38
Views
4
CrossRef citations to date
0
Altmetric
Teacher's Corner

A Matrix Formulation on How Deviant an Observation Can Be

Pages 205-209 | Received 01 Jul 1990, Published online: 27 Feb 2012

References

  • Arnold , B. C. 1974 . “Schwarz, Regression, and Extreme Deviance” . The American Statistician , 28 : 22 – 23 .
  • Arnold , B. C. 1988 . “Bounds on the Expected Maximum” . Communications in Statistics, A – Theory and Methods , 17 : 2135 – 2150 .
  • Arnold , B. C. and Balakrishnan , N. 1989 . “Relations, Bounds and Approximations for Order Statistics” , New York : Springer-Verlag . (Lecture Notes in Statistics, No. 53)
  • Arnold , B. C. and Groeneveld , R. A. 1974 . “Bounds for Deviations Between Sample and Population Statistics” . Biometrika , 61 : 387 – 389 .
  • Arnold , B. C. and Groeneveld , R. A. 1978 . “Bounds on Deviations of Estimates Arising in Finite Population Regression Models” . Communications in Statistics, A , 7 : 1173 – 1179 .
  • Arnold , B. C. and Groeneveld , R. A. 1979 . “Bounds on Expectations of Linear Systematic Statistics Based on Dependent Samples” . The Annals of Statistics , 7 : 220 – 223 .
  • Arnold , B. C. and Groeneveld , R. A. 1981 . “Maximal Deviation Between Sample and Population Means in Finite Populations” . Journal of the American Statistical Association , 76 : 443 – 445 .
  • Beesack , P. R. 1973 . “On Bounds for the Range of Ordered Values” . In Univerzitet u Beogradu, Publikacije Elektrotechničkog Fakulteeta, Serija Matematika i Fizika 93 – 96 . No. 412–460
  • Beesack , P. R. 1976 . “On Bounds for the Range of Ordered Variates II” . Aequationes Mathematicae , 14 : 293 – 301 .
  • Boyd , A. V. 1971 . “Bounds for Order Statistics” . In Univerzitet u Beogradu, Publikacije Elektrotehničkog Fakulteeta, Serija Matematika i Fizika 31 – 32 . No. 357–380
  • Brunk , H. D. 1959 . “Note on Two Papers of K. R. Nair” . Journal of the Indian Society of Agricultural Statistics , 11 : 186 – 189 .
  • David , H. A. 1988 . “General Bounds and Inequalities in Order Statistics” . Communications in Statistics, A – Theory and Methods , 17 : 2119 – 2134 .
  • David , H. A. 1990 . “Problem 90–4” . Bulletin of the Institute of Mathematical Statistics , 19 : 608
  • David , H. A. , Hartley , H. O. and Pearson , E. S. 1954 . “The Distribution of the Ratio, in a Single Normal Sample, of Range to Standard Deviation” . Biometrika , 41 : 482 – 493 .
  • Dwass , M. 1975 . “The Extreme Deviations Inequality” . The American Statistician , 28 : 108
  • Farnum , N. R. 1989 . “An Alternative Proof of Samuelson's Inequality and Its Extensions” . The American Statistician , 43 : 46 – 47 .
  • Hawkins , D. M. 1971 . “On the Bounds of the Range of Order Statistics” . Journal of the American Statistical Association , 66 : 644 – 645 .
  • Hotelling , H. and Solomons , L. M. 1932 . “The Limits of a Measure of Skewness” . The Annals of Mathematical Statistics , 3 : 141 – 142 .
  • Kabe , D. G. 1980 . “On Extensions of Samuelson's Inequality” . The American Statistician , 34 : 249
  • Loynes , R. M. 1979 . “A Note on Prescott's Upper Bound for Normed Residuals” . Biometrika , 66 : 387 – 389 .
  • Mallows , C. L. and Richter , D. 1969 . “Inequalities of Chebyshev Type Involving Conditional Expectations” . The Annals of Mathematical Statistics , 40 : 1922 – 1932 .
  • Murty , V. N. 1989 . “A Note on Samuelson's Inequality” . The American Statistician , 44 : 64 – 65 .
  • Nair , K. R. 1948 . “Certain Symmetrical Properties of Unbiased Estimates of Variance and Covariance” . Journal of the Indian Society of Agricultural Statistics , 1 : 162 – 172 .
  • Nair , K. R. 1956 . “A Note on the Estimation of Mean Change” . Journal of the Indian Society of Agricultural Statistics , 8 : 122 – 124 .
  • Nair , K. R. 1959 . “A Tail-Piece to Brunk's Paper” . Journal of the Indian Society of Agricultural Statistics , 11 : 189 – 190 .
  • O'Cinneide , C. A. 1990 . “The Mean Is Within One Standard Deviation of Any Median” . The American Statistician , 44 : 292 – 293 .
  • Pearson , E. S. and Sekar , C. Chandra . 1936 . “The Efficiency of Statistical Tools and a Criterion for the Rejection of Outlying Observations” . Biometrika , 28 : 308 – 320 .
  • Prescott , P. 1977 . “An Upper Bound for Any Linear Function of Normed Residuals” . Communications in Statistics, B–Simulation and Computation , 6 : 83 – 88 .
  • Quesenberry , C. P. 1974 . “The Extreme Deviations Inequality” . The American Statistician , 28 : 112
  • Samuelson , P. A. 1968 . “How Deviant Can You Be? . Journal of the American Statistical Association , 63 : 1522 – 1525 .
  • Shapiro , S. S. and Wilk , M. B. 1965 . “An Analysis of Variance Test for Normality (Complete Samples) . Biometrika , 52 : 591 – 611 .
  • Stephansky , W. 1971 . “Rejecting Outliers by Maximum Normed Residual” . The Annals of Mathematical Statistics , 42 : 35 – 45 .
  • Stephansky , W. 1972 . “Rejecting Outliers in Factorial Designs” . Technometrics , 14 : 469 – 479 .
  • Thompson , W. R. 1935 . “On a Criterion for the Rejection of Observations and the Distribution of the Ratio of Deviation to Sample Standard Deviation” . The Annals of Mathematical Statistics , 6 : 214 – 219 .
  • Thomson , G. W. 1955 . “Bounds for the Ratio of Range to Standard Deviation” . Biometrika , 42 : 268 – 269 .
  • Wolkowicz , H. and Styan , G. P. H. 1979 . “Extensions of Samuelson's Inequality” . The American Statistician , 62 : 634 – 637 .
  • Wolkowicz , H. and Styan , G. P. H. 1980 . “Reply” . The American Statistician , 34 : 250

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.