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Volumn 36, Issue 3, 2008, Pages 1299-1323

Multivariate spacings based on data depth: I. Construction of nonparametric multivariate tolerance regions

Author keywords

Data depth; Depth order statistics; Multivariate spacings; Statistically equivalent blocks; Tolerance region

Indexed keywords


EID: 51049089539     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/07-AOS505     Document Type: Article
Times cited : (40)

References (31)
  • 2
    • 2642550931 scopus 로고    scopus 로고
    • On exponential representations of Log-spacings of extreme order statistics
    • MR1965977
    • BEIRLANT, J., DIERCKX, G., GUILLOU, A. and STACARONRICACARON, C. (2002). On exponential representations of Log-spacings of extreme order statistics. Extremes 5 157-180. MR1965977
    • (2002) Extremes , vol.5 , pp. 157-180
    • BEIRLANT, J.1    DIERCKX, G.2    GUILLOU, A.3    STACARONRICACARON, C.4
  • 3
    • 0007192338 scopus 로고
    • Asymptotically minimal multivariate tolerance sets
    • MR0596720
    • CHATTERJEE, S. K. and PATRA, N. K. (1980). Asymptotically minimal multivariate tolerance sets. Calcutta Statist. Assoc. Bull. 29 73-93. MR0596720
    • (1980) Calcutta Statist. Assoc. Bull , vol.29 , pp. 73-93
    • CHATTERJEE, S.K.1    PATRA, N.K.2
  • 4
    • 0018668867 scopus 로고
    • An optimal statistic based on higher order gaps
    • MR0556744
    • CRESSIE, N. (1979). An optimal statistic based on higher order gaps. Biometrika 66 619-627. MR0556744
    • (1979) Biometrika , vol.66 , pp. 619-627
    • CRESSIE, N.1
  • 5
    • 0001155761 scopus 로고
    • On a class of problems related to the random division of an interval
    • MR0058891
    • DARLING, D. ( 1953). On a class of problems related to the random division of an interval. Ann. Math. Statist. 24 239-253. MR0058891
    • (1953) Ann. Math. Statist , vol.24 , pp. 239-253
    • DARLING, D.1
  • 7
    • 51049105808 scopus 로고    scopus 로고
    • DOHOHO, D. (1982). Breakdown properties of multivariate location estimators. Ph.D. qualifying paper, Harvard Univ.
    • DOHOHO, D. (1982). Breakdown properties of multivariate location estimators. Ph.D. qualifying paper, Harvard Univ.
  • 8
    • 51049122009 scopus 로고    scopus 로고
    • DONOHO, D. and GASKO, M. (1992). Breakdown properties of location estimates based on half-space depth and projected outlyingness. Ann. Statist. 20 1803-1827. MR1193313
    • DONOHO, D. and GASKO, M. (1992). Breakdown properties of location estimates based on half-space depth and projected outlyingness. Ann. Statist. 20 1803-1827. MR1193313
  • 9
    • 0001513080 scopus 로고
    • Strong bounds for weighted empirical distribution functions based on uniform spacings
    • MR0920258
    • EINMAHL, J. H. J. and VAN ZUIJLEN. M. (1988). Strong bounds for weighted empirical distribution functions based on uniform spacings. Ann. Probab.16108-125. MR0920258
    • (1988) Ann. Probab , vol.16 , pp. 108-125
    • EINMAHL, J.H.J.1    VAN ZUIJLEN, M.2
  • 10
    • 0242403850 scopus 로고
    • Sequentially determined statistically equivalent blocks
    • MR0043425
    • FRASER, D. (1951). Sequentially determined statistically equivalent blocks. Ann. Math. Statist. 22 372-381. MR0043425
    • (1951) Ann. Math. Statist , vol.22 , pp. 372-381
    • FRASER, D.1
  • 11
    • 51049088465 scopus 로고    scopus 로고
    • GUTTMAN, I. (1970). Statistical Tolerance Regions: Classical and Bayesian. Charles Griffin, London. MR0317473
    • GUTTMAN, I. (1970). Statistical Tolerance Regions: Classical and Bayesian. Charles Griffin, London. MR0317473
  • 12
    • 38249039038 scopus 로고
    • On powerful distributional tests based on sample spacings
    • MR0853053
    • HALL, P. (1986). On powerful distributional tests based on sample spacings. J. Multivariate Anal. 19 201-224. MR0853053
    • (1986) J. Multivariate Anal , vol.19 , pp. 201-224
    • HALL, P.1
  • 13
    • 0031519463 scopus 로고    scopus 로고
    • Convergence of depth contours for multivariate datasets
    • MR 1439311
    • HE, X. and WANG, G. (1997). Convergence of depth contours for multivariate datasets. Ann. Statist. 25 495-504. MR 1439311
    • (1997) Ann. Statist , vol.25 , pp. 495-504
    • HE, X.1    WANG, G.2
  • 14
    • 0001016811 scopus 로고
    • A bivariate sign test
    • MR0070921
    • HODGES, J. (1955). A bivariate sign test. Ann. Math. Statistics 26 523-527. MR0070921
    • (1955) Ann. Math. Statistics , vol.26 , pp. 523-527
    • HODGES, J.1
  • 15
    • 1842600519 scopus 로고
    • Two-sided tolerance limits for normal populations-some improvements
    • HOWE, W. G. (1969). Two-sided tolerance limits for normal populations-some improvements. J. Amer. Statist. Assoc. 64 610-620.
    • (1969) J. Amer. Statist. Assoc , vol.64 , pp. 610-620
    • HOWE, W.G.1
  • 16
    • 0001767349 scopus 로고
    • On a notion of data depth based on random simplices
    • MR1041400
    • LIU. R. (1990). On a notion of data depth based on random simplices. Ann. Statist.18405-414. MR1041400
    • (1990) Ann. Statist , vol.18 , pp. 405-414
    • LIU, R.1
  • 17
    • 0033147626 scopus 로고    scopus 로고
    • Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion)
    • MR 1724033
    • LIU, R., PARELIUS, J. and SINGH, K. (1999). Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion). Ann. Statist. 27783-858. MR 1724033
    • (1999) Ann. Statist , vol.27 , pp. 783-858
    • LIU, R.1    PARELIUS, J.2    SINGH, K.3
  • 18
    • 21144467323 scopus 로고
    • Ordering directional data: Concepts of data depth on circles and spheres
    • MR1186260
    • LIU, R. and SINGH, K. (1992). Ordering directional data: Concepts of data depth on circles and spheres. Ann. Statist. 20 1468-1484. MR1186260
    • (1992) Ann. Statist , vol.20 , pp. 1468-1484
    • LIU, R.1    SINGH, K.2
  • 19
    • 0040598406 scopus 로고
    • A quality index based on data depth and multivariate rank tests
    • MR1212489
    • LIU, R. and SINGH, K. (1993). A quality index based on data depth and multivariate rank tests. J. Amer. Statist. Assoc. 88 252-260. MR1212489
    • (1993) J. Amer. Statist. Assoc , vol.88 , pp. 252-260
    • LIU, R.1    SINGH, K.2
  • 20
    • 0002975203 scopus 로고
    • On the generalized distance in statistics
    • MAHALANOBIS, P. C. (1936). On the generalized distance in statistics. Proc. Nat. Inst. Sci. India 12 49-55.
    • (1936) Proc. Nat. Inst. Sci. India , vol.12 , pp. 49-55
    • MAHALANOBIS, P.C.1
  • 24
    • 0001038382 scopus 로고
    • Nonparametric estimation. II. Statistical equivalent blocks and tolerance regions - the continuous case
    • MR0023033
    • TUKEY, J. (1947). Nonparametric estimation. II. Statistical equivalent blocks and tolerance regions - the continuous case. Ann. Math. Statist. 18 529-539. MR0023033
    • (1947) Ann. Math. Statist , vol.18 , pp. 529-539
    • TUKEY, J.1
  • 26
    • 0002502739 scopus 로고
    • An extension of Wilks' method for setting tolerance limits
    • MR0007965
    • WALD, A. (1943). An extension of Wilks' method for setting tolerance limits. Ann. Math. Statist. 14 45-55. MR0007965
    • (1943) Ann. Math. Statist , vol.14 , pp. 45-55
    • WALD, A.1
  • 27
    • 0039318571 scopus 로고
    • Asymptotic power of certain tests of fit based on sample spacings
    • MR0096327
    • WEISS, L. (1957). Asymptotic power of certain tests of fit based on sample spacings. Ann. Math. Statist. 28 783-786. MR0096327
    • (1957) Ann. Math. Statist , vol.28 , pp. 783-786
    • WEISS, L.1
  • 28
    • 0041466052 scopus 로고
    • Large sample theory of spacings statistics for tests of fit for the composite hypothesis
    • MR1210431
    • WELLS, M., JAMMALAMADAKA, S. R. and TIWARI, R. (1993). Large sample theory of spacings statistics for tests of fit for the composite hypothesis. J. Roy. Statist. Soc. Ser. B Stat. Methodol. 55 189-203. MR1210431
    • (1993) J. Roy. Statist. Soc. Ser. B Stat. Methodol , vol.55 , pp. 189-203
    • WELLS, M.1    JAMMALAMADAKA, S.R.2    TIWARI, R.3
  • 29
    • 0002765765 scopus 로고
    • Determination of sample sizes for setting tolerance limits
    • MR0004451
    • WILKS, S. S. (1941). Determination of sample sizes for setting tolerance limits. Ann. Math. Statist. 12 91-96. MR0004451
    • (1941) Ann. Math. Statist , vol.12 , pp. 91-96
    • WILKS, S.S.1
  • 30
    • 0242428127 scopus 로고    scopus 로고
    • Projection based depth functions and associated medians
    • MR2012822
    • ZUO, Y. (2003). Projection based depth functions and associated medians. Ann. Statist. 31 1460-1490. MR2012822
    • (2003) Ann. Statist , vol.31 , pp. 1460-1490
    • ZUO, Y.1
  • 31
    • 0034347414 scopus 로고    scopus 로고
    • Structural properties and convergence results for contours of sample statistical depth functions
    • MR1790006
    • ZUO, Y. and SERFLING, R. (2000). Structural properties and convergence results for contours of sample statistical depth functions. Ann. Statist. 28 483-499. MR1790006
    • (2000) Ann. Statist , vol.28 , pp. 483-499
    • ZUO, Y.1    SERFLING, R.2


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