Testing Uniformity Via Log-Spline Modeling

References

• Barron , A. R. and Sheu , C. 1991 . Approximation of density functions by sequences of exponential families . Ann. Statist. , 19 : 1347 – 1369 .
   Web of Science ®Google Scholar
• Bickel , P. J. and Ritov , Y. 1992 . “ Testing for goodness of fit: A new approach ” . In Non-parametric Statistics and Related Topics , Edited by: Saleh , A. K. Md. E. Amsterdam : North-Holland .
   Google Scholar
• Bogdan , M. 1995 . Data driven versions of Pearson's chi-square test for uniformity . J. Statist. Comput. Simul. , 52 : 217 – 237 .
   Web of Science ®Google Scholar
• Chui , C. K. 1992 . An Introduction to Wavelets , Boston : Academic Press .
   Google Scholar
• Cressie , N. and Read , T. R. C. 1989 . Pearson's χ2 and the loglikelihood ratio statistic G 2: A comparative review . Int. Statist, Rev. , 57 : 19 – 43 .
   Web of Science ®Google Scholar
• Davis , P. J. 1979 . Circulant Matrices , New York : Wiley .
   Google Scholar
• De Boor , C. 1978 . A Practical Guide to Splines , New York : Springer .
   Google Scholar
• Eubank , R. L. , Hart , J. D. and LaRiccia , V. N. 1993 . Testing goodness of fit via non-parametric function estimation techniques . Comm. Statist. Theory Methods , 22 : 3327 – 3354 .
   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 . Ann. Statist. , 20 : 2071 – 2086 .
   Web of Science ®Google Scholar
• Fan , J. “ Tests of significance based on wavelet thresholding and Neyman's truncation ” . Manuscript
   Google Scholar
• Gantmacher , F. R. 1988 . The Theory of Matrices , Moscow : Nauka .
   Google Scholar
• Gregory , G. G. 1977 . Large sample theory for U-statistics and tests of fit . Ann. Statist. , 5 : 110 – 123 .
   Web of Science ®Google Scholar
• Inglot , T. , Kallenberg , W. C. M. and Ledwina , T. 1993 . Asymptotic behaviour of some bilinear functionals of the empirical process . Math. Methods of Statist. , 2 : 316 – 336 .
   Google Scholar
• Inglot , T. , Kallenberg , W. C. M. and Ledwina , T. 1994 . Power approximations to and power comparison of certain goodness-of-fit tests . Scand. J. Statist. , 21 : 131 – 145 .
   Web of Science ®Google Scholar
• Inglot , T. and Ledwina , T. 1995 . Asymptotic optimality of data driven Neyman's tests . Ann. Statist. , to appear
   Google Scholar
• Ingster , Yu. I. 1982 . Minimax nonparametric detection of signals in white Gaussian noise . Problems Inform. Transmission , 18 : 130 – 140 .
   Google Scholar
• Ingster , Yu. I. 1993a . Asymptotically minimax hypothesis testing for nonparametric alternatives . I Math. Methods of Statist. , 2 : 85 – 114 .
   Google Scholar
• Ingster , Yu. I. 1993b . Asymptotically minimax hypothesis testing for nonparametric alternatives . II Math. Methods of Statist. , 2 : 171 – 189 .
   Google Scholar
• Ingster , Yu. I. 1993c . Asymptotically minimax hypothesis testing for nonparametric alternatives . III Math. Methods of Statist. , 2 : 249 – 268 .
   Google Scholar
• Kallenberg , W. C. M. and Ledwina , T. 1995a . Consistency and Monte Carlo simulation of a data driven version of smooth goodness-of-fit tests . Ann. Statist. , 23 : 1594 – 1608 .
   Web of Science ®Google Scholar
• Kallenberg , W. C. M. and Ledwina , T. 1995b . On data driven Neyman's test . Probab. Math. Statist. , 15 : 409 – 426 .
   Google Scholar
• Kim , J. 1992 . Testing goodness-of-fit via order selection criteria , Texas A&M Univeristy . Ph. D. dissertation
   Google Scholar
• Ledwina , T. 1994 . Data driven version of Neyman's smooth test of fit . J. Amer. Statist. Assoc. , 89 : 1000 – 1005 .
   Web of Science ®Google Scholar
• Mann , H. B. and Wald , A. 1942 . On the choice of the number of class intervals in the application of the chi-square test . Ann. Math. Statist. , 13 : 306 – 317 .
   Google Scholar
• Marsaglia , G. and Zaman , A. 1991 . A new class of random numbers generators . Ann. Appl. probab. , 1 : 462 – 480 .
   Google Scholar
• Neyman , J. 1937 . ‘Smooth test’ for goodness of fit . Skand. Aktuarietidskr. , 20 : 149 – 199 .
   Google Scholar
• Pearson , K. 1900 . On the criterion that a given system of deviations from the probable in the case of correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling . Phil. May. , 50 : 157 – 172 .
   Google Scholar
• Prohorov , A. V. 1973 . On sums of random vectors . Theory. Probab. Appl. , 18 : 186 – 188 .
   Google Scholar
• Oosterhoff , J. 1985 . The choice of cells in chi-square tests . Statist. Neer. , 39 : 115 – 128 .
   Google Scholar
• Shorack , G. R. and Wellner , J. A. 1986 . Empirical Processes with Applications to Statistics , New York : Wiley .
   Google Scholar
• Stone , C. J. 1990 . Large sample inference for log-spline models . Ann. Statist. , 18 : 717 – 741 .
   Web of Science ®Google Scholar
• Schwarz , G. 1978 . Estimating the dimension of a model . Ann. Statist. , 6 : 461 – 464 .
   Web of Science ®Google Scholar