On minimum Fisher information distributions with restricted support and fixed variance

Information Sciences

Volumn 179, Issue 22, 2009, Pages 3832-3842

  Bercher, J F ^a   Vignat, C ^a  

^a UNIVERSITÉ PARIS EST   (France)

Author keywords

Differential equations; Fisher information; Minimization problems; Whittaker functions

Indexed keywords

BOUNDED SUBSET; ESTIMATION ERRORS; ESTIMATION THEORY; EXPLICIT EXPRESSIONS; FISHER INFORMATION; FIXED VARIANCE; INFERENCE PROBLEM; LOCATION PARAMETERS; MINIMIZATION PROBLEMS; PHYSICAL PROCESS; POSITIVE REAL; WHITTAKER FUNCTION; WHITTAKER FUNCTIONS;

DIFFERENTIAL EQUATIONS; OPTIMIZATION;

FISHER INFORMATION MATRIX;

EID: 69549108110     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2009.07.013     Document Type: Article

References (38)

1. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, ninth Dover printing, tenth GPO printing ed., Dover Publications, 1964.
2. Ali M.M., and Nadarajah S. Information matrices for normal and Laplace mixtures. Information Sciences 177 3 (2007) 947-955
3. Balasco M., Lapenna V., Lovallo M., Romano G., Siniscalchi A., and Telesca L. Fisher information measure analysis of earth's apparent resistivity. International Journal of Nonlinear Science 5 3 (2008) 230-236
4. D. Boekee, An extension of the Fisher information measure, in: I. Csiszár, P. Elias (eds.), Topics in Information Theory Proc. 2nd Colloquium on Information Theory; Keszthely, Hungary, 25-29 August 1975, vol. 16, János Bolyai Mathematical Society and North-Holland, Keszthely, Hungary, 1977.
5. Borwein J.M., Lewis A.S., Limber M.N., and Noll D. Maximum entropy reconstruction using derivative information part 2: computational results. Numerische Mathematik 69 3 (1995) 243-256
6. Borwein J.M., Lewis A.S., and Noll D. Maximum entropy reconstruction using derivative information, part 1: Fisher information and convex duality. Mathematics of Operations Research 21 (1996) 442-468
7. Cohen M. The Fisher information and convexity. IEEE Transactions on Information Theory 14 4 (1968) 591-592
8. Dasgupta A. Stein's identity, Fisher information, and projection pursuit: a triangulation. Journal of Statistical Planning and Inference 137 11 (2007) 3394-3409
9. Frank S.A. Natural selection maximizes Fisher information. Journal of Evolutionary Biology 22 2 (2009) 231-244
10. Frieden B.R. Fisher information, disorder, and the equilibrium distributions of physics. Physical Review A 41 8 (1990) 4265-4276
11. Frieden B.R. Science from Fisher Information: A Unification (2004), Cambridge University Press
12. Frieden B.R., and Binder P.M. Physics from Fisher information: a unification. American Journal of Physics 68 (2000) 1064
13. Gelfand I.M., and Fomin S.V. Calculus of Variations (2000), Dover Publications
14. Gradshteyn I., and Ryzhik I. Table of Integrals, Series and Products (1966), Academic P
15. Huber P.J. Robust statistics: a review. The Annals of Mathematical Statistics 43 3 (1972) 1041-1067
16. Lovallo M., Marchese F., Pergola N., and Telesca L. Fisher information measure of temporal fluctuations in satellite advanced very high resolution radiometer (AVHRR) thermal signals recorded in the volcanic area of Etna (Italy). Communications in Nonlinear Science and Numerical Simulation 14 1 (2009) 174-181
17. Martin M.T., Pennini F., and Plastino A. Fisher's information and the analysis of complex signals. Physics Letters A 256 2-3 (1999) 173-180
18. Mathai A. Basic Concepts in Information Theory and Statistics: Axiomatic Foundations and Applications (1975), Wiley, New York
19. Montenegro M., Casals M.R., Lubiano M.A., and Ángeles Gil M. Two-sample hypothesis tests of means of a fuzzy random variable. Information Sciences 133 1-2 (2001) 89-100
20. Nagy A. Fisher information in density functional theory. The Journal of Chemical Physics 119 18 (2003) 9401-9405
21. Nordebo S., Gustafsson M., and Nilsson B. Fisher information analysis for two-dimensional microwave tomography. Inverse Problems 23 3 (2007) 859-877
22. Romera E., and Dehesa J.S. Weizsäcker energy of many-electron systems. Physical Review A 50 1 (1994) 256-266
23. Sen K.D., Antolín J., and Angulo J.C. Fisher-Shannon analysis of ionization processes and isoelectronic series. Physical Review A 76 3 (2007) 32502
24. Sánchez-Ruiz J., and Dehesa J.S. Fisher information of orthogonal hypergeometric polynomials. Journal of Computational and Applied Mathematics 182 1 (2005) 150-164
25. Telesca L., Lapenna V., and Lovallo M. Fisher information analysis of earthquake-related geoelectrical signals. Natural Hazards and Earth System Sciences 5 4 (2005) 561-564
26. Tsairidis C., Ferentinos K., and Papaioannou T. Information and random censoring. Information Sciences 92 1-4 (1996) 159-174
27. E. Uhrmann-Klingen, Fisher-Minimale Dichten auf Kompacten intervallen (in German), Ph.D. thesis, Essen, 1992.
28. Uhrmann Klingen E. Minimal Fisher information distributions with compact-supports. Sankhya: The Indian Journal of Statistics 57 3 (1995) 360-374
29. Vignat C., and Bercher J.F. Analysis of signals in the Fisher-Shannon information plane. Physics Letters A 312 1-2 (2003) 27-33
30. Vignat C., and Bercher J.-F. On Fisher information inequalities and score functions in non-invertible linear systems. Journal of Inequalities in Pure and Applied Mathematics 4 4 (2003) 71
31. Wang Z.X., and Guo D.R. Special Functions (1989), World Scientific Pub. Co. Inc.
32. Whittaker E.T., and Watson G.N. A Course of Modern Analysis. 4th ed. (1927), Cambridge University Press
33. Wu E.K.H. Distributions minimizing Fisher information for scale in [var epsilon]-contamination neighbourhoods. Statistics & Probability Letters 14 5 (1992) 373-383
34. Wu E.K.H., and Chan P.S. Distributions minimizing Fisher information for location in Kolmogorov neighbourhoods. Annals of the Institute of Statistical Mathematics 49 3 (1997) 541-554
35. Xu B., Chen Q., Wu Z., and Wang Z. Analysis and approximation of performance bound for two-observer bearings-only tracking. Information Sciences 178 8 (2008) 2059-2078
36. Yáñez R.J., Sánchez-Moreno P., Zarzo A., and Dehesa J.S. Fisher information of special functions and second-order differential equations. Journal of Mathematical Physics 49 (2008) 082104
37. Zivojnovic V. Minimum Fisher information of moment-constrained distributions with application to robust blind identification. Signal Processing 65 2 (1998) 297-313
38. V. Zivojnovic, D. Noll, Minimum Fisher information spectral analysis, in: ICASSP-97, IEEE International Conference on Acoustics, Speech, and Signal Processing, vol. 5, 1997.