Testing Gaussianity with the characteristic function: The i.i.d. case

Signal Processing

Volumn 53, Issue 2-3, 1996, Pages 245-255

  Zoubir, A M ^a   Arnold, M J ^a  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

CHARACTERISTIC FUNCTION; GAUSSIANITY; TEST STATISTIC DISTRIBUTIONS;

PROBLEM SOLVING; SAMPLING; SPURIOUS SIGNAL NOISE; STATISTICAL TESTS;

SIGNAL PROCESSING;

EID: 0030235527     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/0165-1684(96)00089-8     Document Type: Article

References (33)

1. M.J. Arnold, D.R. Iskander and A.M. Zoubir, "Testing Gaussianity with the characteristic function", Proc. Internat. Conf. Acoust. Speech Signal Processing (ICASSP), Detroit, USA, May 1995, Vol. III, pp. 2012-2015.
2. M.J. Arnold, A.M. Zoubir and B. Boashash, "Estimation of the characteristic function", IEEE Signal Processing/ATHOS Workshop on Higher-Order Statistics, Begur, Spain, June 1995, pp. 231-235.
3. D.R. Brillinger, "An introduction to polyspectra", Ann. Math. Statist. Vol. 36, October 1965, pp. 1351-1374.
4. D.R. Brillinger, "Parameter estimation for non-Gaussian processes via second order and third order spectra with an application to some endocrine data", in: Proc. 3rd workshop on advanced methods of physiological system modelling, Plenum Press, New York, 1989, pp. 53-61.
5. D.R. Brillinger and M. Rosenblatt, "Asymptotic theory of estimates of kth order spectra", in: B. Harris, ed., Spectral Analysis of Time Series, Wiley, New York, 1967, Chapter 7, pp. 153-188.
6. M.J. Campbell and A.M. Walker, "A survey of statistical work on the MacKenzie River series of annual Canadian lynx trappings for the years 1821-1934", J. Roy. Statist. Soc. Ser. A, Vol. 140, 1977, pp. 411-431.
7. K.C. Chandra, "Chi-squared goodness-of-fit tests based on dependent observations", in: G.P. Patil, C. Taillie and B.A. Baldessari, eds., Statistical Distributions in Scientific Work, Reidel, Dordrecht, 1981, pp. 35-49.
8. E. Conte and M. Longo, "Characterisation of radar clutter as a spherically invariant random process", IEE Proc. F, Vol. 134, 1987, pp. 191-197.
9. H. Cramér, Mathematical Methods for Statistics, Princeton University Press, Princeton, NJ, 1966.
10. J.W. Dalle Molle and M.J. Hinich, "The trispectrum", in: Proc. Workshop on Higher-Order Spectral Analysis, Vail, Colorado, 1989, pp. 68-72.
11. R.F. Dwyer, "Range and Dopler information from fourth-order spectra", IEEE J. Oceanic Engineering, Vol. 16, No. 3, July 1991, pp. 233-243.
12. T.W. Epps, "Testing that a stationary time series is Gaussian", Ann. Statist., Vol. 15, No. 4, 1987, pp. 1683-1698.
13. T.W. Epps, 1992, Personal communication.
14. A. Feuerverger and R.A. Mureika, "The empirical characteristic function and its applications", Ann. Statist., Vol. 5, No. 1, 1977, pp. 88-97.
15. T. Gasser, "Goodness-of-fit tests for correlated data", Biometrika, Vol. 62, 1975, pp. 563-570.
16. G.B. Giannakis and M.K. Tsatsanis, "Time-domain tests for Gaussianity and time-reversibility", IEEE Trans. Signal Process., Vol. 42, 1994, pp. 3460-3472.
17. M.J. Hinich, "Testing for Gaussianity and linearity of a stationary time series", J. Time Series Anal., Vol. 3, No. 3, 1982, pp. 169-176.
18. M.J. Hinich and D.M. Patterson, "Identification of the coefficients in a non-linear time series of the quadratic type", J. Econometrics, Vol. 30, 1985, pp. 269-288.
19. D.R. Iskander, M.J. Arnold and A.M. Zoubir, "Testing Gaussianity using higher order statistics: The small sample size case", in: Proc. IEEE Signal Processing/ATHOS Workshop on Higher-Order Statistics, Begur, Spain, June 1995, pp. 191-195.
20. D. Kletter and H. Messer, "Suboptimal detection of non-Gaussian signal by third-order statistics", IEEE Trans. Acoust. Speech Signal Process., Vol. 38, 1990, pp. 901-909.
21. I.A. Koutrouvelis, "A goodness-of-fit test of simple hypotheses based on the empirical characteristic function", Biometrika, Vol. 67, No. 1, 1980, pp. 238-240.
22. E.B. Manoukian, Modern Concepts and Theorems of Mathematical Statistics, Springer, New York, 1986.
23. D.S. Moore, "The effect of dependence on chi-squared tests of fit", Ann. Statist., Vol. 10, 1982, pp. 1163-1171.
24. E. Moulines, K. Choukri and M. Charbit, "Testing that a multivariate stationary time series is Gaussian", in: Proc. 6th IEEE SSAP Workshop on Statistical Signal and Array Processing, Victoria, Canada, 1992, pp. 185-188.
25. E. Moulines, J.W. Dalle Molle, K. Choukri and M. Charbit, "Testing that a stationary time series is Gaussian: time domain vs. frequency domain approaches", in: Proc. IEEE Signal Processing Workshop on Higher-Order Statistics, South Lake Tahoe, California, June 1993, pp. 336-340.
26. E.S. Pearson, R.B. D'Agostino and K.O. Bowman, "Tests for departure from normality: comparison of powers", Biometrika, Vol. 64, No. 2, 1977, pp. 231-246.
27. T.S. Rao, "The bispectral analysis of nonlinear stationary tme-series with reference to bilinear time-series model", in: D.R. Brillinger and P.R. Krishnaiah, eds., Handbook of Statistics, North-Holland, Amsterdam, 1983, Vol. 3, pp. 293-319.
28. S.S. Shapiro, M.B. Wilk and H.J. Chen, "Comparative study of various tests of normality", J. Amer. Statist. Assoc., Vol. 63, 1968, pp. 1343-1372.
29. B.W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London, 1986.
30. T. Subba Rao and M.M. Gabr, "A test for linearity of stationary time series", J. Time Series Anal., Vol. 1, 1980, pp. 45-158.
31. M. Waldmeier, The Sunspot Activity in the Years 1610-1960, Schulthess, Zürich, 1961.
32. A.M. Zoubir, "Gaussianity test for zero-skewed real and complex data", in: Proc. IEEE Signal Processing Workshop on Higher-Order Statistics, South Lake Tahoe, California, June 1993, pp. 327-331.
33. A.M. Zoubir and J.F. Böhme, "Application of higher-order spectra to the analysis and detection of knock in combustion engines", in: B. Boashash, E.J. Powers and A.M. Zoubir, eds., Higher Order Statistical Signal Processing, Longman Cheshire, Melbourne, 1995, Chapter 9.