Abstract
We describe methods to establish identifiability and information-regularity of parameters in normal distributions. Parameters are considered identifiable when they are determined uniquely by the probability distribution and they are information-regular when their Fisher information matrix is full rank. In normal distributions, information-regularity implies local identifiability, but the converse is not always true. Using the theory of holomorphic mappings, we show when the converse is true, allowing information-regularity to be established without having to explicitly compute the information matrix. Some examples are given.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. E. Caines,Linear Stochastic Systems, New York: Wiley, 1988.
G. H. Golub and V. Pereyra, The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate,SIAM J. Numer. Anal., vol. 10, no. 2, pp. 413–432, April 1973.
R. C. Gunning,Introduction to Holomorphic Functions of Several Variables, Volume I: Function Theory, Pacific Grove: Brooks/Cole, 1990.
R. C. Gunning,Introduction to Holomorphic Functions of Several Variables, Volume II: Local Theory, Pacific Grove: Brooks/Cole, 1990.
B. Hochwald and A. Nehorai, Identifiability in array processing models with vector-sensor applications,IEEE Trans. Signal Processing, vol. 44, no. 1, pp. 83–95, Jan. 1996.
J. Pila, Geometric and arithmetic postulation of the exponential function,J. Australian Math. Soc., vol. 54A, pp. 111–127, 1993.
A. Wald, Note on the consistency of the maximum likelihood estimate,Ann. Math. Statist., vol. 20, pp. 595–601, 1949.
A. Wald, Tests of statistical hypotheses concerning several parameters when the number of observations is large,Trans. Amer. Math. Soc., vol. 54, pp. 426–482, 1943.
M. Wax and I. Zizkind, On unique localization of multiple sources by passive sensor arrays,IEEE Trans. Acoust. Speech, Signal Processing, vol. 37, no. 7, pp. 996–1000, July 1989.
Author information
Authors and Affiliations
Additional information
This work was supported by the Air Force Office of Scientific Research under Grant no. F49620-93-1-0096, the National Science Foundation under Grant no. MIP-9122753, and the Office of Naval Research under Grant no. N00014-91-J-1298.
Rights and permissions
About this article
Cite this article
Hochwald, B., Nehorai, A. On identifiability and information-regularity in parametrized normal distributions. Circuits Systems and Signal Process 16, 83–89 (1997). https://doi.org/10.1007/BF01183177
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01183177