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REGRESSION ANALYSIS

Wavelets for Nonparametric Stochastic Regression with Mixing Stochastic Process

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Pages 373-385 | Received 20 Jan 2006, Accepted 27 Apr 2007, Published online: 30 Jan 2008

References

  • Antoine , J. P. , Murenzi , R. , Vandergheynst , P. , Ali , S. T. ( 2004 ). Two-dimensional Wavelets and Their Relatives. Cambridge UK : Cambridge University Press .
  • Antoniadis , A. ( 1994 ). Smoothing noisy data with coiflets . Statistica Sinica 4 : 651 – 678 .
  • Antoniadis , A. , Pham , D. T. ( 1995 ). Wavelet regression for random or irregular design. Technical Report RT 148, IMAG-LMC , University of Grenoble , France .
  • Antoniadis , A. , Pham , D. T. ( 1998 ). Wavelet regression for random or irregular design . Computat. Statist. Data Anal. 28 : 353 – 369 .
  • Antoniadis , A. , Fan , J. ( 2001 ). Regularisation of wavelet approximations (with discussion) . J. Amer. Statist. Assoc. 96 : 937 – 967 .
  • Antoniadis , A. , Grégoire , G. , McKeague , I. ( 1994 ). Wavelet methods for curve estimation . J. Amer. Statist. Assoc. 89 : 1340 – 1353 .
  • Antoniadis , A. , Gregoire , G. , Vial , P. ( 1997 ). Random design wavelet curve smoothing . Statist. Probab. Lett. 35 : 225 – 232 .
  • Daubechies , I. ( 1992 ). Ten Lectures on Wavelets. CBMS-NSF regional conferences series in applied mathematics . Philadelphia : SIAM .
  • Delouille , V. , Franke , J. , von Sachs , R. (2001). Nonparametric stochastic regression with design-adapted wavelets. Sankhya, Ser. A 63:328–366.
  • Delouille , V. , Simoens , J. , von Sachs , R. ( 2004 ). Smooth design-adapted wavelets for nonparametric stochastic regression . J. Amer. Statist. Assoc. 99 : 643 – 659 .
  • Delyon , B. , Juditsky , A. ( 1997 ). On the computation of wavelet cofficients . J. Approximation Theor. 88 : 47 – 79 .
  • Donoho , D. L. , Johnstone , I. M. , Kerkyacharian , G. , Picard , D. ( 1995 ). Wavelet shrinkage: asymptopia (with discussion) . J. Roy. Statist. Soc. Ser. B 57 ( 2 ): 301 – 370 .
  • Donoho , D. L. , Johnstone , I. M. , Kerkyacharian , G. , Picard , D. ( 1996 ). Density estimation by wavelet thresholding . Ann. Statist. 2 : 508 – 539 .
  • Doosti , H. , Fakoor , V. , Chaubey , P. Y. ( 2005 ). Wavelet linear density estimation for negative associated sequences . J. Indian Stat. Assoc. 44 : 127 – 135 .
  • Doukhan , P. , Leon , J. R. ( 1990 ). Une note sur la déviation quadratique déstimateurs de densités par projections orthogonales . C.R. Acad. Sci. Pairs t310 ( 1 ): 425 – 430 .
  • Eubank , R. L. ( 1988 ). Spline Smoothing and Nonparametric Regression . New York : Marcel Dekker .
  • Härdle , W. , Kerkyacharian , G. , Picard , D. , Tsybabov , A. ( 1998 ). Wavelets: Approximation and Statistical Applications. New York : Springer-Verlag .
  • Huang , S. Y. ( 1999 ). Density estimation by wavelet-based reproducting kernels . Statistica Sinica 9 : 137 – 151 .
  • Kerkyacharian , G. , Picard , D. ( 1992 ). Density estimation in Besov spaces . Statist. Probab. Lett. 13 : 15 – 24 .
  • Kovac , A. , Silverman , B. W. ( 2000 ). Extending the scope of wavelet regression methods by cofficient-dependent thresholding . J. Amer. Statist. Assoc. 95 : 172 – 183 .
  • Leblance , F. ( 1996 ). Wavelet linear density estimator for a discrete-time stochastic process: L p -losses . Stat. Probabil. Lett. 27 : 71 – 84 .
  • Meyer , Y. ( 1990 ). Ondelettes et Operateurs . Paris : Hermann .
  • Müller , H. G. ( 1988 ). Nonparametric Regression Analysis of Longitudinal Data . Vol. 46 . Lecture Notes in Statistics . Berlin : Springer-Verlag .
  • Pensky , M. , Vidakovic , B. ( 2001 ). On non-equally spaced wavelet regression . Ann. Inst. Statist. Math. 53 : 681 – 690 .
  • Rosenblatt , M. ( 1991 ). Stochastic Curve Estimation . NSF-CBMS Regional Conference Series in Probability and Statistics, 3 . Hayward, California : Institute of Mathematical Statistics .
  • Sardy , S. , Percival , D. B. , Bruce , A. G. , Gao , H. Y. , Stuetzle , W. ( 1999 ). Wavelet de-noising for unequally spaced data . Statist. Comput. 9 : 65 – 75 .
  • Tribiel , H. ( 1992 ). Theory of Function Space II . Verlag, Berlin : BirkhaBirkhauser .
  • Tribouley , K. ( 1995 ). Density estimation by cross-validation with wavelet method . Statistica Neerlandica 45 : 41 – 62 .
  • Vidakovic , B. ( 1999 ). Statistical Modeling by Wavelets . New York : Wiley .

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