메뉴 건너뛰기




Volumn 100, Issue 470, 2005, Pages 410-428

Sufficient dimension reduction via inverse regression: A minimum discrepancy approach

Author keywords

Inverse regression estimator; Sliced average variance estimation; Sliced inverse regression; Sufficient dimension reduction

Indexed keywords


EID: 20444454672     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214504000001501     Document Type: Article
Times cited : (298)

References (41)
  • 1
    • 0037461021 scopus 로고    scopus 로고
    • Effective dimension reduction methods for tumor classification using gene expression data
    • Antoniadis, A., Lambert-Lacroix, S., and Leblack, F. (2003), "Effective Dimension Reduction Methods for Tumor Classification Using Gene Expression Data," Bioinformatics, 19, 563-570.
    • (2003) Bioinformatics , vol.19 , pp. 563-570
    • Antoniadis, A.1    Lambert-Lacroix, S.2    Leblack, F.3
  • 2
    • 0038713181 scopus 로고    scopus 로고
    • Using linear smoothers to assess the structural dimension of regressions
    • Bura, E. (2003), "Using Linear Smoothers to Assess the Structural Dimension of Regressions," Statistica Sinica, 13, 143-162.
    • (2003) Statistica Sinica , vol.13 , pp. 143-162
    • Bura, E.1
  • 3
    • 0035532137 scopus 로고    scopus 로고
    • Estimating structural dimensions of regressions via parametric inverse regressions
    • Bura, E., and Cook, R. D. (2001 a), "Estimating Structural Dimensions of Regressions via Parametric Inverse Regressions," Journal of the Royal Statistical Society, Ser. B, 63, 393-410.
    • (2001) Journal of the Royal Statistical Society, Ser. B , vol.63 , pp. 393-410
    • Bura, E.1    Cook, R.D.2
  • 4
    • 0442280663 scopus 로고    scopus 로고
    • Extending sliced inverse regression: The weighted chi-squared test
    • _ (2001b), "Extending Sliced Inverse Regression: The Weighted Chi-Squared Test," Journal of the American Statistical Association, 96, 996-1003.
    • (2001) Journal of the American Statistical Association , vol.96 , pp. 996-1003
  • 5
    • 0038494601 scopus 로고    scopus 로고
    • Graphical methods for class prediction using dimension reduction techniques on DNA microarray data
    • Bura, E., and Pfeiffer, R. M. (2003), "Graphical Methods for Class Prediction Using Dimension Reduction Techniques on DNA Microarray Data," Bioinformatics, 19, 1252-1258.
    • (2003) Bioinformatics , vol.19 , pp. 1252-1258
    • Bura, E.1    Pfeiffer, R.M.2
  • 6
    • 0032367227 scopus 로고    scopus 로고
    • Can SIR be as popular as multiple linear regression?
    • Chen, C.-H., and Li, K. C. (1998), "Can SIR Be as Popular as Multiple Linear Regression?' Statistica Sinica, 8, 289-316.
    • (1998) Statistica Sinica , vol.8 , pp. 289-316
    • Chen, C.-H.1    Li, K.C.2
  • 7
    • 0036278223 scopus 로고    scopus 로고
    • Sufficient dimension reduction in regressions with categorical predictors
    • Chiaromonte, F., Cook, R. D., and Li, B. (2002), "Sufficient Dimension Reduction in Regressions With Categorical Predictors," The Annals of Statistics, 30, 475-497.
    • (2002) The Annals of Statistics , vol.30 , pp. 475-497
    • Chiaromonte, F.1    Cook, R.D.2    Li, B.3
  • 9
    • 0030328726 scopus 로고    scopus 로고
    • Graphics for regressions with a binary response
    • _ (1996), "Graphics for Regressions With a Binary Response," Journal of the American Statistical Association, 91, 983-992.
    • (1996) Journal of the American Statistical Association , vol.91 , pp. 983-992
  • 11
    • 0032340644 scopus 로고    scopus 로고
    • Principal Hessian directions revisited
    • _ (1998b), "Principal Hessian Directions Revisited," Journal of the American Statistical Association, 93, 84-100.
    • (1998) Journal of the American Statistical Association , vol.93 , pp. 84-100
  • 12
    • 15844416978 scopus 로고    scopus 로고
    • Testing predictor contributions in sufficient dimension reduction
    • _ (2004), "Testing Predictor Contributions in Sufficient Dimension Reduction," The Annals of Statistics, 32, 1062-1092.
    • (2004) The Annals of Statistics , vol.32 , pp. 1062-1092
  • 14
    • 0036284461 scopus 로고    scopus 로고
    • Dimension reduction for conditional mean in regression
    • Cook, R. D., and Li, B. (2002), "Dimension Reduction for Conditional Mean in Regression," The Annals of Statistics, 30, 455-474.
    • (2002) The Annals of Statistics , vol.30 , pp. 455-474
    • Cook, R.D.1    Li, B.2
  • 16
    • 84881499895 scopus 로고
    • Discussion of "sliced inverse regression for dimension reduction,"
    • by K. C. Li
    • Cook, R. D., and Weisberg, S. (1991), Discussion of "Sliced Inverse Regression for Dimension Reduction," by K. C. Li, Journal of the American Statistical Association, 86, 328-332.
    • (1991) Journal of the American Statistical Association , vol.86 , pp. 328-332
    • Cook, R.D.1    Weisberg, S.2
  • 18
    • 0012657603 scopus 로고    scopus 로고
    • Dimension reduction and visualization in discriminant analysis
    • Cook, R. D., and Yin, X. (2001), "Dimension Reduction and Visualization in Discriminant Analysis," Australian and New Zealand Journal of Statistics, 43, 147-199.
    • (2001) Australian and New Zealand Journal of Statistics , vol.43 , pp. 147-199
    • Cook, R.D.1    Yin, X.2
  • 19
    • 0023288435 scopus 로고
    • Computational experience with confidence regions and confidence intervals in nonlinear least squares
    • Donaldson, J. R., and Schnabel, R. B. (1987), "Computational Experience With Confidence Regions and Confidence Intervals in Nonlinear Least Squares," Technometrics, 29, 76-82.
    • (1987) Technometrics , vol.29 , pp. 76-82
    • Donaldson, J.R.1    Schnabel, R.B.2
  • 20
    • 0001669894 scopus 로고
    • A method of generating best asymptotically normal estimates with application to the estimation of bacterial densities
    • Ferguson, T. (1958), "A Method of Generating Best Asymptotically Normal Estimates With Application to the Estimation of Bacterial Densities," The Annals of Mathematical Statistics, 29, 1046-1062.
    • (1958) The Annals of Mathematical Statistics , vol.29 , pp. 1046-1062
    • Ferguson, T.1
  • 21
    • 21144465864 scopus 로고
    • Tail areas of linear combinations of chi-squares and non-central chi-squares
    • Field, C. (1993), "Tail Areas of Linear Combinations of Chi-Squares and Non-central Chi-squares," Journal of Statistical Computation and Simulation, 45, 243-248.
    • (1993) Journal of Statistical Computation and Simulation , vol.45 , pp. 243-248
    • Field, C.1
  • 22
    • 0036822251 scopus 로고    scopus 로고
    • Dimension reduction based on canonical correlation
    • Fung, W. K., He, X., Li, L., and Shi, P. (2002), "Dimension Reduction Based on Canonical Correlation," Statistical Sinica, 12, 1093-1113.
    • (2002) Statistical Sinica , vol.12 , pp. 1093-1113
    • Fung, W.K.1    He, X.2    Li, L.3    Shi, P.4
  • 23
    • 0036934876 scopus 로고    scopus 로고
    • A note on outlier sensitivity of sliced inverse regression
    • Gather, U., Hilker, T., and Becker, C. (2002), "A Note on Outlier Sensitivity of Sliced Inverse Regression," Statistics, 13, 271-281.
    • (2002) Statistics , vol.13 , pp. 271-281
    • Gather, U.1    Hilker, T.2    Becker, C.3
  • 24
    • 0041753016 scopus 로고
    • On almost linearity of low-dimensional projections from high-dimensional data
    • Hall, P., and Li, K. C. (1993), "On Almost Linearity of Low-Dimensional Projections From High-Dimensional Data," The Annals of Statistics, 21, 867-889.
    • (1993) The Annals of Statistics , vol.21 , pp. 867-889
    • Hall, P.1    Li, K.C.2
  • 25
    • 0033423359 scopus 로고    scopus 로고
    • Nearest-neighbor inverse regression
    • Hsing, T. (1999), "Nearest-Neighbor Inverse Regression," The Annals of Statistics. 27, 697-731.
    • (1999) The Annals of Statistics , vol.27 , pp. 697-731
    • Hsing, T.1
  • 26
    • 0000906634 scopus 로고
    • An asymptotic theory for sliced inverse regression
    • Hsing, T., and Carroll, R. J. (1992) "An Asymptotic Theory for Sliced Inverse Regression," The Annals of Statistics, 20, 1040-1061.
    • (1992) The Annals of Statistics , vol.20 , pp. 1040-1061
    • Hsing, T.1    Carroll, R.J.2
  • 27
    • 0037191703 scopus 로고    scopus 로고
    • Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems
    • Kiers, H. A. L. (2002), "Setting Up Alternating Least Squares and Iterative Majorization Algorithms for Solving Various Matrix Optimization Problems," Computational Statistics & Data Analysis, 41, 157-170.
    • (2002) Computational Statistics & Data Analysis , vol.41 , pp. 157-170
    • Kiers, H.A.L.1
  • 28
    • 0242679764 scopus 로고    scopus 로고
    • Dimension reduction for the conditional mean in regressions with categorical predictors
    • Li, B., Cook, R. D., and Chiaromonte, F. (2003), "Dimension Reduction for the Conditional Mean in Regressions With Categorical Predictors," The Annals of Statistics, 31, 1636-1668.
    • (2003) The Annals of Statistics , vol.31 , pp. 1636-1668
    • Li, B.1    Cook, R.D.2    Chiaromonte, F.3
  • 30
    • 84950441056 scopus 로고
    • On principal Hessian directions for data visualization and dimension reduction: Another application of Stein's Lemma
    • _ (1992), "On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma," Journal of the American Statistical Association, 87, 1025-1039.
    • (1992) Journal of the American Statistical Association , vol.87 , pp. 1025-1039
  • 31
    • 0031536236 scopus 로고    scopus 로고
    • Nonlinear confounding in high-dimensional regression
    • _ (1997), "Nonlinear Confounding in High-Dimensional Regression," The Annals of Statistics, 57, 577-612.
    • (1997) The Annals of Statistics , vol.57 , pp. 577-612
  • 34
    • 0002832234 scopus 로고
    • Algorithms for separable nonlinear least squares problems
    • Ruhe, A., and Wedin, P. A. (1980), "Algorithms for Separable Nonlinear Least Squares Problems," SIAM Review, 22, 318-337.
    • (1980) SIAM Review , vol.22 , pp. 318-337
    • Ruhe, A.1    Wedin, P.A.2
  • 35
    • 21344478847 scopus 로고
    • Determining the dimensionality in sliced inverse regression
    • Schott, J. R. (1994), "Determining the Dimensionality in Sliced Inverse Regression" Journal of the American Statistical Association, 89, 141-148.
    • (1994) Journal of the American Statistical Association , vol.89 , pp. 141-148
    • Schott, J.R.1
  • 36
    • 0012487730 scopus 로고
    • Asymptotic theory of overparameterized structural models
    • Shapiro, A. (1986), "Asymptotic Theory of Overparameterized Structural Models," Journal of the American Statistical Association, 81, 142-149.
    • (1986) Journal of the American Statistical Association , vol.81 , pp. 142-149
    • Shapiro, A.1
  • 37
    • 0032338774 scopus 로고    scopus 로고
    • Assessing the number of linear components in a general regression problem
    • Velilla, S. (1998), "Assessing the Number of Linear Components in a General Regression Problem," Journal of the American Statistical Association, 93, 1088-1098.
    • (1998) Journal of the American Statistical Association , vol.93 , pp. 1088-1098
    • Velilla, S.1
  • 39
    • 1142265318 scopus 로고    scopus 로고
    • Using the bootstrap to select one of a new class of dimension reduction methods
    • Ye, Z., and Weiss, R. E. (2003), "Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods," Journal of the American Statistical Association, 98, 968-979.
    • (2003) Journal of the American Statistical Association , vol.98 , pp. 968-979
    • Ye, Z.1    Weiss, R.E.2
  • 40
    • 0038153750 scopus 로고    scopus 로고
    • Asymptotics for kernel estimate of sliced inverse regression
    • Zhu, L.-X., and Fang, K.-T. (1996), "Asymptotics for Kernel Estimate of Sliced Inverse Regression,'' The Annals of Statistics, 24, 1053-1068.
    • (1996) The Annals of Statistics , vol.24 , pp. 1053-1068
    • Zhu, L.-X.1    Fang, K.-T.2
  • 41
    • 0001601159 scopus 로고
    • Asymptotics of sliced inverse regression
    • Zhu, L.-X., and Ng, K. W. (1995), "Asymptotics of Sliced Inverse Regression," Statistica Sinica, 5, 727-736.
    • (1995) Statistica Sinica , vol.5 , pp. 727-736
    • Zhu, L.-X.1    Ng, K.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.