Robust Frequency Estimation Using Elemental Sets

Journal of Computational and Graphical Statistics

Volumn 9, Issue 1, 2000, Pages 196-214

  Smyth, Gordon K ^a   Hawkins, Douglas M ^b  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

High breakdown; High efficiency; Least median of squares; Least trimmed sum of squares; MM estimators; Sums of exponential function

Indexed keywords

EID: 23044518574     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.2000.10474874     Document Type: Article

References (24)

1. Andrews, D. F., and Herzberg, A. M. (1985), Data. A Collection of Problems From Many Fields for the Student and Research Worker, New York: Springer.
2. Atkinson, A. C., and Weisberg, S. (1991), “Simulated Annealing for the Detection of Multiple Outliers Using Least Squares and Least Median of Squares Fitting,” in Directions on Robust Statistics: Part I, eds. W. Stahel and S. Weisberg, New York: Springer, pp. 7-20.
3. Brockwell, P. J., and Davis, R. A. (1991), Time Series. Theory and Methods (2nd ed.), New York: Springer.
4. Fisher, N. I., Lewis, T., and Embleton, B. J. J. (1987), Statistical Analysis of Spherical Data, Cambridge, UK: Cambridge University Press.
5. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J., and Stahel, W. A. (1986), Robust Statistics. The Approach Based on Influence Functions, New York: Wiley.
6. Hawkins, D. M. (1993), “The Accuracy of Elemental Set Approximations for Regression,” Journal of the American Statistical Association, 88, 580-589.
7. Hawkins, D. M., Bradu, D., and Kass, G. V. (1984), “Location of Several Outliers in Multiple Regression Data Using Elemental Sets,” Technometrics, 26, 197-208.
8. Kahn, M., Mackisack, M. S., Osborne, M. R., and Smyth, G.K. (1992), “On the Consistency of Prony’s Method and Related Algorithms,” Journal of Computational and Graphical Statistics, 1, 329-349.
9. Kundu, D., and Kannan, N. (1997), “Constrained Maximum Likelihood Estimators for Superimposed Exponential Signals,” Communications in Statistics-Simulation and Computation, 26, 733-764.
10. Kay, S. M., and Marple, S. L. (1981), “Spectrum Analysis-A Modem Perspective,” Proceedings of the IEEE, 69, 1380-1419.
11. Mackisack, M. S., Osbome, M. R., and Smyth, G. K. (1994), “A Modified Prony Algorithm for Estimating Sinusoidal Frequencies,” Journal of Statistical Computing and Simulation, 49, 111-124.
12. Marazzi, M. (1991), “Algorithms and Programs for Robust Linear Regression,” in Directions in Robust Statistics and Diagnostics, Part I, eds. W. Stahel and S. Weisberg, New York: Springer-Verlag, pp. 183-200.
13. Osbome, M. R., and Smyth, G. K. (1991), “A Modified Prony Algorithm for Fitting Functions Defined by Difference Equations,” SIAM Journal on Scientific and Statistical Computing, 12, 362-382.
14. Osbome, M. R., and Smyth, G. K. (1995), “A Modified Prony Algorithm for Exponential Function Fitting,” SIAM Journal on Scientific and Statistical Computing, 16, 119-138.
15. Prony, R. (1795), “Essai Experimental et Analytique,” Journal de L’Ecole Polytechnique, 2, 24-76.
16. Reimann, J. D. (1994), Frequency Estimation Using Unequally-Spaced Astronomical Data, unpublished Ph.D. Thesis, University of California, Berkeley.
17. Rice, J. A., and Rosenblatt, M. (1988), “On Frequency Estimation,” Biometrika, 75, 477-484.
18. Rousseeuw, P. J. (1984), “Least-Median of Squares Regression,” Journal of the American Statistical Association, 79, 871-880.
19. Roussseeuw, P. J. and Leroy, A. M. (1987), Robust Regression and Outlier Detection, New York: Wiley.
20. Smyth, G. K. (in press), “Employing Symmetry Constraints for Improved Frequency Estimation by Eigenanal-ysis Methods,” Technometrics.
21. Stromberg, A. J. (1993), “Computation of High Breakdown Nonlinear Regression Parameters,” Journal of the American Statistical Association, 88, 237-244.
22. Stromberg, A. J. (1995), “Consistency of the Least Median of Squares Estimator in Nonlinear Least Squares,” Communications in Statistics-Theory and Methods, 24, 1971-1984.
23. Stromberg, A. J., and Ruppert, D. (1992), “Breakdown in Nonlinear Regression," Journal of the American Statistical Association, 87, 991-997.
24. Yohai, V. J. (1987), “High Breakdown Point and High Efficiency Robust Estimates for Regression,” The Annals of Statistics, 15, 642-656.