Robust-Resistant Spectrum Estimation

Proceedings of the IEEE

Volumn 70, Issue 9, 1982, Pages 1097-1115

  Martin, R Douglas ^a   Thomson, David J ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b LUCENT TECHNOLOGIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOREGRESSIVE APPROXIMATION; NON-GAUSSIAN NOISE; ROBUST-RESISTANT SPECTRUM ESTIMATION; SPECTRAL DENSITY;

SPECTRUM ANALYSIS;

EID: 0020183045     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/PROC.1982.12434     Document Type: Article

References (58)

1. H. Akaike, “Information theory and an extension of the maximum-likelihood principle,” in 2nd International Symposium Inf. Theory, B. N. Petrov and F. Csake, Eds. Hungary: Akademiai Kiado, pp. 267-281, 1973.
2. H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Auto. Control, vol. AC-19, pp. 716-722, 1974.
3. D. F. Andrews, P. J. Bickel, F. R. Hampel, P. J. Huber, W. F. Rogers, and J. W. Tukey et al., Robust Estimates of Location-Survey and Advances. Princeton, NJ: Princeton Univ. Press, 1972.
4. K. N. Berk, “Consistent autoregressive spectral estimates,” Ann. Statist., vol. 2, pp. 489-502, 1974.
5. R. B. Blackman and J. W. Tukey, “The measurement of power spectra from the point of view of communications engineering,” Bell Syst. Tech. J., vol. 37, 1958 (reprinted by Dover).
6. G.E.P. Box, “Non-normality and tests on variances,” Blometrika, vol. 40, pp. 318-335, 1953.
7. D. R. Brillinger, Time Series: Data Analysis and Theory. New York: Holt, Reinhart, and Winston, 1980.
8. O. Bustos, “Asymptotic behavior of general m-estimates for contaminated autoregressive processes,” Dep. Estatistica e Informatica, Univ. Federal de Pernambuco, Brazil, Tech. Rep., 1979.
9. O. Bustos, “Qualitative robustness for general processes,” Inst. of Pure and App. Math. (IMPA), Rio de Janeiro, Brazil, Tech. Rep., 1980.
10. K. Campbell, “Recursive computation of M-estimates for the parameters of a finite autoregression,” Los Alamos Sci. Lab., Tech. Rep. LA-UR-79-1963.
11. D. Cox, “Metrics on stochastic processes and qualitative robustness,” Tech. Rep. 3, Dep. Statistics, Univ. of Washington, Seattle.
12. D. R. Cox and D. V. Hinkley, Theoretical Statistics. New York: Halstead, 1974.
13. L. Denby and R. D. Martin, “Robust estimation of the first-order autoregressive parameter,” J. Amer. Statist. Ass., vol. 74, no. 365, pp. 140-146, Mar. 1979.
14. W. P. Dunsmuir, “Fitting ARMA models with missing data,” in Applied Time Series II, D. F. Findley, Ed. New York: Academic Press, 1981.
15. R. Gnanadesikan, Methods for Statistical Data Analysis of Multivariate Observations. New York: Wiley, 1977.
16. U. Grenander and M. Rosenblatt, Statistical Analysis of Stationary Time Series. New York: Wiley, 1957.
17. U. Grenander and M. Rosenblatt, Abstract Inference. New York: Wiley, 1981.
18. F. R. Hampel, “Contributions to the theory of robust estima-tion,” Ph.D. dissertation, Dep. of Statistics, Univ. of California, Berkeley, CA, 1968.
19. F. R. Hampel, “A general qualitative definition of robustness,” Ann. Math. Stat., vol. 42, pp. 1887-1895, 1971.
20. F. R. Hampel, “The influence curve and its role in robust estimation,” J. Amer. Statis. Ass., vol. 69, pp. 383-393, 1974.
21. P. J. Huber, “Robust estimation of a location parameter,” Ann. Math. Statist., vol. 35, pp. 73-101, 1964.
22. P. J. Huber, Robust Statistics. New York: Wiley, 1981.
23. A. H. Jazwinski, Stochastic Processes and Filtering Theory. New York: Academic Press, 1970.
24. R. H. Jones, “Maximum-likelihood fitting of ARMA models to time series with missing observations,” Technometrics, vol. 22, pp. 389-396, 1980.
25. R. H. Jones, “Fitting a continuous-time autoregression to discrete data,” in Applied Time Series Analysis II, D. F. Findley, Ed. New York: Academic Press, 1980.
26. R. E. Kalman, “A new approach to linear filtering and prediction problems,” Trans. Amer. Soc. Mech. Engrs., J. Basic Eng., vol. 82, pp. 35-45, 1960.
27. B. Kleiner, R. D. Martin, and D. J. Thomson, “Robust estimation of power spectra (with discussion),” J. Royal Statist. Soc., Ser. B,vol. 41, no. 3, pp. 313-351, 1979.
28. L. H. Koopmans, The Spectral Analysis of Time Series. New York: Academic Press, 1974.
29. C. H. Lee and R. D. Martin, “M-estimates for ARMA processes,” Dept. of Statist., Univ. of Washington, Seattle, Tech. Rep. 22, 1982.
30. E. L. Lehmann, Testing Statistical Hypotheses. New York, Wiley, 1959.
31. C. L. Mallows, “Some theory of nonlinear smoothers,” Ann. Statist., vol. 8, pp. 695-715, 1980.
32. R. D. Martin, “Robust estimation of signal amplitude,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 596-606, 1972.
33. R. D. Martin and C. J. Masreliez, “Robust estimation via stochastic approximation,” IEEE Trans. Inform. Theory, vol. IT-21, pp. 263-271, 1975.
34. R. D. Martin and J. E. Zeh, “Robust generalized M-estimates for autoregressive parameters, including small-sample behavior,” Dep. Elec. Eng., Univ. of Washington, Seattle, WA, Tech. Rep. 214, 1978.
35. R. D. Martin, “Robust estimation for time series autoregressions,” in: R. L. Launer and G. N. Wilkinson, Eds., Robustness in Statistics. New York: Academic Press, 1979, pp. 147-176.
36. R. D. Martin, “Approximate conditional-mean type smoothers and interpolators,” in Smoothing Techniques for Curve Estimation, T. Gasser and M. Rosenblatt, Eds. Berlin: Springer, pp. 117-143, 1979.
37. R. D. Martin, “Robust estimation of autoregressive models,” in Directions in Time Series, D. R. Brillinger and G. C. Tiao, Eds. Haywood, CA: Institute of Mathematical Statistics Publication, pp. 228-254, 1980.
38. R. D. Martin, “Robust methods for time series,” in Applied Time Series II, D. F. Findley, Ed. New York: Academic Press, 1981.
39. R. D. Martin, “The Cramer-Rao lower bound and robust M-estimates for autoregressions,” Biometrika, vol. 69, no. 2, 1982.
40. R. D. Martin, “Robust smoothers and outlier interpolators,” unpublished notes, available on request.
41. C. J. Masreliez, “Approximate non-Gaussian filtering with linear state and observation relations,” IEEE-Trans. Automat. Contr.,vol. AC-20, pp. 361-371, 1975.
42. J. S. Meditch, “Orthogonal projections and discrete optimal linear smoothing,” SIAM J. Contr., vol. 5, no. 1, pp. 74-89, 1967.
43. J. S. Meditch, Stochastic Optimal Linear Estimation and Control. New York: McGraw-Hill, 1969.
44. P. Papantoni-Kazakos and R. M. Gray, “Robustness of estimators on stationary observations,” Ann. Probability, vol. 7, no. 6, pp. 989-1002, 1979.
45. E. Parzen, “Some recent advances in time-series modelling,” IEEE Trans. Automat. Contr.,vol. AC-19, pp. 723-730, 1974.
46. E. S. Pearson and H. O. Hartley, Biometrika Tables for Statisticians, Vol. I. Cambridge, UK: Cambridge Univ. Press, 1966.
47. E. L. Price and V. D. Vandelinde, “Robust estimation using the Robbins-Monro stochastic approximation algorithm,” IEEE Trans. Informat. Theory, vol. IT-25, pp. 698-704, 1979.
48. P. F. Thall, “Huber-sense robust M-estimation of a scale parameter, with application to the exponential distribution,” J. Amer. Statist. Assoc., vol. 74, pp. 147-152, 1979.
49. D. J. Thomson, “Spectrum estimation techniques for characterization and development of WT4 waveguide, part I,” Bell Syst. Tech. J., vol. 56, pp. 1769-1815, 1977.
50. D. J. Thomson, “Spectrum estimation techniques for characterization and development of WT4 waveguide, part II,” Bell Syst. Tech. J., vol. 56, pp. 1769-1815, 1977.
51. D. J. Thomson, “Spectrum estimation and harmonic analysis,” this issue, pp. 1055-1096.
52. J. W. Tukey, “A survey on sampling from contaminated distributions,” in Contributions to Probability and Statistics, I. Olkin, Ed. Stanford, CA: Stanford Univ. Press, 1960.
53. J. W. Tukey, “An introduction to the calculations of numerical spectrum analysis,” in Advanced Seminar on Spectral Analysis of Time Series, B. Harris, Ed. New York: Wiley, 1967, pp. 25-46.
54. P. D. Welch, “The use of the fast Fourier transform for estimation of spectra: A method based on time averaging over short, modified periodograms,” IEEE Trans. Audio Electroacoust., vol. AU-15, pp. 70-74, 1967.
55. V. J. Yohai, G. Boente, and R. Fraiman, “A definition of qualitative robustness for estimators on discrete-time random processes,” Tech. Rep. 26, Dep. Statistics, Univ. of Washington, Seattle, WA.
56. V. J. Yohai and O. Bustos, “Robust RA-type estimates for ARMA models,” Tech. Rep., Dep. of Mathematics, Ciudad Universitaria, Buenos Aires, Argentina.
57. P. Bloomfield, Fourier Analysis of Time Series. An Introduction. New York: Wiley, 1976.
58. J.W. Tukey, Exploratory Data Analysis. Reading, MA: Addison-Wesley, 1977.