Test of Significance Based on Wavelet Thresholding and Neyman's Truncation

References

• Anderson , T. W. and Darling , D. A. 1952 . “Asymptotic Theory of Certain Goodness-of-Fit Criteria Based on Stochastic Processes,” . Annals of Mathematical Statistics , 23 : 193 – 212 .
   Google Scholar
• Bickel , P. J. 1983 . “Minimax Estimation of a Normal Mean Subject to Doing Well at a Point,” . In Recent Advances in Statistics , Edited by: Rizvi , M. H. , Rustagi , J. S. and Siegmund , D. 511 – 528 . New York : Academic Press .
   Google Scholar
• Bickel , P. J. and Rosenblatt , M. 1973 . “On Some Global Measures of the Deviation of Density Function Estimates,” . The Annals of Statistics , 1 : 1071 – 1095 .
   Web of Science ®Google Scholar
• Bickel , P. J. and Ritov , Y. 1992 . “Testing for Goodness of Fit: A New Approach,” . In Nonparametric Statistics and Related Topics , Edited by: Md , A. K. and Saleh , E. 51 – 57 . Amsterdam : Elsevier .
   Google Scholar
• Bowman , A. W. 1992 . “Density-Based Tests for Goodness of Fit,” . Journal of Statistical Computation and Simulation , 40 : 1 – 13 .
   Google Scholar
• Bowman , A. W. and Foster , P. J. 1993 . “Adaptive Smoothing and Density-Based Tests of Multivariate Normality,” . Journal of the American Statistical Association , 88 : 529 – 37 .
   Web of Science ®Google Scholar
• D'Agostino , R. B. and Stephens , M. A. 1986 . Goodness-of-Fit Techniques , New York : Marcel Dekker .
   Google Scholar
• Darling , D. A. and Erdös , P. 1956 . “A Limit Theorem for the Maximum of Normalized Sums of Independent Random Variables,” . Duke Mathematical Journal , 23 : 143 – 155 .
   Web of Science ®Google Scholar
• Daubechies , I. 1992 . Ten Lectures on Wavelets , Philadelphia : SIAM .
   Google Scholar
• Donoho , D. L. 1995 . “Nonlinear Solution of Linear Inverse Problems by Wavelet-Vaguelette Decomposition,” . Applied and Computational Harmonic Analysis , 2 : 101 – 126 .
   Web of Science ®Google Scholar
• Donoho , D. L. and Johnstone , I. M. 1994 . “Ideal Spatial Adaptation by Wavelet Shrinkage,” . Biometrika , 81 : 425 – 455 .
   Web of Science ®Google Scholar
• Donoho , D. L. and Liu , R. C. 1991 . “Geometrizing Rate of Convergence II,” . The Annals of Statistics , 19 : 633 – 667 .
   Web of Science ®Google Scholar
• Eubank , R. L. and Hart , J. D. 1992 . “Testing Goodness of Fit in Regression via Order Selection Criteria,” . The Annals of Statistics , 20 : 1412 – 1425 .
   Web of Science ®Google Scholar
• Eubank , R. L. and LaRiccia , V. N. 1992 . “Asymptotic Comparison of Cramér—von Mises and Nonparametric Function Estimation Techniques for Testing Goodness of Fit,” . The Annals of Statistics , 20 : 2071 – 2086 .
   Web of Science ®Google Scholar
• Fan , J. 1994 . “Test of Significance Based on Wavelet Thresholding and Neyman's Truncation,” , Université Catholique de Louvain, Institut de Statistique . Discussion Paper 9315
   Google Scholar
• Fan , J. , Hall , P. , Martin , M. and Patil , P. 1993 . “Adaptation to High Spatial Inhomogeneity Based on Wavelets and on Local Linear Smoothing,” , Chapel Hill : University of North Carolina . Institute of Statistics Mimeo Series 2307
   Google Scholar
• Fisher , R. A. and Yates , F. 1938 . Statistical Tables for Biological, Agricultural and Medical Research , Edinburgh : Oliver & Boyd .
   Google Scholar
• Hájek , J. and Šidák , Z. 1967 . Theory of Rank Tests , New York : Academic Press .
   Google Scholar
• Hollander , M. and Wolfe , D. A. 1973 . Nonparametric Statistical Methods , New York : John Wiley .
   Google Scholar
• Ibragimov , I. A. and Hasminksii , R. Z. 1984 . “On Nonparametric Estimation of a Linear Functional in a Gaussian White Noise,” . Theory of Probability and Its Applications , 29 : 19 – 32 .
   Web of Science ®Google Scholar
• Inglot , T. , Kallenberg , W. C. M. and Ledwina , T. 1994 . “Power Approximations to and Power Comparison of Smooth Goodness-of-Fit Tests,” . Scandinavian Journal of Statistics , 21 : 131 – 145 .
   Web of Science ®Google Scholar
• Inglot , T. , Kallenberg , W. C. M. and Ledwina , T. 1995 . “On Selection Rules, With Application to Goodness of Fit for Composite Hypotheses,” unpublished manuscript
   Google Scholar
• Kallenberg , W. C. M. and Ledwina , T. 1994 . “Data-Driven Smooth Tests for Composite Hypotheses,” , University of Twente . Technical Report 1232
   Google Scholar
• Komlós , J. , Major , P. and Tusnády , G. 1975 . “An Approximation of Partial Sums of Independent RV's, and the Sample DF. I,” . Z. Wahrscheinlichkeitsheorie verw. Gebiete , 32 : 111 – 131 .
   Web of Science ®Google Scholar
• Ledwina , T. 1994 . “Data-Driven Version of Neyman's Smooth Test of Fit,” . Journal of the American Statistical Association , 89 : 1000 – 1005 .
   Web of Science ®Google Scholar
• Mallat , S. 1989 . “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,” . IEEE Transactions on Pattern Analysis and Machine Intelligence , 11 : 674 – 693 .
   Web of Science ®Google Scholar
• Meyer , Y. 1990 . Ondelettes , Paris : Hermann .
   Google Scholar
• Neyman , J. 1937 . “Smooth Test for Goodness of Fit,” . Skandinavisk Aktuarietidskrift , 20 : 149 – 199 .
   Google Scholar
• Pinsker , M. S. 1980 . “Optimal Filtering of Square Integrable Signals in Gaussian White Noise,” . Problems of Information Transmission , 16 : 52 – 68 .
   Google Scholar
• Rayner , J. C. W. and Best , D. J. 1989 . Smooth Tests of Goodness of Fit , New York : Oxford University Press .
   Google Scholar
• Shapiro , S. S. and Wilk , M. B. 1965 . “An Analysis-of-Variance Test for Normality,” . Biometrika , 52 : 591 – 611 .
   Web of Science ®Google Scholar
• Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , London : Chapman and Hall .
   Google Scholar
• Wilcoxon , F. 1945 . “Individual Comparisons by Ranking Methods,” . Biometrics Bulletin , 1 : 80 – 83 .
   Google Scholar