메뉴 건너뛰기




Volumn 75, Issue 1, 2000, Pages 62-78

Nonparametric Notions of Multivariate "Scatter Measure" and "More Scattered" Based on Statistical Depth Functions

Author keywords

Halfspace depth; More scattered; Multivariate; Nonparametric; Scatter measure; Statistical depth functions; Statistical inference

Indexed keywords


EID: 0001778586     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmva.1999.1894     Document Type: Article
Times cited : (26)

References (31)
  • 1
    • 84968476146 scopus 로고
    • The integral of a symmetric unimodal function
    • Anderson T. W. The integral of a symmetric unimodal function. Proc. Amer. Math. Soc. 6:1955;170-176.
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 170-176
    • Anderson, T.W.1
  • 2
    • 0030494355 scopus 로고    scopus 로고
    • Some inequalities for symmetric convex sets with applications
    • Anderson T. W. Some inequalities for symmetric convex sets with applications. Ann. Statist. 24:1996;753-762.
    • (1996) Ann. Statist. , vol.24 , pp. 753-762
    • Anderson, T.W.1
  • 4
    • 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
  • 5
  • 7
    • 0002279721 scopus 로고
    • On random variables with comparable peakedness
    • Birnbaum Z. W. On random variables with comparable peakedness. Ann. Math. Statist. 37:1948;1593-1601.
    • (1948) Ann. Math. Statist. , vol.37 , pp. 1593-1601
    • Birnbaum, Z.W.1
  • 8
    • 0042384090 scopus 로고
    • Some distributions of sample means
    • Brown G., Tukey J. W. Some distributions of sample means. Ann. Math. Statist. 7:1946;1-12.
    • (1946) Ann. Math. Statist. , vol.7 , pp. 1-12
    • Brown, G.1    Tukey, J.W.2
  • 9
    • 0001597702 scopus 로고
    • Breakdown properties of location estimates based on halfspace depth and projected outlyingness
    • Donoho D. L., Gasko M. Breakdown properties of location estimates based on halfspace depth and projected outlyingness. Ann. Statist. 20:1992;1803-1827.
    • (1992) Ann. Statist. , vol.20 , pp. 1803-1827
    • Donoho, D.L.1    Gasko, M.2
  • 10
    • 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
  • 11
    • 0031519463 scopus 로고    scopus 로고
    • Convergence of depth contours for multivariate data sets
    • He X., Wang G. Convergence of depth contours for multivariate data sets. Ann. Statist. 25:1997;495-504.
    • (1997) Ann. Statist. , vol.25 , pp. 495-504
    • He, X.1    Wang, G.2
  • 12
    • 0001767349 scopus 로고
    • On a notion of data depth based on random simplices
    • Liu R. Y. On a notion of data depth based on random simplices. Ann. Statist. 18:1990;405-414.
    • (1990) Ann. Statist. , vol.18 , pp. 405-414
    • Liu, R.Y.1
  • 13
    • 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
  • 14
    • 0040598406 scopus 로고
    • A quality index based on data depth and multivariate rank tests
    • Liu R. Y., Singh K. A quality index based on data depth and multivariate rank tests. J. Amer. Statist. Assoc. 88:1993;252-260.
    • (1993) J. Amer. Statist. Assoc. , vol.88 , pp. 252-260
    • Liu, R.Y.1    Singh, K.2
  • 15
    • 38149146121 scopus 로고
    • Halfplane trimming for bivariate distributions
    • Massé J.-C., Theorodescu R. Halfplane trimming for bivariate distributions. J. Multivariate Anal. 48:1994;188-202.
    • (1994) J. Multivariate Anal. , vol.48 , pp. 188-202
    • Massé, J.-C.1    Theorodescu, R.2
  • 16
    • 0011632262 scopus 로고
    • The integral of an invariant unimodal function over an invariant convex set - An inequality and applications
    • Mudholkar G. The integral of an invariant unimodal function over an invariant convex set - An inequality and applications. Proc. Amer. Math. Soc. 17:1966;1327-1333.
    • (1966) Proc. Amer. Math. Soc. , vol.17 , pp. 1327-1333
    • Mudholkar, G.1
  • 18
    • 38249010534 scopus 로고
    • Asymptotics for multivariate trimming
    • Nolan D. Asymptotics for multivariate trimming. Stochastic Process. Appl. 42:1992;157-169.
    • (1992) Stochastic Process. Appl. , vol.42 , pp. 157-169
    • Nolan, D.1
  • 19
    • 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
  • 21
  • 22
    • 0041381971 scopus 로고    scopus 로고
    • The depth function of a population distribution
    • to appear
    • P. J. Rousseeuw, and, I. Ruts, The depth function of a population distribution, Metrika, to appear.
    • Metrika
    • Rousseeuw, P.J.1    Ruts, I.2
  • 24
    • 0002846981 scopus 로고    scopus 로고
    • Computing location depth and regression depth in higher dimensions
    • Rousseeuw P. J., Struyf S. Computing location depth and regression depth in higher dimensions. Statist. Comput. 8:1998;193-203.
    • (1998) Statist. Comput. , vol.8 , pp. 193-203
    • Rousseeuw, P.J.1    Struyf, S.2
  • 26
    • 0042323830 scopus 로고    scopus 로고
    • Computing depth contours of bivariate point clouds
    • Ruts I., Rousseeuw P. J. Computing depth contours of bivariate point clouds. Comput. Statist. Data Anal. 23:1996;153-168.
    • (1996) Comput. Statist. Data Anal. , vol.23 , pp. 153-168
    • Ruts, I.1    Rousseeuw, P.J.2
  • 28
    • 0001565840 scopus 로고    scopus 로고
    • Balanced confidence regions based on Tukey's depth and the bootstrap
    • Yeh A. B., Singh K. Balanced confidence regions based on Tukey's depth and the bootstrap. J. Roy. Statist. Soc. Ser. B. 59:1997;639-652.
    • (1997) J. Roy. Statist. Soc. Ser. B , vol.59 , pp. 639-652
    • Yeh, A.B.1    Singh, K.2
  • 29
    • 0034347419 scopus 로고    scopus 로고
    • General notions of statistical depth function
    • Zuo Y., Serfling R. General notions of statistical depth function. Ann. Statist. 28:2000.
    • (2000) Ann. Statist. , vol.28
    • Zuo, Y.1    Serfling, R.2
  • 30
    • 0034347414 scopus 로고    scopus 로고
    • Structural properties and convergence results for contours of sample statistical depth functions
    • Zuo Y., Serfling R. Structural properties and convergence results for contours of sample statistical depth functions. Ann. Statist. 28:2000.
    • (2000) Ann. Statist. , vol.28
    • Zuo, Y.1    Serfling, R.2
  • 31
    • 0002954623 scopus 로고    scopus 로고
    • On the performance of some robust nonparametric location measures relative to a general notion of multivariate symmetry
    • Zuo Y., Serfling R. On the performance of some robust nonparametric location measures relative to a general notion of multivariate symmetry. J. Statist. Plann. Inference. 84:2000;55-79.
    • (2000) J. Statist. Plann. Inference , vol.84 , pp. 55-79
    • Zuo, Y.1    Serfling, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.