Robustness of Tube Formula Based Confidence Bands

References

• Bhui , B. , Chatterjee , S. and Banerjee , A. 1993 . “Spectral Shift From an Evolving Dust Sphere” . International Journal of Modern Physics. D. Gravitation, Astrophysics, Cosmology , 2 : 489 – 495 .
   Google Scholar
• Box , G. E.P. and Cox , D. R. 1964 . “The Analysis of Transformations” . Journal of the Royal Statistical Society , 26 : 211 – 243 . Series B
   Google Scholar
• Breiman , L. and Friedman , J. H. 1985 . “Estimating Optimal Transformations for Multiple Regression and Correlation” . Journal of the American Statistical Association , 80 : 580 – 619 .
   Web of Science ®Google Scholar
• Carroll , R. and Ruppert , D. 1984 . “Power Transformations with Fitting Theoretical Models to Data” . Journal of the American Statistical Association , 79 : 302 – 328 .
   Google Scholar
• de la Ossa , X. C. and Quevedo , F. 1993 . “Duality Symmetries From Nonabelian Isometries in String Theory” . Nuclear Physics , 403 : 377 – 394 . Series B
   Google Scholar
• Dodd , R. K. and Morris , H. C. 1984 . “Backlund Transformations for Spherically Symmetric Solutions to the Self-Dual Yang-Mills Equations” . Journal of Mathematical Physics , 25 : 669 – 672 .
   Google Scholar
• Faraway , J. J. and Sun , J. 1995 . “Simultaneous Confidence Bands for Linear Regression With Heteroscedastic Errors” . Journal of the American Statistical Association , 90 : 1094 – 1098 .
   Web of Science ®Google Scholar
• Hotelling , H. 1939 . “Tubes and Spheres in n-spaces, and a Class of Statistical Problems” . American Journal of Mathematics , 61 : 440 – 460 .
   Google Scholar
• Johansen , S. and Johnstone , I. M. 1990 . “Hotelling's Theorem on the Volume of Tubes: Some Illustrations in Simultaneous Inference and Data Analysis” . The Annals of Statistics , 18 : 652 – 684 .
   Web of Science ®Google Scholar
• Loader , C. “Nonparametric Regression, Confidence Bands and Bias Correction” . Proceedings of the 25th Symposium on the Interface Between Computer Science and Statistics . pp. 131 – 136 . Fairfax , VA : Interface Foundation of North America .
   Google Scholar
• Naiman , D. Q. 1986 . “Conservative Confidence Bands in Curvilinear Regression” . The Annals of Statistics , 14 : 896 – 906 .
   Web of Science ®Google Scholar
• Naiman , D. Q. 1990 . “Volumes of Tubular Neighborhoods of Spherical Polyhedra and Statistical Inference” . The Annals of Statistics , 18 : 685 – 716 .
   Web of Science ®Google Scholar
• Sun , J. 1993 . “Tail Probabilities of the Maxima of Gaussian Random Fields” . Annals of Probability , 21 : 34 – 71 .
   Web of Science ®Google Scholar
• Sun , J. and Loader , C. 1994 . “Simultaneous Confidence Bands in Linear Regression and Smoothing” . The Annals of Statistics , 22 : 1328 – 1346 .
   Web of Science ®Google Scholar
• Thiemann , T. and Kastrup , H. A. 1993 . “Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation” . Nuclear Physics , 399 : 211 – 258 . Series B
   Google Scholar
• Uusipaikka , E. 1983 . “Exact Confidence Bands for Linear Regression Over Intervals” . Journal of the American Statistical Association , 78 : 638 – 644 .
   Web of Science ®Google Scholar
• Xanthopoulos , B. C. and Dialynas , T. E. 1992 . “Einstein Gravity Coupled to a Massless Conformal Scalar Field in Arbitrary Space-Time Dimensions” . Journal of Mathematical Physics , 33 : 1463 – 1471 .
   Google Scholar
• Young , M. R. 1991 . “Estimating Optimal Transformations for Multivariate Data” , University of Michigan, Department of Biostatistics . unpublished Ph.D. thesis
   Google Scholar
• Zhao , Z. and Dai , X. X. 1992 . “A New Method Dealing With Hawking Effects of Evaporating Black Holes” . Modern Physics Letters A. Particles and and Fields, Gravitation, Cosmology, Nuclear Physics , 7 : 1771 – 1778 .
   Google Scholar