Optimally distinguishable distributions: A new approach to composite hypothesis testing with applications to the classical linear model

IEEE Transactions on Signal Processing

Volumn 57, Issue 7, 2009, Pages 2445-2455

  Razavi, Seyed Alireza ^a   Giurcǎneanu, Ciprian Doru ^a  

^a TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

Generalized likelihood ratio test; Information theoretic criteria; Linear model; Minimum description length; Optimally distinguishable distributions

Indexed keywords

GENERALIZED LIKELIHOOD RATIO TEST; INFORMATION THEORETIC CRITERIA; LINEAR MODEL; MINIMUM DESCRIPTION LENGTH; OPTIMALLY DISTINGUISHABLE DISTRIBUTIONS;

INFORMATION THEORY; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION;

VIDEODISKS;

EID: 67650099968     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2017568     Document Type: Article

References (26)

1. J. Rissanen, Information and Complexity in Statistical Modeling. New York: Springer-Verlag, 2007.
2. P. Grünwald, The Minimum Description Length principle. Cambridge, MA: MIT Press, 2007.
3. M. Li and P. Vitanyi, An Introduction to Kolmogorov Complexity and its Applications. New York: Springer-Verlag, 1997.
4. A. Barron, J. Rissanen, and B. Yu, "The minimum description length principle in coding and modeling," IEEE Trans. Inf. Theory, vol. 44, pp. 2743-2760, Oct. 1998.
5. P. Stoica and Y. Selen, "A review of information criterion rules," IEEE Signal. Process. Mag., vol. 21, no. 4, pp. 36-47, Jul. 2004.
6. G. Qian and H. Künsch, "Some notes on Rissanen's stochastic complexity," IEEE Trans. Inf. Theory, vol. 44, no. 2, pp. 782-786, Mar. 1998.
7. J. Rissanen, "The structure function and distinguishable models of data," Comput. J., vol. 49, no. 6, pp. 657-664, 2006.
8. V. Balasubramanian, "Statistical inference, Occam's razor, and statistical mechanics on the space of probability distributions," Neural Comput., vol. 9, no. 2, pp. 349-368, 1997.
9. J. Rissanen, Optimally Distinguishable Distributions, p. 8, Sep. 2007.
10. S. Kay, Fundamentals of Statistical Signal Processing: Detection theory. Englewood Cliffs, NJ: Prentice-Hall, 1998.
11. S. Razavi and C. Giurcǎneanu, "Composite hypothesis testing by optimally distinguishable distributions," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), Las Vegas, NV, Mar. 4, 2008, pp. 3897-3900.
12. L. Scharf and B. Friedlander, "Matched subspace detectors," IEEE Trans. Signal. Process., vol. 42, no. 8, pp. 2146-2157, Aug. 1994.
13. S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ: Prentice-Hall, 1993. 14 L. Scharf and L. McWhorter, "Geometry of the Cramer-Rao bound" Signal Process., vol. 31, pp. 301-311, 1993.
14. D. Foster and E. George, "The risk inflation criterion for multiple regression" Ann. Stat., vol. 22, no. 4, pp. 1947-1975, 1994.
15. E. Liski, "Normalized ML and the MDL principle for variable selection in linear regression," in Festschrift for Tarmo Pukkila on His 60th Birthday, E. Liski, J. Isotalo, J. Niemelä, S. Puntanen, and G. Styan, Eds. Tampere, Finland: Univ. of Tampere, 2006, pp. 159-172.
16. G. Seber and A. Lee, Linear Regression Analysis. New York: Wiley-Interscience, 2003.
17. H. Akaike; "A new look at the statistical model identification," IEEE Trans. Autom. Control, vol. AC-19, pp. 716-723, Dec. 1974.
18. G. Schwarz, "Estimating the dimension of a model," Ann. Stat., vol. 6, no. 2, pp. 461-464, Mar. 1978.
19. J. Rissanen, "Modeling by shortest data description," Automatica vol. 14, pp. 465-471, 1978.
20. T. Söderström, "On model structure testing in system identification," Int. J. Control, vol. 26, no. 1, pp. 1-18, 1977.
21. P. Stoica, Y. Selen, and J. Li, "On information criteria and the generalized likelihood ratio test of model order selection," IEEE Signal Process. Lett., vol. 11, pp. 794-797, 2004.
22. J. Rissanen, "Hypothesis selection and testing by the MDL principle," Comput. J., vol. 42, no. 4, pp. 260-269, 1999.
23. R. Behrens and L. Scharf, "Signal processing applications of oblique projection operators," IEEE Trans. Signal. Process., vol. 42, no, 6, pp. 1413-1424, Jun. 1994.
24. G. Golub and C. van Loan, Matrix Computations. Baltimore, MD: The Johns Hopkins Univ. Press, 1996.
25. J. Conway and N. Sloane, Sphere Packings, Lattices and Groups. New York: Springer-Verlag, 1988.
26. T. McWhorter and L. Scharf, "Cramer-Rao bounds for deterministic modal analysis," IEEE Trans. Signal. Process., vol. 41, no. 5, pp. 1847-1866, May 1993.