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General

Prospects of Nonparametric Modeling

Pages 1296-1300 | Published online: 17 Feb 2012

References

  • Allen , D. M. 1974 . “The Relationship Between Variable and Data Augmentation and a Method of Prediction” . Technometrics , 16 : 125 – 127 .
  • Antoniadis , A. 1999 . “Wavelets in Statistics: A Review” . Italian Journal of Statistics , (with discussion), to appear
  • Barron , A. , Birgé , L. and Massart , P. 1999 . “Risk Bounds for Model Selection via Penalization” . Probability Theory Related Fields , 113 : 301 – 413 .
  • Bickel , P. J. , Klaassen , A. J. , Ritov , Y. and Wellner , J. A. 1993 . Efficient and Adaptive Inference in Semiparametric Models , Baltimore : Johns Hopkins University Press .
  • Bickel , P. J. and Ritov , Y. 1988 . “Estimating Integrated Squared Density Derivatives: Sharp Order of Convergence Estimates” . Sankhyā , 50 : 381 – 393 . Ser. A
  • Bosq , D. 1998 . Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, , 2nd ed. , Berlin : Springer-Verlag .
  • Bowman , A. W. and Azzalini , A. 1997 . Applied Smoothing Techniques for Data Analysis , London : Oxford University Press .
  • Breiman , L. and Friedman , J. H. 1985 . “Estimating Optimal Transformations for Multiple Regression and Correlation” . Journal of the American Statistical Association , 80 : 580 – 619 . (with discussion)
  • Breiman , L. , Friedman , J. H. , Olshen , R. A. and Stone , C. J. 1993 . CART: Classification and Regression Trees , Belmont , CA : Wadsworth .
  • Brown , L. D. and Low , M. 1996 . “A Constrained Risk Inequality With Applications to Nonparametric Functional Estimation” . The Annals of Statistics , 24 : 2524 – 2535 .
  • Capra , W. B. and Müller , H. G. 1997 . “An Accelerated Time Model for Response Curves” . Journal of the American Statistical Association , 92 : 72 – 83 .
  • Carroll , R. J. , Fan , J. , Gijbels , I. and Wand , M. P. 1997 . “Generalized Partially Linear Single-Index Models” . Journal of the American Statistical Association , 92 : 477 – 489 .
  • Cleveland , W. S. 1979 . “Robust Locally Weighted Regression and Smoothing Scatterplots” . Journal of the American Statistical Association , 74 : 829 – 836 .
  • Cleveland , W. S. , Grosse , E. and Shyu , W. M. 1991 . “Local Regression Models,” . In Statistical Models in S , Edited by: Chambers , J. M. and Hastie , T. J. 309 – 376 . Pacific Grove , CA : Wadsworth & Brooks/Cole .
  • Devroye , L. P. and Györfi , L. 1985 . Nonparametric Density Estimation: The L1View , New York : Wiley .
  • Donoho , D. L. and Johnstone , I. M. 1994 . “Ideal Spatial Adaptation by Wavelet Shrinkage” . Biometrika , 81 : 425 – 455 .
  • Donoho , D. L. , Johnstone , I. M. , Kerkyacharian , G. and Picard , D. 1995 . “Wavelet Shrinkage: Asymptopia?” . Journal of the Royal Statistical Society , 57 : 301 – 369 . Ser. B
  • Duan , N. and Li , K-C. 1991 . “Slicing Regression: A Link-Free Regression Method” . The Annals of Statistics , 19 : 505 – 530 .
  • Donoho , D. L. and Liu , R. C. 1991 . “Geometrizing Rate of Convergence III” . The Annals of Statistics , 19 : 668 – 701 .
  • Efromovich , S. 1999 . Nonparametric Curve Estimation: Methods, Theory and Applications , New York : Springer-Verlag .
  • Efromovich , S. Y. and Pinsker , M. S. 1982 . “Estimation of Square-Integrable Probability Density of a Random Variable” . Problems of Information Transmission , 18 : 175 – 189 .
  • Eubank , R. L. 1988 . Spline Smoothing and Nonparametric Regression , New York : Marcel Dekker .
  • Fan , J. 1991 . “On the Estimation of Quadratic Functionals” . The Annals of Statistics , 19 : 1273 – 1294 .
  • Fan , J. 1993 . “Local Linear Regression Smoothers and Their Minimax Efficiency” . The Annals of Statistics , 21 : 196 – 216 .
  • Fan , J. and Gijbels , I. 1995 . “Data-Driven Bandwidth Selection in Local Polynomial Fitting: Variable Bandwidth and Spatial Adaptation” . Journal of the Royal Statistical Society , 57 : 371 – 394 . Ser. B
  • Fan , J. and Gijbels , I. 1996 . Local Polynomial Modelling and Its Applications , London : Chapman and Hall .
  • Fan , J. , Härdle , W. and Mammen , E. 1998 . “Direct Estimation of Additive and Linear Components for High-Dimensional Data” . The Annals of Statistics , 26 : 943 – 971 .
  • Fan , J. , Zhang , C. and Zhang , J. 2000 . “Generalized Likelihood Ratio Statistics and Wilks Phenomenon” . The Annals of Statistics , to appear
  • Farrell , R. H. 1972 . “On the Best Obtainable Asymptotic Rates of Convergence in Estimation of a Density Function at a Point” . Annals of Mathematical Statistics , 43 : 170 – 180 .
  • Friedman , J. H. 1991 . “Multivariate Adaptive Regression Splines” . The Annals of Statistics , 19 : 1 – 141 . (with discussion)
  • Gasser , T. and Müller , H-G. 1979 . “Kernel Estimation of Regression Functions,” . In Smoothing Techniques for Curve Estimation , 23 – 68 . New York : Springer-Verlag .
  • Green , P. J. and Silverman , B. W. 1994 . Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach , London : Chapman and Hall .
  • Gu , C. and Wahba , G. 1993 . “Smoothing Spline ANOVA With Component-Wise Bayesian ‘Confidence Intervals,’” . Journal of Computing and Graphical Statistics , 2 : 97 – 117 .
  • Györfi , L. , Härdle , W. , Sarda , P. and Vieu , P. 1989 . Nonparametric Curve Estimation from Time Series , Berlin : Springer-Verlag .
  • Hall , P. and Johnstone , I. 1992 . “Empirical Functionals and Efficient Smoothing Parameter Selection” . Journal of the Royal Statistical Society , 54 : 475 – 530 . (with discussion), Ser. B
  • Hall , P. and Patil , P. 1995 . “Formulae for Mean Integrated Squared Error of Nonlinear Wavelet-Based Density Estimators” . The Annals of Statistics , 23 : 905 – 928 .
  • Härdle , W. 1990 . Applied Nonparametric Regression , Boston : Cambridge University Press .
  • Härdle , W. and Stoker , T. M. 1989 . “Investigating Smooth Multiple Regression by the Method of Average Derivatives” . Journal of the American Statistical Association , 84 : 986 – 995 .
  • Hart , J. D. 1997 . Nonparametric Smoothing and Lack-of-Fit Tests , New York : Springer .
  • Hastie , T. J. and Tibshirani , R. 1990 . Generalized Additive Models , London : Chapman and Hall .
  • Hastie , T. J. and Tibshirani , R. 1993 . “Varying-Coefficient Models” . Journal of the Royal Statistical Society , 55 : 757 – 796 . Ser. B
  • Hoover , D. R. , Rice , J. A. , Wu , C. O. and Yang , L-P. 1998 . “Nonpara-metric Smoothing Estimates of Time-Varying Coefficient Models With Longitudinal Data” . Biometrika , 85 : 809 – 822 .
  • Huang , J. 1999 . “Projection Estimation in Multiple Regression With Application to Functional ANOVA Models” . The Annals of Statistics , 26 : 242 – 272 .
  • Ingster , Y. I. 1993a . “Asymptotic Minimax Hypothesis Testing for Nonparametric Alternative I” . Mathematical Methods Statistics , 2 : 85 – 114 .
  • Ingster , Y. I. 1993b . “Asymptotic Minimax Hypothesis Testing for Nonparametric Alternative II” . Mathematical Methods Statistics , 3 : 171 – 189 .
  • Ingster , Y. I. 1993c . “Asymptotic Minimax Hypothesis Testing for Nonparametric Alternative III” . Mathematical Methods Statistics , 4 : 249 – 268 .
  • Jones , M. C. , Marron , J. S. and Sheather , S. J. 1996 . “A Brief Survey of Bandwidth Selection for Density Estimation” . Journal of the American Statistical Association , 91 : 401 – 407 .
  • Lepski , O. V. 1991 . “Asymptotically Minimax Adaptive Estimation I” . Theory Probability Applications , 36 : 682 – 697 .
  • Lepski , O. V. 1992 . “Asymptotically Minimax Adaptive Estimation II” . Theory Probability Applications , 37 ( 3 ) : 433 – 448 .
  • Li , K-C. 1991 . “Sliced Inverse Regression for Dimension Reduction” . Journal of the American Statistical Association , 86 : 316 – 342 . (with discussion)
  • Linton , O. B. and Nielsen , J. P. 1995 . “A Kernel Method of Estimating Structured Nonparametric Regression Based on Marginal Integration” . Biometrika , 82 : 93 – 101 .
  • Kneip , A. and Gasser , T. 1992 . “Statistical Tools to Analyze Data Representing a Sample of Curves” . The Annals of Statistics , 20 : 1266 – 1305 .
  • Marron , J. S. and Padgett , W. J. 1987 . “Asymptotically Optimal Bandwidth Selection From Randomly Right-Censored Samples” . The Annals of Statistics , 15 : 1520 – 1535 .
  • Müller , H-G. 1988 . Nonparametric Regression Analysis of Longitudinal Data
  • Nychka , D. 1995 . “Splines as Local Smoothers” . The Annals of Statistics , 23 : 1175 – 1197 .
  • Ogden , T. 1997 . Essential Wavelets for Statistical Applications and Data Analysis , Boston : Birkhuser .
  • Ramsay , J. O. and Silverman , B. W. 1997 . The Analysis of Functional Data , Berlin : Springer-Verlag .
  • Rosenblatt , M. 1956 . “Remarks on Some Nonparametric Estimates of a Density Function” . Annals of Mathematical Statistics , 27 : 832 – 837 .
  • Rudemo , M. 1982 . “Empirical Choice of Histograms and Kernel Density Estimators” . Scandinavian Journal of Statistics , 9 : 65 – 78 .
  • Ruppert , D. 1997 . “Empirical-Bias Bandwidths for Local Polynomial Nonparametric Regression and Density Estimation” . Journal of the American Statistical Association , 92 : 1049 – 1062 .
  • Samarov , A. M. 1993 . “Exploring Regression Structure Using Nonparametric Functional Estimation” . Journal of the American Statistical Association , 88 : 836 – 847 .
  • Scott , D. W. 1992 . Multivariate Density Estimation: Theory, Practice, and Visualization , New York : Wiley .
  • Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , London : Chapman and Hall .
  • Simonoff , J. S. 1996 . Smoothing Methods in Statistics , New York : Springer .
  • Speckman , P. 1988 . “Kernel Smoothing in Partial Linear Models” . Journal of the Royal Statistical Society , 50 : 413 – 436 . Ser. B
  • Spokoiny , V. G. 1996 . “Adaptive Hypothesis Testing Using Wavelets” . The Annals of Statistics , 24 : 2477 – 2498 .
  • Stone , C. J. 1977 . “Consistent Nonparametric Regression” . The Annals of Statistics , 5 : 595 – 645 .
  • Stone , C. J. 1994 . “The Use of Polynomial Splines and Their Tensor Products in Multivariate Function Estimation” . The Annals of Statistics , 22 : 118 – 184 . (with discussion)
  • Stone , C. J. , Hansen , M. , Kooperberg , C. and Truong , Y. K. 1997 . “Polynomial Splines and Their Tensor Products in Extended Linear Modeling” . The Annals of Statistics , 25 : 1371 – 1470 . (with discussion)
  • Stone , M. 1974 . “Cross-Validatory Choice and Assessment of Statistical Predictions” . Journal of the Royal Statistical Society , 36 : 111 – 147 . (with discussion), Ser. B
  • Tjøstheim , D. and Auestad , B. H. 1994 . “Nonparametric Identification of Nonlinear Time Series: Projections” . Journal of the American Statistical Association , 89 : 1398 – 1409 .
  • Tong , H. 1990 . Non-Linear Time Series: A Dynamical System Approach , London : Oxford University Press .
  • Vidakovic , B. 1999 . Statistical Modeling by Wavelets , New York : Wiley .
  • Wahba , G. 1977 . “A Survey of Some Smoothing Problems and the Method of Generalized Cross-Validation for Solving Them,” . In Applications of Statistics , Edited by: Krisnaiah , P. R. 507 – 523 . Amsterdam : North-Holland .
  • Wahba , G. 1990 . Spline Models for Observational Data , Philadelphia : SIAM .
  • Wand , M. P. and Jones , M. C. 1995 . Kernel Smoothing , London : Chapman and Hall .
  • Yao , Q. and Tong , H. 1994 . “On Prediction and Chaos in Stochastic Systems” . Philosophical Transactions of the Journal of the Royal Statistical Society , 348 : 357 – 369 . Ser. A
  • Zhang , H. P. and Singer , B. 1999 . Recursive Partitioning in the Health Sciences , New York : Springer-Verlag .

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