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On detection of the number of signals in presence of white noise. (English) Zbl 0617.62055
In the area of signal processing, it is of interest to detect the number of signals in presence of noise and to estimate the parameters of the signals. This problem is related to that of finding the multiplicity of the smallest eigenvalue of the covariance matrix of the observation vector. The methods used in this paper fall within the framework of the model selection procedures using information theoretic criteria the consistency of which is established also when the distribution underlying the observations is not necessarily complex Gaussian. The strong consistency of the estimates of the number of signals for different cases is obtained.
Reviewer: Fang Kai-Tai

62H15Multivariate hypothesis testing
62H25Factor analysis and principal components; correspondence analysis
15A18Eigenvalues, singular values, and eigenvectors
62H99Multivariate analysis
Full Text: DOI
[1] Akaike, H.: Information theory and an extension of the maximum likelihood principle. Proceedings of the second international symposium on information theory, supp. To problems of control and information theory, 267-281 (1972)
[2] Anderson, T. W.: Asymptotic theory for principal component analysis. Ann. of math. Statist. 34, 122-148 (1963) · Zbl 0202.49504
[3] Bai, Z. D.: 3rd. Ed. A note on asymptotic joint distribution of the eigenvalues of a noncentral multivariate F matrix. A note on asymptotic joint distribution of the eigenvalues of a noncentral multivariate F matrix (1984)
[4] Bai, Z. D.; Krishnaiah, P. R.; Zhao, L. C.: On rates of convergence of efficient detection criteria in signal processing with white noise. Tech. rept. No. 85-45 (1985)
[5] Bartlett, M. S.: A note on the multiplying factors for various ${\chi}2$ approximations. J. R. Statist. soc. Ser. B 16, 296-298 (1954) · Zbl 0057.35404
[6] Goodman, N. R.: Statistical analysis based on a certain multivariate complex Gaussian distribution (an introduction). Ann. of math. Statist 34, 152-176 (1963) · Zbl 0122.36903
[7] Hall, P.; Heyde, C. C.: 3rd. Ed. martingale limit theory and its application. Martingale limit theory and its application (1980) · Zbl 0462.60045
[8] Hannan, E. J.; Quinn, B. G.: The determination of the order of an autoregression. J. R. Statist. soc. Ser. B 41, 190-195 (1979) · Zbl 0408.62076
[9] Kelker, D.: Distribution theory of spherical distribution and a location scale parameter generalization. Sankhya ser. A 43, 419-430 (1970) · Zbl 0223.60008
[10] Krishnaiah, P. R.: Some recent developments on complex multivariate distributions. J. multivariate anal. 6, 1-30 (1976) · Zbl 0358.62040
[11] Krishnaiah, P. R.: Some developments on real multivariate distributions. Developments in statistics 1, 135-169 (1978) · Zbl 0415.62035
[12] Krishnaiah, P. R., and Lin, J. (in press). Complex elliptical distributons. Commun. in Statist.
[13] Krishnaiah, P. R., and Schuurmann, F. J. (in preparation). Computations of Complex Multivariate Distributions. To be published by North-Holland, Amsterdam/New York. · Zbl 0297.62031
[14] Krishnaiah, P. R.; Waikar, V. B.: Simultaneous tests for equality of latent roots against certain alternatives, I. Ann. inst. Statist. math. 24, 81-85 (1971) · Zbl 0327.62036
[15] Krishnaiah, P. R.; Waikar, V. B.: Simultaneous tests for equality of latent roots against certain alternatives, II. Ann. inst. Statist. math. 24, 81-85 (1972) · Zbl 0327.62036
[16] Liggett, W. S.: Passive sonar: Fitting models to multiple time series. Signal processing, 327-345 (1973)
[17] Rao, C. R.: 3rd. Ed. linear statistical inference and its applications. Linear statistical inference and its applications (1973) · Zbl 0256.62002
[18] Rao, C. R.: Likelihood ratio tests for relationships between two covariance matrices. Studies in econometrics, time series and multivariate statistics (1983) · Zbl 0545.62037
[19] Reznik, M. K.: The law of the iterated logarithm for some classes of stationary processes. Theory probab. Appl. 8, 606-621 (1968) · Zbl 0281.60022
[20] Rissanen, J.: Modeling by shortest data description. Automatica 14, 465-471 (1978) · Zbl 0418.93079
[21] Schmidt, R. O.: Multiple emitter location and signal parameter estimation. Proc. RADC spectrum estimation workshop (1979)
[22] Schwartz, G.: Estimating the dimension of a model. Ann. statist 6, 461-464 (1978) · Zbl 0379.62005
[23] Stout, W. F.: 3rd. Ed. almost sure convergence. Almost sure convergence (1974)
[24] Tufts, D. W.; Kumaresan, R.: Data-adaptive principal component signal processing. Proceedings, 19th IEEE conf. Decision control, 949-954 (1980)
[25] Von Neumann, J.: Some matrix-inequalities and metrization of metric space. Tomsk univ. Rev. 1, 286-300 (1937)
[26] Wax, M.; Kailath, T.: Determination of the number of signals by information theoretic criteria. IEEE trans. Acoustics speech signal process 33 (1984)
[27] Wax, H.; Shan, T. J.; Kailath, T.: Spatio-temporal spectral analysis by eigenstructure methods. IEEE trans. Acoustics speech signal process 32, 817-827 (1984)
[28] Whalen, A. D.: 3rd. Ed. detection of signals in noise. Detection of signals in noise (1971)
[29] Wooding, R. A.: The multivariate distribution of complex normal variables. Biometrika 43, 212-215 (1956) · Zbl 0070.36204
[30] Zhao, L. C., Krishnaiah, P. R., and Bai, Z. D., (in press). Remarks on certain criteria for detection of number of signals. IEEE Trans. Acoustics Speech Signal Process.
[31] Zhao, L. C.; Krishnaiah, P. R.; Bai, Z. D.: On detection of the number of signals when the noise covariance matrix is arbitrary. J. multivariate anal. 20, 26-49 (1986) · Zbl 0617.62056