Description of accuracy using conventional and robust estimates of scale

References

• Andrews , D. F. , Bickel , P. J. , Hampel , F. R. , Huber , P. J. , Rogers , W. H. and Tukey , J. W. 1972 . Robust Estimates of Location: Survey and Advances , Princeton, NJ : Princeton University Press .
   Google Scholar
• Barnett , V. and Lewis , T. 1984 . Outliers in Statistical Data , 2nd ed. , New York : John Wiley .
   Google Scholar
• Beckman , R. J. and Cook , R. D. 1983 . Outlier . . . s . Technometrics , 25 May : 119 – 64 .
   Google Scholar
• Bernoulli , D. 1777 . “ The most probable choice between several discrepant observations and the formation there from of the most likely induction ” . In Biometrika Edited by: Allen , C. G. Vol. 48 , 3 – 13 . Studies in the history of probability and statistics
   Google Scholar
• Bickel , P. J. and Lehmann , E. L. 1976 . Descriptive statistics for nonparametric models III: dispersion . The Annals of Statistics , 4 ( 6 ) : 1139 – 58 .
   Web of Science ®Google Scholar
• Bickel , P. J. and Lehmann , E. L. 1979 . “ Descriptive statistics for nonparametric models IV: spread ” . In Contributions to Statistics: Jaroslav Hajek Memorial Volume , Edited by: Jana Jureckova , D. R. Boston : R. Reidel .
   Google Scholar
• Box , G. E. P. 1953 . Non‐normality and tests on variance . Biometrika , 40 : 318 – 35 .
   Web of Science ®Google Scholar
• Cramer , H. 1974 . Mathematical Methods of Statistics , 30th ed , Princeton, NJ : Princeton University Press .
   Google Scholar
• Donoho , D. L. and Huber , P. J. 1983 . “ The notion of the breakdown point ” . In A Festschrift for Erich L. Lehmann , Edited by: Bickel , P. J. , Docksum , K. L. and Hodges , J. L. 157 – 84 . Belmont, CA : Wadsworth .
   Google Scholar
• Field , C. 1985 . “ Concepts of robustness ” . In A celebration of statistics: The International Statistical Institute centenary volume 369 – 75 . Chapter 5
   Google Scholar
• Fisher , R. A. 1920 . A mathematical examination of the methods of determining the accuracy of an observation by the mean error and the mean square error . Monthly Notices of the Royal Astronomical Society , 80 : 758 – 70 .
   Google Scholar
• Gastwirth , J. L. and Cohen , M. L. 1970 . Small sample behavior of some robust linear estimators of location . Journal of the American Statistical Association , 65 : 946 – 73 .
   Web of Science ®Google Scholar
• Graf , H. P. 1983 . Long‐range correlations and estimation of the self‐similarity parameter , Zurich, , Switzerland : Swiss Federal Institute of Technology (ETH), Department of Statistics . Ph.D. Dissertation
   Google Scholar
• Hampel , F. R. , Ronchetti , E. M. , Rousseeuw , P. J. and Stahel , W. A. 1986 . Robust Statistics: The Approach Based on Influence Functions. , New York : John Wiley & Sons .
   Google Scholar
• Hawkins , D. M. 1980 . “ Monographs on Applied Probability and Statistics ” . In Identification of Outliers , London : Chapman Hall .
   Google Scholar
• Hoaglin , D. C. , Mosteller , F. and Tukey , J. W. , eds. 1983 . Understanding Robust and Exploratory Data Analysis , New York : John Wiley & Sons .
   Google Scholar
• Huber , P. J. 1964 . Robust estimation of a location parameter . The Annals of Mathematical Statistics , 35 : 909 – 27 .
   Google Scholar
• Huber , P. J. 1981 . Robust Statistics , New York : John Wiley & Sons .
   Google Scholar
• Kalafus , R. M. and Chin , G. Y. Measures of accuracy in the NAVSTAR/GPS: 2DRMS vs CEP . Proceedings of the Third Annual Technical Meeting of the Institute of Navigation . January 21–23 , Long Beach, California.
   Google Scholar
• Lachapelle , G. , Falkenberg , W. , Neufeldt , D. and Kielland , P. Marine DGPS using code and carrier in a multipath environment . Proceedings of the Second International Technical Meeting of the Satellite Division of the ION, GPS 87/343–347 . Washington, DC. The Institute of Navigation .
   Google Scholar
• Lawoko , C. R. O. and Mclachlan , G. J. 1985 . Discrimination with autocorrelated observations . Pattern Recognition , 18 ( 2 ) : 145 – 49 .
   Web of Science ®Google Scholar
• Lax , D. A. 1975 . “ An interim report of the Monte Carlo study of robust estimators of width ” . Technical report No. 93, Series 2 New Jersey : Department of Statistics, Princeton University .
   Google Scholar
• Lax , D. A. 1985 . Robust estimators of scale: Finite‐sample performance in long‐tailed symmetric distributions . Journal of the American Statistical Association , 80 ( 391 ) : 736 – 41 .
   Web of Science ®Google Scholar
• Mertikas , S. P. 1988 . “ A statistical investigation into reliable and efficient accuracy measures in positioning ” . Fredericton, N.B., , Canada : Geodesy and Geomatics Engineering, University of New Brunswick . Ph.D. diss.
   Google Scholar
• Mertikas , S. P. 1993 . A study on the performance of covariance matrix estimators . Marine Geodesy , 16 : 259 – 76 .
   Google Scholar
• Mertikas , S. P. , Field , C. and Wells , D. E. GPS accuracy measures: tests and proposals . Proceedings of the Fourth International Geodetic Symposium on Satellite Positioning . 28 April‐2 May , Texas. University of Texas at Austin .
   Google Scholar
• Monahan , D. 1986 . “ Personal communication ” . In Canadian Hydrographic Service Ottawa, Ontario
   Google Scholar
• Portnoy , S. L. 1977 . Robust estimation in dependent situations . Annals of Statistics , 5 : 22 – 43 .
   Web of Science ®Google Scholar
• Portnoy , S. L. 1979 . Further remarks on robust estimation in dependent situations . Annals of Statistics , 7 : 224 – 31 .
   Web of Science ®Google Scholar
• Rey , J. W. 1983 . Introduction to Robust and Quasi‐Robust Statistical Methods , Berlin : SpringerVerlag .
   Google Scholar
• Stahel , W. and Weisberg , S. , eds. 1991 . Directions in Robust Statistics and Diagnostics , New York : Springer‐Verlag .
   Google Scholar
• Stigler , S. M. Contribution to the discussion of the meeting on robust statistics . Proceedings of the 40th session of the International Statistical Institute . Vol. XLVI , pp. 383 – 84 . Warsaw Book 1
   Google Scholar
• Tukey , J. W. 1960 . “ A survey of sampling from contaminated distributions ” . In Contributions to probability and statistics , Edited by: Olkin , I. 448 – 85 . Stanford, CA : Stanford University Press .
   Google Scholar
• Tukey , J. W. , Brown , H. I. and Schwarzschild , M. 1977 . Further progress on robust/resistant widthers , Technical Report No. 129, Series 2 New Jersey : Department of Statistics, Princeton University .
   Google Scholar