standard curveestimation problems(O. Linton, E. Mammen).
Weighted local linear approach to censored nonparametric regression(Z. Cai).
7. Topics In NonparametricsAdaptive quantile regression(S. van de Geer).
Set estimation: an overview and some recent developments(A. Cuevas, A. Rodríguez-Casal).
Nonparametric methods for heavy tailed vector data: a survey with applicationsfrom finance and hydrology (M. M. Meerschaert, Hans-Peter Scheffler).
8. Nonparametrics in FinanceNonparametric methods in continuous-time finance: a selective review(Z. Cai, Y. Hong).
Nonparametric estimation in a stochastic volatility model(J. Franke, W. Härdle, Jens-Peter Kreiss).
Dynamic nonparametric filtering with application to volatility estimation(Ming-Yen Cheng, J. Fan, V. Spokoiny).
A normalizing and variance-stabilizing transformation for financial time series(D. N. Politis).
9. Bioinformatics and BiostatisticsBiostochastics and nonparametrics: oranges and apples?(P. K. Sen).
Some issues concerning length-biased sampling in survival analysis(M. Asgharian, D. B. Wolfson).
Covariate centering and scaling in varying-coefficient regression with application to longitudinal growth studies(C. O. Wu, K. F. Yu, V. W.S. Yuan).
Directed peeling and covering of patient rules(M. LeBlanc, J. Moon, J. Crowley).
10. Resampling and SubsamplingStatistical analysis of survival models with Bayesian bootstrap (J. Lee, Y. Kim).
On optimal variance estimation under different spatial subsampling schemes (D. J. Nordman, S. N. Lahiri).
Locally stationary processes and the local block bootstrap (A. Dowla, E. Paparoditis, D. N. Politis).
11. Time Series and Stochastic ProcessesSpectral analysis and a class of nonstationary processes (M. Rosenblatt).
Curve estimation for locally stationary time series models (R. Dahlhaus).
Assessing spatial isotropy (M. Sherman, Y. Guan, J. A. Calvin).
12. Wavelet and Multiresolution MethodsAutomatic landmark registration of 1D curves (J. Bigot).
Stochastic multiresolution models for turbulence (B. Whitcher, J.B. Weiss, D.W. Nychka, T.J. Hoar).List of Contributors.