By A V Balakrishnan
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Extra resources for Advances in communication systems : theory and applications. Volume 2
The method may be employed in the absence of a priori knowledge of the process statistics and in the absence of detailed knowledge of the relationship between the desired parameters and the observed data. In particular, we need to know only that the regression function satisfies certain regularity conditions and that the regression problem has a unique solution. If sufficient a priori knowledge concerning the statistics of Z(t) and the functional relationship between the parameters and observed data is available, the third advantage can be replaced by the following desirable property : the methods can be made to be asymptotically efficient.
C. Helstrom, " T h e Statistical Theory of Signal Detection" Chap. X I . Pergamon Press, Oxford, 1960. 14. R. W. Hamming, "Numerical Methods for Scientists and Engineers," Chap. X. McGraw-Hill, New York, 1962. 15. M. Abramowitz and I. , "Handbook of Mathematical Functions," p. 920. Natl. Bur. Std. 1964 (AMS 55). 16. Francis Johnson, The solar constant, J. Meteorol. 11, 431-349 (1954). 17. F. Jenkins and H. White, "Fundamentals of Optics," p. 255. McGraw-Hill, New York, 1957. Stochastic Approximation: A Recursive Method for Solving Regression Problems1 DAVID J.
First, the observation interval is divided into short subintervals of convenient fixed length. Only the observations from a single subinterval are handled at a time, and after the data from a subinterval have been processed they are discarded and not used again. Second, the two separate algorithms for estimating statistics and solving equations are combined into a single algorithm. In those situations in which stochastic approximation methods are applicable, their usage yields the following advantages: 1.