메뉴 건너뛰기




Volumn 35, Issue 6, 2007, Pages 2654-2690

A constructive approach to the estimation of dimension reduction directions

Author keywords

Conditional density function; Convergence of algorithm; Double kernel smoothing; Efficient dimension reduction; Root n consistency

Indexed keywords


EID: 49549110291     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/009053607000000352     Document Type: Article
Times cited : (171)

References (35)
  • 1
    • 0001366189 scopus 로고
    • Totally positive matrices
    • MR0884118
    • ANDO, T. (1987). Totally positive matrices. Linear Algebra Appl. 90 165-219. MR0884118
    • (1987) Linear Algebra Appl , vol.90 , pp. 165-219
    • ANDO, T.1
  • 2
    • 0039187894 scopus 로고
    • Estimation of directions of arrival of signals: Asymptotic results
    • S. Haykin, ed, Prentice Hall, Englewood Cliffs, NJ
    • BAI, Z. D., MIAO, B. Q. and RAO, C. R. (1991). Estimation of directions of arrival of signals: Asymptotic results. In Advances in Spectrum Analysis and Array Processing (S. Haykin, ed.) 1 327-347. Prentice Hall, Englewood Cliffs, NJ.
    • (1991) Advances in Spectrum Analysis and Array Processing , vol.1 , pp. 327-347
    • BAI, Z.D.1    MIAO, B.Q.2    RAO, C.R.3
  • 3
    • 0032367227 scopus 로고    scopus 로고
    • Can SIR be as popular as multiple linear regression?
    • MR1624402
    • CHEN, C.-H. and LI, K.-C. (1998). Can SIR be as popular as multiple linear regression? Statist. Sinica 8 289-316. MR1624402
    • (1998) Statist. Sinica , vol.8 , pp. 289-316
    • CHEN, C.-H.1    LI, K.-C.2
  • 4
    • 50849111826 scopus 로고    scopus 로고
    • CHOW, Y. S. and TEICHER, H. (1978). Probability Theory. Independence, Interchangeability, Martingales. Springer, New York. MR0513230
    • CHOW, Y. S. and TEICHER, H. (1978). Probability Theory. Independence, Interchangeability, Martingales. Springer, New York. MR0513230
  • 5
    • 50849132994 scopus 로고    scopus 로고
    • CHUNG, K. L. (1968). A Course in Probability Theory. Harcourt, Brace and World, New York. MR0229268
    • CHUNG, K. L. (1968). A Course in Probability Theory. Harcourt, Brace and World, New York. MR0229268
  • 6
    • 50849115559 scopus 로고    scopus 로고
    • COOK, R. D. (1998). Regression Graphics. Wiley, New York. MR1645673
    • COOK, R. D. (1998). Regression Graphics. Wiley, New York. MR1645673
  • 7
    • 0036284461 scopus 로고    scopus 로고
    • Dimension reduction for conditional mean in regression
    • MR1902895
    • COOK, R. D. and LI, B. (2002). Dimension reduction for conditional mean in regression. Ann. Statist. 30 455-474. MR1902895
    • (2002) Ann. Statist , vol.30 , pp. 455-474
    • COOK, R.D.1    LI, B.2
  • 8
    • 84881499895 scopus 로고
    • Comment on "Sliced inverse regression for dimension reduction," by K.-C. Li
    • COOK, R. D. and WEISBERG, S. (1991). Comment on "Sliced inverse regression for dimension reduction," by K.-C. Li. J. Amer. Statist. Assoc. 86 328-332.
    • (1991) J. Amer. Statist. Assoc , vol.86 , pp. 328-332
    • COOK, R.D.1    WEISBERG, S.2
  • 9
    • 0032622766 scopus 로고    scopus 로고
    • A general class of exponential inequalities for martingales and ratios
    • MR1681153
    • DE LA PEÑA, V. H. (1999). A general class of exponential inequalities for martingales and ratios. Ann. Probab. 27 537-564. MR1681153
    • (1999) Ann. Probab , vol.27 , pp. 537-564
    • DE LA PEÑA, V.H.1
  • 10
    • 28044442060 scopus 로고    scopus 로고
    • On semiparametric M-estimation in single-index regression
    • MR2181975
    • DELECROIX, M., HRISTACHE, M. and PATILEA, V. (2005). On semiparametric M-estimation in single-index regression. J. Statist. Plann. Inference 136 730-769. MR2181975
    • (2005) J. Statist. Plann. Inference , vol.136 , pp. 730-769
    • DELECROIX, M.1    HRISTACHE, M.2    PATILEA, V.3
  • 11
    • 50849109589 scopus 로고    scopus 로고
    • FAN, J. and GIJBELS, I. (1996). Local Polynomial Modelling and Its Applications. Chapman and Hall, London. MR1383587
    • FAN, J. and GIJBELS, I. (1996). Local Polynomial Modelling and Its Applications. Chapman and Hall, London. MR1383587
  • 12
    • 50849129668 scopus 로고    scopus 로고
    • FAN, J. and YAO, Q. (2003). Nonlinear Time Series: Nonparametric and Parametric Methods. Springer, New York. MR1964455
    • FAN, J. and YAO, Q. (2003). Nonlinear Time Series: Nonparametric and Parametric Methods. Springer, New York. MR1964455
  • 13
    • 0001400429 scopus 로고    scopus 로고
    • Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems
    • MR1399164
    • FAN, J., YAO, Q. and TONG, H. (1996). Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. Biometrika 83 189-206. MR1399164
    • (1996) Biometrika , vol.83 , pp. 189-206
    • FAN, J.1    YAO, Q.2    TONG, H.3
  • 14
    • 21144469983 scopus 로고
    • Optimal smoothing in single-index models
    • MR1212171
    • HÄRDLE, W., HALL, P. and ICHIMURA, H. (1993). Optimal smoothing in single-index models. Ann. Statist. 21 157-178. MR1212171
    • (1993) Ann. Statist , vol.21 , pp. 157-178
    • HÄRDLE, W.1    HALL, P.2    ICHIMURA, H.3
  • 15
    • 0002470428 scopus 로고
    • Investigating smooth multiple regression by the method of average derivatives
    • MR1134488
    • HÄRDLE, W. and STOKER, T. M. (1989). Investigating smooth multiple regression by the method of average derivatives. J. Amer. Statist. Assoc. 84 986-995. MR1134488
    • (1989) J. Amer. Statist. Assoc , vol.84 , pp. 986-995
    • HÄRDLE, W.1    STOKER, T.M.2
  • 16
    • 84950437480 scopus 로고
    • Comment on "Sliced inverse regression for dimension reduction," by K.-C. Li
    • HÄRDLE, W. and TSYBAKOV, A. B. (1991). Comment on "Sliced inverse regression for dimension reduction," by K.-C. Li. J. Amer. Statist. Assoc. 86 333-335.
    • (1991) J. Amer. Statist. Assoc , vol.86 , pp. 333-335
    • HÄRDLE, W.1    TSYBAKOV, A.B.2
  • 17
    • 0004044304 scopus 로고
    • The strong law of large numbers for U-statistics
    • No. 302, Inst. Statist, Univ. North Carolina
    • HOEFFDING, W. (1961). The strong law of large numbers for U-statistics. Mimeo Report No. 302, Inst. Statist., Univ. North Carolina.
    • (1961) Mimeo Report
    • HOEFFDING, W.1
  • 18
    • 0041708566 scopus 로고    scopus 로고
    • Direct semiparametric estimation of single-index models with discrete covariates
    • MR1439104
    • HOROWITZ, J. L. and HÄRDLE, W. (1996). Direct semiparametric estimation of single-index models with discrete covariates. J. Amer. Statist. Assoc. 91 1632-1640. MR1439104
    • (1996) J. Amer. Statist. Assoc , vol.91 , pp. 1632-1640
    • HOROWITZ, J.L.1    HÄRDLE, W.2
  • 19
    • 0035528162 scopus 로고    scopus 로고
    • Structure adaptive approach for dimension reduction
    • MR1891738
    • HRISTACHE, M., JUDITSKY, A., POLZEHL, J. and SPOKOINY, V. (2001). Structure adaptive approach for dimension reduction. Ann. Statist. 29 1537-1566. MR1891738
    • (2001) Ann. Statist , vol.29 , pp. 1537-1566
    • HRISTACHE, M.1    JUDITSKY, A.2    POLZEHL, J.3    SPOKOINY, V.4
  • 20
    • 0035539851 scopus 로고    scopus 로고
    • Direct estimation of the index coefficient in a single-index model
    • MR1865333
    • HRISTACHE, M., JUDITSKY, A. and SPOKOINY, V. (2001). Direct estimation of the index coefficient in a single-index model. Ann. Statist. 29 595-623. MR1865333
    • (2001) Ann. Statist , vol.29 , pp. 595-623
    • HRISTACHE, M.1    JUDITSKY, A.2    SPOKOINY, V.3
  • 21
    • 26444566340 scopus 로고    scopus 로고
    • Contour regression: A general approach to dimension reduction
    • MR2166556
    • LI, B., ZHA, H. and CHIAROMONTE, F. (2005). Contour regression: A general approach to dimension reduction. Ann. Statist. 33 1580-1616. MR2166556
    • (2005) Ann. Statist , vol.33 , pp. 1580-1616
    • LI, B.1    ZHA, H.2    CHIAROMONTE, F.3
  • 22
    • 84945116550 scopus 로고
    • Sliced inverse regression for dimension reduction (with discussion)
    • MR1137117
    • LI, K.-C. (1991). Sliced inverse regression for dimension reduction (with discussion). J. Amer. Statist. Assoc. 86 316-342. MR1137117
    • (1991) J. Amer. Statist. Assoc , vol.86 , pp. 316-342
    • LI, K.-C.1
  • 23
    • 84950441056 scopus 로고
    • On principal Hessian directions for data visualization and dimension reduction: Another application of Stein's lemma
    • MR1209564
    • LI, K.-C. (1992). On principal Hessian directions for data visualization and dimension reduction: Another application of Stein's lemma. J. Amer. Statist. Assoc. 87 1025-1039. MR1209564
    • (1992) J. Amer. Statist. Assoc , vol.87 , pp. 1025-1039
    • LI, K.-C.1
  • 24
    • 24944530035 scopus 로고    scopus 로고
    • Principal Hessian directions for regression with measurement error
    • MR2081310
    • LUE, H.-H. (2004). Principal Hessian directions for regression with measurement error. Biometrika 91 409-423. MR2081310
    • (2004) Biometrika , vol.91 , pp. 409-423
    • LUE, H.-H.1
  • 25
    • 0001194690 scopus 로고
    • Weak and strong uniform consistency of kernel regression estimates
    • MR0679685
    • MACK, Y. P. and SILVERMAN, B. W. (1982). Weak and strong uniform consistency of kernel regression estimates. Z. Wahrsch. Verw. Gebiete 61 405-415. MR0679685
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.61 , pp. 405-415
    • MACK, Y.P.1    SILVERMAN, B.W.2
  • 26
    • 21144467148 scopus 로고
    • Exploring regression structure using nonparametric functional estimation
    • MR1242934
    • SAMAROV, A. M. (1993). Exploring regression structure using nonparametric functional estimation. J. Amer. Statist. Assoc. 88 836-847. MR1242934
    • (1993) J. Amer. Statist. Assoc , vol.88 , pp. 836-847
    • SAMAROV, A.M.1
  • 27
    • 50849108935 scopus 로고    scopus 로고
    • SCOTT, D. W. (1992). Multivariate Density Estimation: Theory, Practice and Visualization. Wiley, New York. MR1191168
    • SCOTT, D. W. (1992). Multivariate Density Estimation: Theory, Practice and Visualization. Wiley, New York. MR1191168
  • 28
    • 50849110598 scopus 로고    scopus 로고
    • SILVERMAN, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London. MR0848134
    • SILVERMAN, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London. MR0848134
  • 29
    • 33750048824 scopus 로고    scopus 로고
    • WORLD HEALTH ORGANIZATION , Bonn, Germany
    • WORLD HEALTH ORGANIZATION (2003). Reports on a WHO/HEI working group. Bonn, Germany.
    • (2003) Reports on a WHO/HEI working group
  • 30
    • 33845728000 scopus 로고    scopus 로고
    • Asymptotic distributions for two estimators of the single-index model
    • MR2328530
    • XIA, Y. (2006). Asymptotic distributions for two estimators of the single-index model. Econometric Theory 22 1112-1137. MR2328530
    • (2006) Econometric Theory , vol.22 , pp. 1112-1137
    • XIA, Y.1
  • 31
    • 50849098605 scopus 로고    scopus 로고
    • XIA, Y. (2006). A constructive approach to the estimation of dimension reduction directions. Technical report, Dept. Statistics and Applied Probability, National Univ. Singapore.
    • XIA, Y. (2006). A constructive approach to the estimation of dimension reduction directions. Technical report, Dept. Statistics and Applied Probability, National Univ. Singapore.
  • 32
    • 0036660836 scopus 로고    scopus 로고
    • Single-index volatility models and estimation
    • MR1929964
    • XIA, Y., TONG, H. and LI, W. K. (2002). Single-index volatility models and estimation. Statist. Sinica 12 785-799. MR1929964
    • (2002) Statist. Sinica , vol.12 , pp. 785-799
    • XIA, Y.1    TONG, H.2    LI, W.K.3
  • 33
    • 0036428498 scopus 로고    scopus 로고
    • An adaptive estimation of dimension reduction space (with discussion)
    • MR1924297
    • XIA, Y., TONG, H., LI, W. K. and ZHU, L. (2002). An adaptive estimation of dimension reduction space (with discussion). J. R. Stat. Soc. Ser. B. Stat. Methodol. 64 363-410. MR1924297
    • (2002) J. R. Stat. Soc. Ser. B. Stat. Methodol , vol.64 , pp. 363-410
    • XIA, Y.1    TONG, H.2    LI, W.K.3    ZHU, L.4
  • 34
    • 0036432553 scopus 로고    scopus 로고
    • Dimension reduction for the conditional kth moment in regression
    • MR1904698
    • YIN, X. and COOK, R. D. (2002). Dimension reduction for the conditional kth moment in regression. J. R. Stat. Soc. Ser. B Stat. Methodol. 64 159-175. MR1904698
    • (2002) J. R. Stat. Soc. Ser. B Stat. Methodol , vol.64 , pp. 159-175
    • YIN, X.1    COOK, R.D.2
  • 35
    • 21244477445 scopus 로고    scopus 로고
    • Direction estimation in single-index regressions
    • MR2201365
    • YIN, X. and COOK, R. D. (2005). Direction estimation in single-index regressions. Biometrika 92 371-384. MR2201365
    • (2005) Biometrika , vol.92 , pp. 371-384
    • YIN, X.1    COOK, R.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.