The Annals of Statistics

Sufficient dimensions reduction in regressions with categorical predictors

Francesca Chiaromonte, R.Dennis Cook, and Bing Li

Full-text: Open access

Abstract

In this article, we describe how the theory of sufficient dimension reduction, and a well-known inference method for it (sliced inverse regression), can be extended to regression analyses involving both quantitative and categorical predictor variables. As statistics faces an increasing need for effective analysis strategies for high-dimensional data, the results we present significantly widen the applicative scope of sufficient dimension reduction and open the way for a new class of theoretical and methodological developments.

Article information

Source
Ann. Statist., Volume 30, Number 2 (2002), 475-497.

Dates
First available in Project Euclid: 14 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1021379862

Digital Object Identifier
doi:10.1214/aos/1021379862

Mathematical Reviews number (MathSciNet)
MR1902896

Zentralblatt MATH identifier
1012.62036

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G09: Resampling methods 62H05: Characterization and structure theory

Keywords
Central subspace graphics SAVE SIR visualization

Citation

Chiaromonte, Francesca; Cook, R.Dennis; Li, Bing. Sufficient dimensions reduction in regressions with categorical predictors. Ann. Statist. 30 (2002), no. 2, 475--497. doi:10.1214/aos/1021379862. https://projecteuclid.org/euclid.aos/1021379862


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References

  • CARROLL, R. J. and LI, K.-C. (1995). Binary regressors in dimension reduction models: A new look at treatment comparisons. Statist. Sinica 5 667-688.
  • CHIAROMONTE, F. and COOK, R. D. (2002). Sufficient dimension reduction and graphics in regression. Ann. Inst. Statist. Math. To appear.
  • COOK, R. D. (1998). Regression Graphics. Wiley, New York.
  • COOK, R. D. and CRITCHLEY, F. (2000). Identifying regression outliers and mixtures graphically. J. Amer. Statist. Assoc. 95 781-794.
  • COOK, R. D. and WEISBERG, S. (1991). Discussion of "Sliced inverse regression for dimension reduction." J. Amer. Statist. Assoc. 86 328-332.
  • COOK, R. D. and WEISBERG, S. (1994). An Introduction to Regression Graphics. Wiley, New York.
  • COOK, R. D. and WEISBERG, S. (1999a). Graphics in statistical analysis: Is the medium the message? Amer. Statist. 53 29-37.
  • COOK, R. D. and WEISBERG, S. (1999b). Applied Regression Including Computing and Graphics. Wiley, New York.
  • DAWID, A. P. (1979). Conditional independence in statistical theory (with discussion). J. Roy. Statist. Soc. Ser. B 41 1-31.
  • EATON, M. L. and TYLER, D. E. (1994). The asymptotic distribution of singular values with applications to canonical correlations and correspondence analysis. J. Multivariate Anal. 50 238-264.
  • LI, K.-C. (1991). Sliced inverse regression for dimension reduction (with discussion). J Amer. Statist. Assoc. 86 316-342.
  • 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.
  • LI, K.-C. and DUAN, N. (1989). Regression analysis under link violation. Ann. Statist. 17 1009- 1052.
  • NEVILL, A. M. and HOLDER, R. L. (1995). Body mass index: A measure of fatness or leanness? British Journal of Nutrition 73 507-516.
  • SCHOTT, J. (1994). Determining the dimensionality in sliced inverse regression. J. Amer. Statist. Assoc. 89 141-148.
  • VELILLA, S. (1998). Assessing the number of linear components in a general regression problem. J. Amer. Statist. Assoc. 93 1088-1098.
  • UNIVERSITY PARK, PENNSYLVANIA 16802 E-MAIL: chiaro@stat.psu.edu R. D. COOK SCHOOL OF STATISTICS 1994 BUFORD AVENUE UNIVERSITY OF MINNESOTA ST. PAUL, MINNESOTA 55108 E-MAIL: dennis@stat.umn.edu B. LI DEPARTMENT OF STATISTICS PENNSYLVANIA STATE UNIVERSITY 326 THOMAS BUILDING
  • UNIVERSITY PARK, PENNSYLVANIA 16802 E-MAIL: bing@stat.psu.edu