Nonparametric Regression as an Example of Model Choice

References

• Brockmann , M. , Gasser , T. , Herrmann , E. ( 1993 ). Locally adaptive bandwidth choice for kernel regression estimators . J. Amer. Statist. Assoc. 88 : 1302 – 1309 .
   Web of Science ®Google Scholar
• Daubechies , I. ( 1992 ). Ten Lectures on Wavelets . Philadelphia : SIAM .
   Google Scholar
• Davies , P. L. ( 1995 ). Data features . Statistica Neerlandica 49 : 185 – 245 .
   Google Scholar
• Davies , P. L. ( 2003 ). Approximating data and Statistical procedures – I. Approximating data . Technical Report 7/2003, SFB 475, Departement of Statistics, University of Dortmund, Germany .
   Google Scholar
• Davies , P. L. , Kovac , A. ( 2001 ). Local extremes, runs, strings and multiresolution (with discussion and rejoinder) . Ann. Statist. 29 : 1 – 65 .
   Web of Science ®Google Scholar
• Davies , P. L. , Kovac , A. ( 2004 ). Densities, spectral densities and modality . Ann. Statist. 32 : 1093 – 1136 .
   Google Scholar
• Davies , P. L. , Kovac , A. ( 2006 ). Quantifiying the cost of simultaneous non-parametric approximation of several samples . Technical Report .
   Google Scholar
• Donoho , D. L. , Johnstone , I. M. ( 1994 ). Ideal spatial adaptation by wavelet shrinkage . Biometrika 81 : 425 – 455 .
   Web of Science ®Google Scholar
• Dümbgen , L. , Spokoiny , V. G. ( 2001 ). Multiscale testing of qualitative hypotheses . Ann. Statist. 29 : 124 – 152 .
   Google Scholar
• Grünwald , P. ( 2000 ). Model selection based on minimum description length . J. Mathemat. Psychol. 44 : 133 – 152 .
   PubMed Web of Science ®Google Scholar
• Herrmann , E. ( 1997 ). Local bandwidth choice in kernel regression estimation . J. Computat. Graph. Statist. 6 : 35 – 54 .
   Web of Science ®Google Scholar
• Kovac , A. ( 2007 ). Smooth functions and local extreme values . Computat. Statist. Data Anal. 51 : 5155 – 5171 .
   Google Scholar
• Nason , G. P. , Silverman , B. W. ( 1994 ). The discrete wavelet transform in S . J. Computat. Graph. Statist. 3 : 163 – 191 .
   Google Scholar
• Polzehl , J. , Spokoiny , V. G. ( 2000 ). Adaptive weights smoothing with applications to image restoration . J. Roy. Statist. Soc. B 62 : 335 – 354 .
   Google Scholar
• Polzehl , J. , Spokoiny , G. ( 2003 ). Varying coefficient regression modeling . Preprint .
   Google Scholar
• Rissanen , J. ( 1987 ). Stochastic complexity . J. Roy. Statis. Soc. B 49 : 223 – 239 .
   Google Scholar
• Rissanen , J. ( 1989 ). Stochastic Complexity in Statistical Inquiry . Singapore : World Scientific .
   Google Scholar
• Rissanen , J. ( 1996 ). Fisher information and stochastic complexity . IEEE Trans. Inform. Theor. 42 : 40 – 47 .
   Web of Science ®Google Scholar
• Rissanen , J. ( 2000 ). MDL denoising . IEEE Trans. Inform. Theor. 46 : 2537 – 2760 .
   Web of Science ®Google Scholar