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28. , “Differential geometric theory of statistics,” in Differential Geom[4] etry in Statistical Inference, S. S. Gupta, Ed. Hayward, CA: Inst. Math. , 1987, vol. 10, IMS Lecture Notes—Monograph Series. , Methods of Information Geometry. Providence, RI: Amer. [5] Math. , 2000. Originally published in Japanese as Joho kika no hoho (Tokyo, Japan: Iwanami Shoten, 1993). [6] , “Information geometry on hierarchy of probability distributions,” IEEE Trans. Inf. Theory, vol. 47, no. 5, pp. 1701–1711, Jul.

Pattern Anal. , vol. 20, no. 8, pp. 790–802, Aug. 1998. [31] S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces. New York: Academic, 1978. , Groups and Geometric Analysis. New York: Academic, 1984. [32] [33] U. Helmke and J. B. Moore, Optimization and Dynamical Systems. Berlin, Germany: Springer-Verlag, 1994. [34] H. Hendriks, “A Cramér–Rao type lower bound for estimators with values on a manifold,” J. , vol. 38, pp. 245–261, 1991. [35] B. M. Hochwald and T. L. Marzetta, “Unitary space-time modulation for multiple-antenna communications in Rayleigh flat fading,” IEEE Trans.

PROBLEM FORMULATION Consider linear observation equations of an unknown common parameter , where the observed data is contaminated with noise, namely (1) where and are the unknown random parameter and the noise, respectively. , is the dimension of the estimated parameter , and is the dimension of the observation of the th sensor. , and Var . The observation here is not necessarily the original sensor measurement. It may also be a precan be the estimate at processed sensor data. In particular, the th sensor.

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