메뉴 건너뛰기




Volumn 32, Issue 2, 2005, Pages 327-350

On maximum depth and related classifiers

Author keywords

Bayes risk; Cross validation; Data depth; Elliptic symmetry; Kernel density estimation; Location shift model; Mahalanobis distance; Misclassification rate; Vapnik Chervonenkis dimension

Indexed keywords


EID: 19744370419     PISSN: 03036898     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9469.2005.00423.x     Document Type: Review
Times cited : (89)

References (48)
  • 1
    • 0030540155 scopus 로고    scopus 로고
    • On a geometric notion of quantiles for multivariate data
    • Chaudhuri, P. (1996). On a geometric notion of quantiles for multivariate data. J. Amer. Statist. Assoc. 91, 862-872.
    • (1996) J. Amer. Statist. Assoc. , vol.91 , pp. 862-872
    • Chaudhuri, P.1
  • 2
    • 21344492438 scopus 로고
    • Sign tests in multidimension: Inference based on the geometry of the data cloud
    • Chaudhuri, P. & Sengupta, D. (1993). Sign tests in multidimension: Inference based on the geometry of the data cloud. J. Amer. Statist. Assoc. 88, 1363-1370.
    • (1993) J. Amer. Statist. Assoc. , vol.88 , pp. 1363-1370
    • Chaudhuri, P.1    Sengupta, D.2
  • 4
    • 0036016389 scopus 로고    scopus 로고
    • Comparison between various regression depth methods and the support vector machine to approximate the minimum number of misclassifications
    • Christmann, A., Fischer, P. & Joachims, T. (2002). Comparison between various regression depth methods and the support vector machine to approximate the minimum number of misclassifications. Comput. Statist. 17, 273-287.
    • (2002) Comput. Statist. , vol.17 , pp. 273-287
    • Christmann, A.1    Fischer, P.2    Joachims, T.3
  • 5
    • 0007777923 scopus 로고    scopus 로고
    • Classification via kernel product estimators
    • Cooley, C. A. & MacEachern S. N. (1998). Classification via kernel product estimators. Biometrika 85, 823-833.
    • (1998) Biometrika , vol.85 , pp. 823-833
    • Cooley, C.A.1    MacEachern, S.N.2
  • 7
    • 0035729565 scopus 로고    scopus 로고
    • Robust linear discriminant analysis using S-estimators
    • Croux, C. & Dehon, C. (2001). Robust linear discriminant analysis using S-estimators. Canad. J. Statist. 29, 473-492.
    • (2001) Canad. J. Statist. , vol.29 , pp. 473-492
    • Croux, C.1    Dehon, C.2
  • 9
    • 0001597702 scopus 로고
    • Breakdown properties of location estimates based on half-space depth and projected outlyingness
    • Donoho, D. & Gasko, M. (1992). Breakdown properties of location estimates based on half-space depth and projected outlyingness. Ann. Statist. 20, 1803-1827.
    • (1992) Ann. Statist. , vol.20 , pp. 1803-1827
    • Donoho, D.1    Gasko, M.2
  • 11
    • 0000764772 scopus 로고
    • The use of multiple measurements in taxonomic problems
    • Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Ann Eugen. 7, 179-188.
    • (1936) Ann Eugen. , vol.7 , pp. 179-188
    • Fisher, R.A.1
  • 13
    • 0003440665 scopus 로고    scopus 로고
    • Another approach to polychotomous classification
    • Department of Statistics, Stanford University, Stanford
    • Friedman, J. H. (1996). Another approach to polychotomous classification. Technical report, Department of Statistics, Stanford University, Stanford.
    • (1996) Technical Report
    • Friedman, J.H.1
  • 14
    • 3142733500 scopus 로고    scopus 로고
    • Optimal smoothing in kernel discriminant analysis
    • Ghosh, A. K. & Chaudhuri, P. (2004a). Optimal smoothing in kernel discriminant analysis. Statist. Sinica 14, 457-483.
    • (2004) Statist. Sinica , vol.14 , pp. 457-483
    • Ghosh, A.K.1    Chaudhuri, P.2
  • 15
    • 19744364736 scopus 로고    scopus 로고
    • On data depth and distribution free discriminant analysis using separating surfaces
    • in press
    • Ghosh, A. K. & Chaudhuri, P. (2004b). On data depth and distribution free discriminant analysis using separating surfaces. Bernoulli, (in press).
    • (2004) Bernoulli
    • Ghosh, A.K.1    Chaudhuri, P.2
  • 16
    • 0031519463 scopus 로고    scopus 로고
    • Convergence of depth contours for multivariate data sets
    • He, X. & Wang, G. (1997). Convergence of depth contours for multivariate data sets. Ann. Statist. 25, 495-504.
    • (1997) Ann. Statist. , vol.25 , pp. 495-504
    • He, X.1    Wang, G.2
  • 17
    • 0011908457 scopus 로고    scopus 로고
    • High breakdown estimation or multiple populations with applications to discriminant analysis
    • He, X. & Fung, W. K. (2000). High breakdown estimation or multiple populations with applications to discriminant analysis. J. Multivariate Anal. 72, 151-162.
    • (2000) J. Multivariate Anal. , vol.72 , pp. 151-162
    • He, X.1    Fung, W.K.2
  • 18
    • 19744362101 scopus 로고    scopus 로고
    • Cluster analysis based on data depth
    • (eds H. A. L. Kiers, J. P. Rasson, P. J. F. Groenen and M. Schader), Springer, Berlin
    • Hoberg, R. (2000). Cluster analysis based on data depth. Data analysis, classification and related methods (eds H. A. L. Kiers, J. P. Rasson, P. J. F. Groenen and M. Schader), Springer, Berlin, pp. 17-22.
    • (2000) Data Analysis, Classification and Related Methods , pp. 17-22
    • Hoberg, R.1
  • 19
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • Hoeffding, W. (1963). Probability inequalities for sums of bounded random variables. J. Am. Statist. Assoc. 58, 13-30.
    • (1963) J. Am. Statist. Assoc. , vol.58 , pp. 13-30
    • Hoeffding, W.1
  • 22
    • 19744375379 scopus 로고    scopus 로고
    • Clustering and classification based on the LI data depth
    • Jornsten, R. (2004). Clustering and classification based on the LI data depth. J. Multivariate Anal. 90, 67-89.
    • (2004) J. Multivariate Anal. , vol.90 , pp. 67-89
    • Jornsten, R.1
  • 23
    • 0031493777 scopus 로고    scopus 로고
    • M-estimation, convexity and quantiles
    • Koltchinskii, V. I. (1997). M-estimation, convexity and quantiles. Ann. Statist. 25, 435-477.
    • (1997) Ann. Statist. , vol.25 , pp. 435-477
    • Koltchinskii, V.I.1
  • 24
    • 0001767349 scopus 로고
    • On notion of data depth-based on random simplicies
    • Liu, R. (1990). On notion of data depth-based on random simplicies. Ann. Statist. 18, 405-414.
    • (1990) Ann. Statist. , vol.18 , pp. 405-414
    • Liu, R.1
  • 25
    • 0040598406 scopus 로고
    • A quality index based on data depth and multivariate rank tests
    • Liu, R. & Singh, K. (1993). A quality index based on data depth and multivariate rank tests. J. Am. Statist. Assoc. 88, 252-260.
    • (1993) J. Am. Statist. Assoc. , vol.88 , pp. 252-260
    • Liu, R.1    Singh, K.2
  • 26
    • 0033147626 scopus 로고    scopus 로고
    • Multivariate analysis of the data-depth: Descriptive statistics and inference
    • Liu, R., Parelius, J. & Singh, K. (1999). Multivariate analysis of the data-depth: descriptive statistics and inference. Ann. Statist. 27, 783-858.
    • (1999) Ann. Statist. , vol.27 , pp. 783-858
    • Liu, R.1    Parelius, J.2    Singh, K.3
  • 28
    • 0037001542 scopus 로고    scopus 로고
    • On depth and deep points: A calculus
    • Mizera, I. (2002). On depth and deep points: a calculus. Ann. Statist. 30, 1681-1736.
    • (2002) Ann. Statist. , vol.30 , pp. 1681-1736
    • Mizera, I.1
  • 30
    • 38249010534 scopus 로고
    • Asymptotics for multivariate trimming
    • Nolan, D. (1992). Asymptotics for multivariate trimming. Stochastic Process Appl. 42, 157-169.
    • (1992) Stochastic Process Appl. , vol.42 , pp. 157-169
    • Nolan, D.1
  • 31
    • 0000107573 scopus 로고
    • Descriptive statistics for multivariate distributions
    • Oja, H. (1983). Descriptive statistics for multivariate distributions. Statist. Probab. Lett. 1, 327-332.
    • (1983) Statist. Probab. Lett. , vol.1 , pp. 327-332
    • Oja, H.1
  • 32
    • 84941328385 scopus 로고
    • Control methods used in a study of the vowels
    • Peterson, G. E. & Barney, H. L. (1952). Control methods used in a study of the vowels. J. Acoust. Soc. Am. 24, 175-184.
    • (1952) J. Acoust. Soc. Am. , vol.24 , pp. 175-184
    • Peterson, G.E.1    Barney, H.L.2
  • 34
    • 0000696616 scopus 로고
    • Neural networks and related methods for classification
    • Ripley, B. D. (1994). Neural networks and related methods for classification (with discussion.) J. Roy. Statist. Soc. Ser. B 56, 409-456.
    • (1994) J. Roy. Statist. Soc. Ser. B , vol.56 , pp. 409-456
    • Ripley, B.D.1
  • 35
    • 0002564033 scopus 로고
    • Multivariate estimation with high breakdown point
    • (eds W. Grossmann, G. Pflug, I. Vincze and W. Wertz), Reidel, Dordrecht
    • Rousseeuw, P. (1985). Multivariate estimation with high breakdown point. Mathematical statistics and applications (eds W. Grossmann, G. Pflug, I. Vincze and W. Wertz), Reidel, Dordrecht, pp. 283-297.
    • (1985) Mathematical Statistics and Applications , pp. 283-297
    • Rousseeuw, P.1
  • 36
  • 37
    • 0002846981 scopus 로고    scopus 로고
    • Computing location depth and regression depth in higher dimensions
    • Rousseeuw, P. J. & Struyf, A. (1998). Computing location depth and regression depth in higher dimensions. Statist. Comput. 8, 193-203.
    • (1998) Statist. Comput. , vol.8 , pp. 193-203
    • Rousseeuw, P.J.1    Struyf, A.2
  • 39
    • 0032680362 scopus 로고    scopus 로고
    • A fast algorithm for the minimum covariance determinant estimator
    • Rousseeuw, P. J. & Van Driessen, K. (1999). A fast algorithm for the minimum covariance determinant estimator, Technometrics 41, 212-223.
    • (1999) Technometrics , vol.41 , pp. 212-223
    • Rousseeuw, P.J.1    Van Driessen, K.2
  • 41
    • 2142736121 scopus 로고    scopus 로고
    • A depth function and a scale curve based on spatial quantiles
    • (ed. Y. Dodge), Birkhaeuser
    • 1-Norm and Related Methods (ed. Y. Dodge), Birkhaeuser, 25-38.
    • (2002) 1-Norm and Related Methods , pp. 25-38
    • Serfling, R.1
  • 42
    • 0003857154 scopus 로고
    • Technical report, Department of Statistics, Rutgers University, Piscataway
    • Singh, K. (1991). A notion of majority depth. Technical report, Department of Statistics, Rutgers University, Piscataway.
    • (1991) A Notion of Majority Depth
    • Singh, K.1
  • 43
    • 0003926139 scopus 로고
    • Research report 31, Fachgruppe fur Statistik, ETH, Zurich
    • Stahel, W. A. (1981). Breakdown of covariance estimators. Research report 31, Fachgruppe fur Statistik, ETH, Zurich.
    • (1981) Breakdown of Covariance Estimators
    • Stahel, W.A.1
  • 47
    • 0034347419 scopus 로고    scopus 로고
    • General notions of statistical depth function
    • Zuo, Y. & Serfling, R. (2000a). General notions of statistical depth function. Ann. Statist. 28, 461-482.
    • (2000) Ann. Statist. , vol.28 , pp. 461-482
    • Zuo, Y.1    Serfling, R.2
  • 48
    • 0034347414 scopus 로고    scopus 로고
    • Structural properties and convergence results for contours of sample statistical depth functions
    • Zuo, Y. & Serfling, R. (2000b). Structural properties and convergence results for contours of sample statistical depth functions. Ann. Statist. 28, 483-499.
    • (2000) Ann. Statist. , vol.28 , pp. 483-499
    • Zuo, Y.1    Serfling, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.