Nonparametric overlap coefficient estimation using ranked set sampling

References

• Al-Saleh , M. F. and Samawi , H. M. 2007 . Inference on Overlapping Coefficients in Two Exponential Populations . Journal of Modern Statistical Science , 6 ( 2 ) : 503 – 516 .
   Google Scholar
• Al-Saidy , O. , Samawi , H. M. and Al-Saleh , M. F. 2005 . Inference on Overlapping Coefficients under the Weibull Distribution: Equal Shape Parameter . ESAIM Probability and Statistics (P&S) , 9 : 206 – 219 .
   Google Scholar
• Anderson, G., Linton, O., and Whang, Y, (2009), ‘Nonparametric Estimation of a Polarization Measure’, Discussion Paper, University of Toronto, The London School of Economics and Seoul National University
   Google Scholar
• Bradley, E.L., and Piantadosi, S. (1982), ‘The Overlapping Coefficient as a Measure of Agreement Between Distributions’, Technical Report, Department of Biostatistics and Biomathematics, University of Alabama at Birmingham, Birmingham, AL
   Google Scholar
• Chen , Z. 1999 . Density Estimation using Ranked-Set Sampling Data . Environmental and Ecological Statistics , 6 : 135 – 146 .
   Web of Science ®Google Scholar
• Chen , E. J. and Kelton , W. D. Empirical Evaluation of Data-Based Density Estimation . Proceedings of the 2006 Winter Simulation Conference . pp. 333 – 341 .
   Google Scholar
• Chen , Z. H. , Sinha , B. K. and Bai , Z. 2004 . Ranked Set Sampling: Theory and Applications , New York : Springer .
   Google Scholar
• Cheng , M. Y. 1997 . Boundary-Aware Estimators of Integrated Density Derivative . Journal of the Royal Statistical Society , 59 : 191 – 203 . Ser. B
   Google Scholar
• Cheng , M. Y. , Fan , J. and Marron , J. S. 1997 . On Automatic Boundary Corrections . The Annals of Statistics , 25 : 1691 – 1708 .
   Web of Science ®Google Scholar
• Clemons , T. E. 1996 . “ The Overlapping Coefficient for Two Normal Probability Functions with Unequal Variances ” . Birmingham, AL : Department of Biostatistics, University of Alabama at Birmingham . unpublished thesis
   Google Scholar
• Clemons , T. E. and Bradley , E. L. Jr. 2000 . A Nonparametric Measure of the Overlapping Coefficient . Computational Statistics & Data Analysis , 34 : 51 – 61 .
   Web of Science ®Google Scholar
• Cline , D. B.H. and Hart , J. D. 1991 . Kernel Estimation of Densities of Discontinuous Derivatives . Statistics , 22 : 69 – 84 .
   Google Scholar
• Cowling , A. and Hall , P. 1996 . On Pseudo-data Methods for Removing Boundary Effects in Kernel Density Estimation . Journal of the Royal Statistical Society , 58 : 551 – 563 . Ser. B
   Google Scholar
• Davis , J. W. , Shackford , S. R. , Mackersie , R. C. and Hoyt , D. B. 1988 . Base Deficit as a Guide to Volume Resuscitation . Journal of Trauma , 28 : 1464 – 1467 .
   PubMedGoogle Scholar
• Davis , J. W. , Mackersie , R. C. , Holbrook , T. L. and Hoyt , D. B. 1991 . Base Deficit as an Indicator of Significant Abdominal Injury . Annals of Emerging Medicine , 20 ( 8 ) : 1406 – 1407 .
   Web of Science ®Google Scholar
• Federer, W.T., Powers, L.R., and Payne, M.G. (1963), ‘Studies on Statistical Procedures Applied to Chemical Genetic Data from Sugar Beets’, Technical Bulletin 77, Agricultural experimentation Station, Colorado State University
   Google Scholar
• Gasser , T. , Müller , H. G. and Mammitzsch , V. 1985 . Kernels for nonparametric Curve Estimation . Journal of the Royal Statistical Society , 47 : 238 – 252 . Ser. B
   Google Scholar
• Hall , P. and Park , B. U. 2002 . New Methods for Bias Correction at End Points and Boundaries . The Annals of Statistics , 30 : 1460 – 1479 .
   Web of Science ®Google Scholar
• Harner , E. J. and Whitmore , R. C. 1977 . Multivariate Measures of Niche Overlap using Discriminant Analysis . Theoretical Population Biology , 12 : 21 – 36 .
   PubMed Web of Science ®Google Scholar
• Ichikawa , M. 1993 . A Meaning of the Overlapped Area under Probability Density Curves of Stress and Strength . Reliability Engineering & System Safety , 41 : 203 – 204 .
   Web of Science ®Google Scholar
• Inman , H. F. and Bradley , E. L. 1989 . The Overlapping Coefficient as a Measure of Agreement Between Probability Distributions and Point Estimation of the Overlap of Two Normal Densities . Communication in Statistics, Part A – Theory and Methods , 18 : 3851 – 3874 .
   Web of Science ®Google Scholar
• Jones , M. C. 1993 . Simple Boundary Correction for Kernel Density Estimation . Statistics and Computing , 3 : 135 – 146 .
   Web of Science ®Google Scholar
• Kaur , A. , Patil , G. P. , Sinha , A. K. and Tailie , C. 1995 . Ranked Set Sampling: An Annotated Bibliography . Environmental and Ecological Statistics , 2 : 25 – 54 .
   Web of Science ®Google Scholar
• MacArthur , R. H. 1972 . Geographical Ecology , New York : Harper and Row .
   Google Scholar
• Marron , J. S. and Ruppert , D. 1994 . Transformations to Reduce Boundary Bias in Kernel Density Estimation . Journal of the Royal Statistical Society , 56 : 653 – 671 . Ser. B
   Google Scholar
• Matusita , K. 1955 . Decision Rules Based on the Distance for Problem of Fit, Two Samples, and Estimation . Annals of Mathematical Statistics , 26 : 631 – 640 .
   Google Scholar
• McIntyre , G. A. 1952 . A Method for Unbiased Selective Samplings using Ranked Sets . Australian Journal of Agricultural Research , 3 : 385 – 390 .
   Google Scholar
• Morisita , M. 1959 . Measuring Interspecific Association and Similarity Between Communities . Memoirs of the Faculty of Kyushu University. Series E. Biology , 3 : 36 – 80 .
   Google Scholar
• Mulekar , M. S. and Mishra , S. N. 1994 . Overlap Coefficient of Two Normal Densities: Equal Means Case . Journal of the Japan Statistical Society , 24 : 169 – 180 .
   Google Scholar
• Mulekar , M. S. and Mishra , S. N. 2000 . Confidence Interval Estimation of Overlap: Equal Means Case . Computational Statistics & Data Analysis , 34 : 121 – 137 .
   Web of Science ®Google Scholar
• Müller , H. G. 1991 . Smooth Optimum Kernel Estimators Near End Points . Biometrika , 78 : 521 – 530 .
   Web of Science ®Google Scholar
• Patil , G. P. , Sinha , A. K. and Taillie , C. 1999 . Ranked Set Sampling: A Bibliography . Environmental and Ecological Statistics , 6 : 91 – 98 .
   Web of Science ®Google Scholar
• Reiser , B. and Faraggi , D. 1999 . Confidence Intervals for the Overlapping Coefficient: the Normal Equal Variance Case . The Statistician , 48 ( 3 ) : 413 – 418 .
   Google Scholar
• Rosenblatt , M. 1971 . Curve Estimates . Annals of Mathematical Statistics , 42 : 1815 – 1842 .
   Google Scholar
• Samawi , H. M. and Al-Sakeer , O. A.M. 2001 . On the Estimation of the Distribution Function using Extreme and Median Ranked Set Sampling . Biometrical Journal , 43 : 357 – 373 .
   Web of Science ®Google Scholar
• Samawi , H. M. and Al-Saleh , M. F. 2008 . Inference on Overlapping Coefficients in Two Exponential Populations using Ranked Set Sample . Communication of Korean of Statistical Society , 15 ( 2 ) : 147 – 159 .
   Google Scholar
• Samawi , H. M. , Woodworth , G. G. and Lemke , J. H. 1998 . Power Estimation for Two-Sample Tests using Importance and Antithetic Resampling . Biometrical Journal , 40 ( 3 ) : 341 – 354 .
   Web of Science ®Google Scholar
• Samawi , H. M. , Al-Saleh , M. F. and Al-Saidy , O. 2009 . The Matched Pair Sign Test using Bivariate Ranked Set Sampling for Different Ranking Based Schemes . Statistical Methodology , 6 : 397 – 407 .
   Google Scholar
• Schmid , F. and Schmidt , A. 2006 . Nonparametric Estimation of the Coefficient of Overlapping-Theory and Empirical Application . Computational Statistics & Data Analysis , 50 ( 6 ) : 1583 – 1596 .
   Web of Science ®Google Scholar
• Schuster , E. F. 1985 . Incorporating Support Constraints into Nonparametric Estimators of Densities . Communications in Statistics, Part A – Theory and Methods , 14 : 1123 – 1136 .
   Web of Science ®Google Scholar
• Serfing , R. J. 1980 . Approximation Theorems of Mathematical Statistics , New York, Chichester, Brisbane, Toronto, Singapore : John Wiley & Sons, Inc .
   Google Scholar
• Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , London : Chapman and Hall .
   Google Scholar
• Slobodchikoff , C. N. and Schulz , W. C. 1980 . Measures of Niche Overlap . Ecology , 61 : 1051 – 1055 .
   Web of Science ®Google Scholar
• Sneath , P. H.A. 1977 . A Method for Testing the Distinctness of Clusters: A Test of the Disjunction of Two Clusters in Euclidean Space as Measured by Their Overlap . Journal of Mathematical Geology , 9 : 123 – 143 .
   Google Scholar
• Tremblay , L. N. , Feliciano , D. V. and Rozycki , G. S. 2002 . Assessment of Initial Base Deficit as a Predictor of Outcome: Mechanism Does Make a Difference . American Surgeon , 68 : 689 – 694 .
   PubMed Web of Science ®Google Scholar
• Van Kerm , P. 2003 . Adaptive Kernel Density Estimation . The Stata Journal , 3 ( 2 ) : 148 – 156 .
   Web of Science ®Google Scholar
• Wand , M. P. and Jones , M. C. 1995 . Kernel Smoothing , London : Chapman and Hall .
   Google Scholar
• Wand , M. P. , Marron , J. S. and Ruppert , D. 1991 . Transformations in Density Estimation (with Discussion) . Journal of the American Statistical Association , 86 : 343 – 361 .
   Web of Science ®Google Scholar
• Wegman , E. J. 1972 . Nonparametric Probability Density Estimation: A Summary of Available Methods . Technometrics , 14 ( 3 ) : 533 – 546 .
   Web of Science ®Google Scholar
• Wegman , E. J. 1982 . “ Kalman Filtering ” . In Encyclopedia of Statistics , Edited by: Johnson , N. and Kotz , S. New York : John Wiley .
   Google Scholar
• Weitzman , M. S. 1970 . “ Measures of Overlap of Income Distributions of White and Negro Families in the United States ” . Washington, DC : Department of Commerce, Bureau of Census . Technical Paper No. 22
   Google Scholar
• Zhang , S. and Karunamuni , R. J. 1998 . On Kernel Density Estimation Near Endpoints . Journal of Statistical Planning and Inference , 70 : 301 – 316 .
   Web of Science ®Google Scholar
• Zhang , S. and Karunamuni , R. J. 2000 . On Nonparametric Density Estimation at the Boundary . Nonparametric Statistics , 12 : 197 – 221 .
   Web of Science ®Google Scholar
• Zhang , S. , Karunamuni , R. J. and Jones , M. C. 1999 . An Improved Estimator of the Density Function at the Boundary . Journal of the American Statistical Association , 448 : 1231 – 1241 .
   Google Scholar