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Volumn 123, Issue 2, 2004, Pages 259-278

Nonparametric multivariate descriptive measures based on spatial quantiles

Author keywords

Kurtosis; Location; Multivariate distributions; Nonparametric; Peakedness; Scale; Skewness; Spatial quantiles; Tailweight

Indexed keywords


EID: 2142656338     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(03)00156-3     Document Type: Article
Times cited : (52)

References (67)
  • 2
    • 0031486458 scopus 로고    scopus 로고
    • Skewness for multivariate distributions: Two approaches
    • Avérous J. Meste M. Skewness for multivariate distributions: two approaches Ann. Statist. 25 1997 1984-1997
    • (1997) Ann. Statist. , vol.25 , pp. 1984-1997
    • Avérous, J.1    Meste, M.2
  • 3
    • 0040060115 scopus 로고    scopus 로고
    • Median balls: An extension of the interquantile intervals to multivariate distributions
    • Avérous J. Meste M. Median balls: an extension of the interquantile intervals to multivariate distributions J. Multivariate Anal. 63 1997 222-241
    • (1997) J. Multivariate Anal. , vol.63 , pp. 222-241
    • Avérous, J.1    Meste, M.2
  • 6
    • 0030542498 scopus 로고    scopus 로고
    • Concepts and measures for skewness with data-analytic implications
    • Benjamini Y. Krieger A.M. Concepts and measures for skewness with data-analytic implications Canad. J. Statist. 24 1996 131-140
    • (1996) Canad. J. Statist. , vol.24 , pp. 131-140
    • Benjamini, Y.1    Krieger, A.M.2
  • 7
    • 0001744526 scopus 로고
    • Descriptive statistics for nonparametric models. I. Introduction
    • Bickel P.J. Lehmann E.L. Descriptive statistics for nonparametric models. I. Introduction Ann. Statist. 3 1975 1038-1044
    • (1975) Ann. Statist. , vol.3 , pp. 1038-1044
    • Bickel, P.J.1    Lehmann, E.L.2
  • 8
    • 0001744526 scopus 로고
    • Descriptive statistics for nonparametric models. II. Location
    • Bickel P.J. Lehmann E.L. Descriptive statistics for nonparametric models. II. Location Ann. Statist. 4 1975 1045-1069
    • (1975) Ann. Statist. , vol.4 , pp. 1045-1069
    • Bickel, P.J.1    Lehmann, E.L.2
  • 9
    • 0000157578 scopus 로고
    • Descriptive statistics for nonparametric models. III. Dispersion
    • Bickel P.J. Lehmann E.L. Descriptive statistics for nonparametric models. III. Dispersion Ann. Statist. 4 1976 1139-1158
    • (1976) Ann. Statist. , vol.4 , pp. 1139-1158
    • Bickel, P.J.1    Lehmann, E.L.2
  • 10
    • 0003260532 scopus 로고
    • Descriptive statistics for nonparametric models. IV. Spread
    • Jurečková, J. (Ed.), Academia, Prague
    • Bickel, P.J., Lehmann, E.L., 1979. Descriptive statistics for nonparametric models. IV. Spread. In: Jurečková, J. (Ed.), Contributions to Statistics: Jaroslav Hájek Memorial Volume. Academia, Prague, pp. 33-40.
    • (1979) Contributions to Statistics: Jaroslav Hájek Memorial Volume , pp. 33-40
    • Bickel, P.J.1    Lehmann, E.L.2
  • 11
    • 0002279721 scopus 로고
    • On random variables with comparable peakedness
    • Birnbaum Z.W. On random variables with comparable peakedness Ann. Math. Statist. 19 1948 76-81
    • (1948) Ann. Math. Statist. , vol.19 , pp. 76-81
    • Birnbaum, Z.W.1
  • 14
  • 16
    • 6644225562 scopus 로고    scopus 로고
    • On affine equivariant multivariate quantiles
    • Chakraborty B. On affine equivariant multivariate quantiles Ann. Inst. Statist. Math. 53 2001 380-403
    • (2001) Ann. Inst. Statist. Math. , vol.53 , pp. 380-403
    • Chakraborty, B.1
  • 17
    • 0032365498 scopus 로고    scopus 로고
    • Operating transformation and retransformation on spatial median and angle test
    • Chakraborty B. Chaudhuri P. Oja H. Operating transformation and retransformation on spatial median and angle test Statist. Sin. 8 1998 767-784
    • (1998) Statist. Sin. , vol.8 , pp. 767-784
    • Chakraborty, B.1    Chaudhuri, P.2    Oja, H.3
  • 18
    • 0030540155 scopus 로고    scopus 로고
    • On a geometric notion of quantiles for multivariate data
    • Chaudhuri P. On a geometric notion of quantiles for multivariate data J. Amer. Statist. Assoc. 91 1996 862-872
    • (1996) J. Amer. Statist. Assoc. , vol.91 , pp. 862-872
    • Chaudhuri, P.1
  • 19
    • 21344492438 scopus 로고
    • Sign tests in multidimension: Inference based on the geometry of the data cloud
    • Chaudhuri P. Sengupta D. Sign tests in multidimension: inference based on the geometry of the data cloud J. Amer. Statist. Assoc. 88 1993 1363-1370
    • (1993) J. Amer. Statist. Assoc. , vol.88 , pp. 1363-1370
    • Chaudhuri, P.1    Sengupta, D.2
  • 20
    • 0031312391 scopus 로고    scopus 로고
    • An approach to multivariate rank tests in multivariate analysis of variance
    • Choi K. Marden J. An approach to multivariate rank tests in multivariate analysis of variance J. Amer. Statist. Assoc. 92 1997 1581-1590
    • (1997) J. Amer. Statist. Assoc. , vol.92 , pp. 1581-1590
    • Choi, K.1    Marden, J.2
  • 22
    • 0002992274 scopus 로고
    • Measures of location and asymmetry
    • Doksum K.A. Measures of location and asymmetry Scand. J. Statist. 2 1975 11-22
    • (1975) Scand. J. Statist. , vol.2 , pp. 11-22
    • Doksum, K.A.1
  • 23
    • 0008903066 scopus 로고
    • A review of selected topics in multivariate probability inequalities
    • Eaton M.L. A review of selected topics in multivariate probability inequalities Ann. Statist. 10 1982 11-43
    • (1982) Ann. Statist. , vol.10 , pp. 11-43
    • Eaton, M.L.1
  • 26
    • 0001906808 scopus 로고
    • Statistics by intercomparison: With remarks on the Law of Frequency of Error
    • Galton F. Statistics by intercomparison: with remarks on the Law of Frequency of Error Philos. Mag. 4th Ser. 49 1875 33-46
    • (1875) Philos. Mag. 4th Ser. , vol.49 , pp. 33-46
    • Galton, F.1
  • 28
    • 0032327088 scopus 로고    scopus 로고
    • A class of quantile measures for kurtosis
    • Groeneveld R.A. A class of quantile measures for kurtosis Amer. Statistician 51 1998 325-329
    • (1998) Amer. Statistician , vol.51 , pp. 325-329
    • Groeneveld, R.A.1
  • 29
    • 0000718216 scopus 로고
    • Measuring skewness and kurtosis
    • Groeneveld R.A. Meeden G. Measuring skewness and kurtosis Statistician 33 1984 391-399
    • (1984) Statistician , vol.33 , pp. 391-399
    • Groeneveld, R.A.1    Meeden, G.2
  • 30
    • 0001897788 scopus 로고
    • What is the center of an area, or the center of a population?
    • Hayford J.F. What is the center of an area, or the center of a population? J. Amer. Statist. Assoc. 8 1902 47-58
    • (1902) J. Amer. Statist. Assoc. , vol.8 , pp. 47-58
    • Hayford, J.F.1
  • 31
  • 32
    • 51249179014 scopus 로고
    • Some extension of Haldane's multivariate median and its application
    • Isogai T. Some extension of Haldane's multivariate median and its application Ann. Inst. Statist. Math. 37 1985 289-301
    • (1985) Ann. Inst. Statist. Math. , vol.37 , pp. 289-301
    • Isogai, T.1
  • 33
    • 0003020432 scopus 로고
    • A multivariate signed sum test for the one sample location problem
    • Jan S.L. Randles R.H. A multivariate signed sum test for the one sample location problem J. Nonparametric Statist. 4 1994 49-63
    • (1994) J. Nonparametric Statist. , vol.4 , pp. 49-63
    • Jan, S.L.1    Randles, R.H.2
  • 34
    • 0000044484 scopus 로고
    • The median of a finite measure on a Banach space
    • Y. Dodge (Ed.), Amsterdam: North-Holland
    • 1-Norm and Related Methods 1987 217-230 North-Holland Amsterdam
    • (1987) 1-Norm and Related Methods , pp. 217-230
    • Kemperman, J.H.B.1
  • 37
    • 0040982525 scopus 로고
    • Bahadur-Kiefer approximation for spatial quantiles
    • Hoffman-Jørgensen, J., Kuelbs, J., Marcus, M. (Eds.), Birkhaüser, Basel
    • Koltchinskii, V., 1994. Bahadur-Kiefer approximation for spatial quantiles. In: Hoffman-Jørgensen, J., Kuelbs, J., Marcus, M. (Eds.), Probability in Banach Spaces. Birkhaüser, Basel, pp. 394-408.
    • (1994) Probability in Banach Spaces , pp. 394-408
    • Koltchinskii, V.1
  • 38
    • 0031493777 scopus 로고    scopus 로고
    • M-estimation, convexity and quantiles
    • Koltchinskii V. M-estimation, convexity and quantiles Ann. Statist. 25 1997 435-477
    • (1997) Ann. Statist. , vol.25 , pp. 435-477
    • Koltchinskii, V.1
  • 40
    • 0033147626 scopus 로고    scopus 로고
    • Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion)
    • Liu R.Y. Parelius J.M. Singh K. Multivariate analysis by data depth: descriptive statistics, graphics and inference (with discussion) Ann. Statist. 27 1999 783-858
    • (1999) Ann. Statist. , vol.27 , pp. 783-858
    • Liu, R.Y.1    Parelius, J.M.2    Singh, K.3
  • 41
    • 0001352378 scopus 로고
    • Breakdown points of affine equivariant estimators of multivariate location and covariance matrices
    • Lopuhaä H.P. Rousseeuw J. Breakdown points of affine equivariant estimators of multivariate location and covariance matrices Ann. Statist. 19 1991 229-248
    • (1991) Ann. Statist. , vol.19 , pp. 229-248
    • Lopuhaä, H.P.1    Rousseeuw, J.2
  • 42
    • 0000222112 scopus 로고
    • Skewness and asymmetry: Measures and orderings
    • MacGillivray H.L. Skewness and asymmetry: measures and orderings Ann. Statist. 14 1986 994-1011
    • (1986) Ann. Statist. , vol.14 , pp. 994-1011
    • MacGillivray, H.L.1
  • 43
    • 0001488013 scopus 로고
    • Shape properties of the g-and-h and Johnson families
    • MacGillivray H.L. Shape properties of the g-and-h and Johnson families Comm. Statist.-Theory Methods 21 1992 1233-1250
    • (1992) Comm. Statist.-Theory Methods , vol.21 , pp. 1233-1250
    • MacGillivray, H.L.1
  • 44
  • 45
    • 0032367214 scopus 로고    scopus 로고
    • Bivariate QQ-plots and spider web plots
    • Sankhya B 36, 115-128
    • Marden J.I. Bivariate QQ-plots and spider web plots Statist. Sin. 8 1998 813-826 Sankhya B 36, 115-128
    • (1998) Statist. Sin. , vol.8 , pp. 813-826
    • Marden, J.I.1
  • 46
    • 2942611661 scopus 로고
    • Measures of multivariate skewness and kurtosis with applications
    • Mardia K.V. Measures of multivariate skewness and kurtosis with applications Biometrika 57 1970 519-530
    • (1970) Biometrika , vol.57 , pp. 519-530
    • Mardia, K.V.1
  • 47
    • 0000904196 scopus 로고
    • Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies
    • Mardia K.V. Applications of some measures of multivariate skewness and kurtosis in testing normality and robustness studies Sankhya B 36 1974 115-128
    • (1974) Sankhya B , vol.36 , pp. 115-128
    • Mardia, K.V.1
  • 48
    • 0007213629 scopus 로고
    • The meaning of kurtosis: Darlington reexamined
    • Moors J.J.A. The meaning of kurtosis: darlington reexamined Amer. Statistician 40 1986 283-284
    • (1986) Amer. Statistician , vol.40 , pp. 283-284
    • Moors, J.J.A.1
  • 49
    • 0000354169 scopus 로고
    • Multivariate spatial sign and rank methods
    • Möttönen J. Oja H. Multivariate spatial sign and rank methods J. Nonparametric Statist. 5 1995 201-213
    • (1995) J. Nonparametric Statist. , vol.5 , pp. 201-213
    • Möttönen, J.1    Oja, H.2
  • 50
    • 0031490487 scopus 로고    scopus 로고
    • On the efficiency of multivariate spatial sign and rank tests
    • Möttönen J. Oja H. Tienari J. On the efficiency of multivariate spatial sign and rank tests Ann. Statist. 25 1997 542-552
    • (1997) Ann. Statist. , vol.25 , pp. 542-552
    • Möttönen, J.1    Oja, H.2    Tienari, J.3
  • 51
    • 0001673501 scopus 로고
    • On location, scale, skewness and kurtosis of univariate distributions
    • Oja H. On location, scale, skewness and kurtosis of univariate distributions Scand. J. Statist. 8 1981 154-168
    • (1981) Scand. J. Statist. , vol.8 , pp. 154-168
    • Oja, H.1
  • 52
    • 0000107573 scopus 로고
    • Descriptive statistics for multivariate distributions
    • Oja H. Descriptive statistics for multivariate distributions Statist. Probab. Lett. 1 1983 327-333
    • (1983) Statist. Probab. Lett. , vol.1 , pp. 327-333
    • Oja, H.1
  • 53
    • 0000721571 scopus 로고
    • Peakedness in multivariate distributions
    • Gupta, S.S., Berger, J.O. (Eds.), Springer, Berlin
    • Olkin, I., Tong, Y.L., 1988. Peakedness in multivariate distributions. In: Gupta, S.S., Berger, J.O. (Eds.), Statistical Decision Theory and Related Topics IV, Vol. 2. Springer, Berlin, pp. 373-384.
    • (1988) Statistical Decision Theory and Related Topics IV , vol.2 , pp. 373-384
    • Olkin, I.1    Tong, Y.L.2
  • 54
    • 79951913194 scopus 로고
    • Nonparametric statistical data modeling (with discussion)
    • Parzen E. Nonparametric statistical data modeling (with discussion) J. Amer. Statist. Assoc. 74 1979 105-131
    • (1979) J. Amer. Statist. Assoc. , vol.74 , pp. 105-131
    • Parzen, E.1
  • 55
    • 0000678972 scopus 로고
    • Contributions to the mathematical theory of evolution II. Skew variation in homogeneous material
    • Pearson K. Contributions to the mathematical theory of evolution II. Skew variation in homogeneous material Philos. Trans. Roy. Statist. Soc. London Ser. A 186 1895-343
    • (1895) Philos. Trans. Roy. Statist. Soc. London Ser. A , vol.186 , pp. 343
    • Pearson, K.1
  • 56
    • 0000306680 scopus 로고
    • 1 norm in statistical inference
    • 1 norm in statistical inference Sankhyā Ser. A 50 1988 289-313
    • (1988) Sankhyā Ser. A , vol.50 , pp. 289-313
    • Rao, C.R.1
  • 58
    • 0036797184 scopus 로고    scopus 로고
    • Generalized quantile processes based on multivariate depth functions, with applications in nonparametric multivariate analysis
    • Serfling R. Generalized quantile processes based on multivariate depth functions, with applications in nonparametric multivariate analysis J. Multivariate Anal. 83 2002 232-247
    • (2002) J. Multivariate Anal. , vol.83 , pp. 232-247
    • Serfling, R.1
  • 59
    • 0036012647 scopus 로고    scopus 로고
    • Quantile functions for multivariate analysis: Approaches and applications
    • Serfling R. Quantile functions for multivariate analysis: approaches and applications Statist. Neerlandica 56 2002 214-232
    • (2002) Statist. Neerlandica , vol.56 , pp. 214-232
    • Serfling, R.1
  • 60
    • 2142736121 scopus 로고    scopus 로고
    • A depth function and a scale curve based on spatial quantiles
    • Dodge, Y. (Ed.), Birkhaüser, Basel (modified postprint available at www.utdallas.edu/~serfling)
    • 1-Norm and Related Methods, Birkhaüser, Basel, pp. 25-38. (modified postprint available at www.utdallas.edu/~serfling)
    • (2002) 1-Norm and Related Methods , pp. 25-38
    • Serfling, R.1
  • 61
    • 0000083925 scopus 로고
    • A theorem on convex sets with applications
    • Sherman S. A theorem on convex sets with applications Ann. Math. Statist. 26 1955 763-767
    • (1955) Ann. Math. Statist. , vol.26 , pp. 763-767
    • Sherman, S.1
  • 62
    • 0000356499 scopus 로고
    • A survey of multidimensional medians
    • Small C.G. A survey of multidimensional medians Int. Statist. Inst. Rev. 58 1990 263-277
    • (1990) Int. Statist. Inst. Rev. , vol.58 , pp. 263-277
    • Small, C.G.1
  • 64
    • 0036489065 scopus 로고    scopus 로고
    • Inference based on multivariate M-estimators based on bivariate censored data
    • Van Keilegom I. Hettmansperger T. Inference based on multivariate M-estimators based on bivariate censored data J. Amer. Statist. Assoc. 97 2002 328-336
    • (2002) J. Amer. Statist. Assoc. , vol.97 , pp. 328-336
    • Van Keilegom, I.1    Hettmansperger, T.2
  • 67
    • 0001778586 scopus 로고    scopus 로고
    • Nonparametric notions of multivariate "scatter measure" and "more scattered" based on statistical depth functions
    • Zuo Y. Serfling R. Nonparametric notions of multivariate "scatter measure" and "more scattered" based on statistical depth functions J. Multivariate Anal. 75 2000 62-78
    • (2000) J. Multivariate Anal. , vol.75 , pp. 62-78
    • Zuo, Y.1    Serfling, R.2


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