Noise: a nonstandard analysis. (Analyse non standard du bruit.) (French) Zbl 1093.94009
Summary: Thanks to the nonstandard formalization of fast oscillating functions, due to P. Cartier and Y. Perrin [Diener, F.; Dienier, M. (Eds.), Nonstandard Analysis in Practice, Springer, Berlin, 195–204 (1995; Zbl 0848.26015)], an appropriate mathematical framework is derived for new non-asymptotic estimation techniques, which do not necessitate any statistical analysis of the noise corrupting any sensor. Various applications are deduced for multiplicative noises, for the length of the parametric estimation windows, and for burst errors.
MSC:
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 94A34 | Rate-distortion theory in information and communication theory |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
Keywords:
non-asymptotic estimation; multiplicative noises; length of the parametric estimation windows; burst errorsCitations:
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