By John G. Webster (Editor)
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Additional resources for 29.Information Theory
To limit the number of parameters some smoothness or regularity assumptions have to be stated concerning f. Generally speaking, smoothness conditions require that the unknown function f belongs to a restricted class, such that, given an approximation technique, any function from the class can be ‘‘well’’ approximated, using a limited number of parameters. The choice of the approximation method is crucial for the quality of estimation and heavily depends on the prior information available about the unknown function f [refer to Ref.
A semi-norm is a norm, except it does not satisfy the condition: ʈ f ʈ ϭ 0 implies f ϭ 0. The following semi-norms are commonly used: ʈ f ʈ ϭ (͐ f 2(x)dx)1/2, (L2norm), ʈ f ʈ ϭ supx ͉ f(x)͉ (uniform norm, C- or Lȍ-norm), ʈ f ʈ ϭ ͉ f(x0) ͉ (absolute value at a fixed point x0). Then consider the risk function Ra N ( fˆN , f ) = E[a−1 fˆN − f ]2 N (6) ESTIMATION THEORY where aN is a normalizing positive sequence. Letting aN decrease as fast as possible so that the risk still remains bounded yields a notion of a convergence rate.
261: Video Codec for Audiovisual Services at p ϫ 64 kbits/s. ITU-T (CCITT), March 1993. 5. 263: Video Coding for Low Bitrate Communication, ITU-T (CCITT), December 1995. 6. 3 Kbits/s, ITUT (CCITT), October 1995. 7. 728: Coding of Speech at 16 Kbit/s Using Low-Delay Code Excited Linear Prediction (LD-CELP), ITU-T (CCITT), September 1992. 8. R. N. 6–21. 9. R. N. , New York: McGraw-Hill, 1978, pp. 204–215. 10. H. Nyquest, Certain topics in telegraph transmission theory, Trans. AIEE, 47: 617–644, 1928.
29.Information Theory by John G. Webster (Editor)