Abstract
We particularize criteria proposed by one of the authors for estimating the probability densities of a random vector of size N to the case of even N. For the presentation convenience in this case, two-dimensional vectors are treated as complex random variables and the probability densities of their absolute values and arguments are estimated. The estimation algorithms are synthesized on the basis of the obtained criteria under conditions of both presence and absence of complete a priori information on the sample statistic. A number of examples are given to prove that the obtained algorithms are optimal in the statistical sense.
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REFERENCES
P. A. Bakut, ed., Signal Detection Theory [in Russian], Radio i Svyaz', Moscow (1984).
Yu. G. Sosulin, Theory of Detection and Estimation of Stochastic Signals [in Russian], Sovetskoe Radio, Moscow (1978).
B. R. Levin, Theoretical Fundamentals of Statistical Radioengineering, Pt. 3 [in Russian], Sovetskoe Radio, Moscow (1976).
D. Middleton, An Introduction to Statistical Communication Theory, McGraw-Hill New York (1960).
M. A. Ostrovskii and Yu. I. Pakhomov, Radiophys. Quantum Electron., 33, No.6, 507 (1990).
M. A. Ostrovskii, Radiophys. Quantum Electron., 38, No.8, 568 (1995).
Ya. D. Shirman and M. A. Ostrovsky, Radiotekh. Elektron., 35, No.8, 1655 (1990).
M. A. Ostrovsky, Radiophys. Quantum Electron., 40, No.11, 955 (1997).
B. R. Levin, Theoretical Fundamentals of Statistical Radioengineering. Pt. 2 [in Russian], Sovetskoe Radio, Moscow (1968).
B. R. Levin, Theoretical Fundamentals of Statistical Radioengineering, Pt. 1 [in Russian], Sovetskoe Radio, Moscow (1969).
M. A. Ostrovsky and S. A. Ryabinin, Radiophys. Quantum Electron., 41, No.10, 892 (1998).
Ya. Z. Tsypkin, Fundamentals of the Theory of Training Systems [in Russian], Sovetskoe Radio, Moscow (1976).
M. A. Leikikh and M. A. Ostrovsky, Dynamics of Systems. Stability of Dynamical Systems and Control Processes [in Russian], Gorky (1979), p. 86.
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 7, pp. 616–627, July 2005.
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Ostrovsky, M.A., Ukhanov, M.V. Estimation of Probability Densities of the Absolute Value and Argument of Complex Random Variables. Radiophys Quantum Electron 48, 547–557 (2005). https://doi.org/10.1007/s11141-005-0099-1
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DOI: https://doi.org/10.1007/s11141-005-0099-1