Smoothing Spline Density Estimation: A Dimensionless Automatic Algorithm

References

• Aronszajn , N. 1950 . Theory of Reproducing Kernels . Transactions of the American Mathematical Society , 68 : 337 – 404 .
   Web of Science ®Google Scholar
• Bickel , P. and Doksum , K. 1977 . Mathematical Statistics , San Francisco : Holden-Day .
   Google Scholar
• Dongarra , J. J. , Moler , C. B. , Bunch , J. R. and Stewart , G. W. 1979 . LINPACK Users' Guide , Philadelphia : SIAM .
   Google Scholar
• Good , I. J. and Gaskins , R. A. 1971 . Nonparametric Roughness Penalties for Probability Densities . Biometrika , 58 : 255 – 277 .
   Web of Science ®Google Scholar
• Good , I. J. and Gaskins , R. A. 1980 . Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data . Journal of the American Statistical Association , 75 : 42 – 73 . (with discussion)
   Web of Science ®Google Scholar
• Gu , C. “RKPACK and Its Applications: Fitting Smoothing Spline Models,” . Proceedings of the Statistical Computing Section . pp. 42 – 51 . American Statistical Association .
   Google Scholar
• Gu , C. 1992 . Cross-Validating Non-Gaussian Data . Journal of Computational and Graphical Statistics , 1 : 169 – 179 .
   Google Scholar
• Gu , C. , Bates , D. M. , Chen , Z. and Wahba , G. 1989 . The Computation of GCV Functions through Householder Tridiagonalization With Applications to the Fitting of Interaction Spline Models . SIAM Journal on Matrix Analysis and Applications , 10 : 457 – 480 .
   Web of Science ®Google Scholar
• Gu , C. and Qiu , C. Smoothing Spline Density Estimation: Theory . The Annals of Statistics , 21 (in press)
   Web of Science ®Google Scholar
• Gu , C. and Wahba , G. 1991a . Discussion of “Multivariate Adaptive Regression Splines” . The Annals of Statistics , 19 : 115 – 123 . by J. Friedman
   Web of Science ®Google Scholar
• Gu , C. and Wahba , G. 1991b . Smoothing Splines and Analysis of Variance in Function Spaces , Purdue University, Dept. of Statistics . Technical Report 91–29
   Google Scholar
• Gu , C. and Wahba , G. Semiparametric ANOVA With Tensor Product Thin Plate Splines . Journal of the Royal Statistical Society , 55 (in press), Ser. B
   Google Scholar
• Huber , P. 1985 . Projection Pursuit . The Annals of Statistics , 13 : 435 – 475 . (with discussion)
   Web of Science ®Google Scholar
• Klonias , V. K. 1982 . Consistency of a Nonparametric Penalized Likelihood Estimator of the Probability Density Function . The Annals of Statistics , 10 : 811 – 824 .
   Web of Science ®Google Scholar
• Kooperberg , C. and Stone , C. J. 1991 . A Study of Logspline Density Estimation . Computational Statistics and Data Analysis , 12 : 327 – 347 .
   Web of Science ®Google Scholar
• Leonard , T. 1978 . Density Estimation, Stochastic Processes and Prior Information . Journal of the Royal Statistical Society , 40 : 113 – 146 . (with discussion), Ser. B
   Google Scholar
• O'Sullivan , F. 1988 . Fast Computation of Fully Automated Log-Density and Log-Hazard Estimators . SIAM Journal on Scientific and Statistical Computing , 9 : 363 – 379 .
   Web of Science ®Google Scholar
• Scott , D. 1985 . Averaged Shifted Histograms: Effective Nonparametric Density Estimators in Several Dimensions . The Annals of Statistics , 13 : 1024 – 1040 .
   Web of Science ®Google Scholar
• Scott , D. “Choosing Smoothing Parameters in Density Estimators,” . Computer Science and Statistics: Proceedings of the 17th Symposium on the Interface . Edited by: Allen , D. M. pp. 225 – 229 . Amsterdam : North-Holland .
   Google Scholar
• Silverman , B. W. 1982 . On the Estimation of a Probability Density Function by the Maximum Penalized Likelihood Method . The Annals of Statistics , 10 : 795 – 810 .
   Web of Science ®Google Scholar
• Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , New York : Chapman and Hall .
   Google Scholar
• Stone , C. J. and Koo , C.-Y. 1986 . Logspline Density Estimation . Contemporary Mathematics , 59 : 1 – 15 .
   Google Scholar
• Tapia , R. A. and Thompson , J. R. 1978 . Nonparametric Probability Density Estimation , Baltimore : Johns Hopkins University Press .
   Google Scholar
• Wahba , G. 1977 . “ Optimal Smoothing of Density Estimates ” . In Classification and Clustering , Edited by: Van Ryzin , J. 423 – 458 . New York : Academic Press .
   Google Scholar
• Wahba , G. Spline Models for Observational Data . CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 59 . Philadelphia : SIAM .
   Google Scholar
• Whittaker , J. 1990 . Graphical Models in Applied Multivariate Statistics , Chichester , , UK : John Wiley .
   Google Scholar