Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-30T20:27:17.214Z Has data issue: false hasContentIssue false
  • English
  • Français

An application of the minimum discrimination information estimate to compute log-likelihood ratios

Published online by Cambridge University Press:  14 July 2016

E. L. Melnick  and
S. Kullback
E. L. Melnick
Affiliation:
New York University
S. Kullback*
Affiliation:
The George Washington University
*
*Supported in part by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under Grant AFOSR-68–1513.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper the minimum discrimination information estimate is used to compute the log-likelihood ratio or logarithm of the Radon-Nikodym derivative In (dP1/dP2) when the stochastic process {x(t), t∈T) has either the probability measure P1 or P2. One example tests the mean value function of Gaussian processes. The other tests the mean value function of a continuous time Poisson process.

Keywords

MINIMUM DISCRIMINATION INFORMATION ESTIMATEHYPOTHESIS TESTINGTESTING MEAN VALUE FUNCTIONSCOMPUTE LOG-LIKELIHOOD RATIO
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 469 - 474
Copyright
Copyright © Applied Probability Trust 1973 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Brown, M. (1971) Discrimination of Poisson processes. Ann. Math. Statist. 42, 773–776.Google Scholar
[2] Gelfand, I. M. and Yaglom, A. M. (1957) Calculation of the amount of information about a random function contained in another such function. Amer. Math. Soc. Transl. Series 2, 12 (1959), 199–246.Google Scholar
[3] Grenander, U. I. (1950) Stochastic processes and statistical inference. Ark. Mat. 1, 195–277.Google Scholar
[4] Grenander, U. I. (1967) Eight Lectures on Statistical Inference in Stochastic Processes. Technical Report No. 2, May 1967. Division of Applied Mathematics, Brown University.Google Scholar
[5] Ku, H. H., Varner, R. N. and Kullback, S. (1971) On the analysis of multidimensional contingency tables. J. Amer. Statist. Assoc. 66, 55–64.Google Scholar
[6] Kullback, S. (1959) Information Theory and Statistics. Wiley, N. Y.; 1968 Edition, Dover Publications Inc., N.Y. Google Scholar
[7] Kullback, S. (1970) Minimum discrimination information estimation and application. Invited paper presented to Sixteenth Conference on the Design of Experiments in Army Research, Development and Testing. U.S.A. Logistics Management Center, Ft. Lee, VA. 21 October 1970. Proceedings of the conference ARO-D Report 71–3, 1–38.Google Scholar
[8] Kullback, S. and Khairat, M. A. (1966) A note on minimum discrimination information. Ann. Math. Statist. 37, 279–280.Google Scholar
[9] Simon, G. A. (1971) Information Distances and Exponential Families, with Applications to Contingency Tables. Technical Report No. 32, Nov. 26, 1971. Department of Statistics, Stanford University.Google Scholar
[10] Yaglom, A. M. (1963) On the equivalence and perpendicularity of two Gaussian measures in function space. Proceedings of the Symposium on Time Series Analysis, 1962, Brown University. Wiley, New York.Google Scholar