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Theory and Methods

Fused Estimators of the Central Subspace in Sufficient Dimension Reduction

Pages 815-827 | Received 01 Jan 2012, Published online: 13 Jun 2014

REFERENCES

  • Bates, J.M., Granger, C. W.J. (1969), The Combination of Forecasts, Operations Research Quarterly, 20, 451–468.
  • Chiaromonte, F., Cook, R. D., and Li, B. (2002), “Sufficient Dimension Reduction in Regressions with Categorical Predictors,” The Annals of Statistics, 30, 475–497.
  • Cook, R.D. (1998), Regression Graphics: Ideas for Studying Regressions Through Graphics, New York: Wiley.
  • Cook, R.D., Forzani, L. (2008), Principal Fitted Components for Dimension Reduction in Regression, Statistical Science, 23, 485–501.
  • Cook, R.D., Forzani, L. (2009), Likelihood-Based Sufficient Dimension Reduction, Journal of the American Statistical Association, 104, 197–208.
  • Cook, R. D., Forzani, L., and Rothman, A. J. (2012), “Estimating Sufficient Reductions of the Predictors in Abundant High-Dimensional Regressions,” The Annals of Statistics, 40, 353–384.
  • Cook, R.D., Ni, L. (2005), Sufficient Dimension Reduction Via Inverse Regression: A Minimum Discrepancy Approach, Journal of the American Statistical Association, 100, 410–428.
  • Cook, R.D., Weisberg, S. (1991), Discussion of “Sliced Inverse Regression for Dimension Reduction” by K.-C. Li, Journal of the American Statistical Association, 86, 328–332.
  • Cook, R.D., Yin, X. (2001), “Dimension Reduction and Visualization in Discriminant Analysis” (with discussion), Australia/New Zealand Journal of Statistics, 43, 147–199.
  • Dong, Y., Li, B. (2010), Dimension Reduction for Nonelliptically Distributed Predictors: Second Order Methods, Biometrika, 97, 279–294.
  • Hall, P., Li, K.C. (1993), On Almost Linearity of Low Dimensional Projection From High Dimensional Data, The Annals of Statistics, 21, 867–889.
  • Hooper, J. (1959), Simultaneous Equations and Canonical Correlation Theory, Econometrica, 27, 245–256.
  • Hotelling, H. (1936), Relations Between Two Sets of Variates, Biometrika, 28, 321–377.
  • Hsing, T., Carroll, R.J. (1992), An Asymptotic Theory for Sliced Inverse Regression, The Annals of Statistics, 20, 1040–1061.
  • Li, B., Dong, Y. (2009), Dimension Reduction for Nonelliptically Distributed Predictors, The Annals of Statistics, 37, 1272–1298.
  • Li, B., Wang, S. (2007), On Directional Regression for Dimension Reduction, Journal of the American Statistical Association, 102, 997–1008.
  • Li, K.C. (1991), Sliced Inverse Regression for Dimension Reduction, Journal of the American Statistical Association, 86, 316–342.
  • Lindsay, B. (1988), Composite Likelihood Methods, Contemporary Mathematics, 80, 220–239.
  • Luceno, A. (1999), Discrete Approximations to Continuous Univariate Distributions–and Alternative to Simulation, Journal of the Royal Statistical Society, , 61, 345–352.
  • Ma, Y., Zhu, L. (2012), A Semiparametric Approach to Dimension Reduction, Journal of the American Statistical Association, 107, 168–179.
  • Ni, L., Cook, R.D. (2007), A Robust Inverse Regression Estimator, Statistics and Probability Letters, 77, 343–349.
  • Rothman, A.J., Bickel, P.J., Levina, E., Zhu, J. (2008), Sparse Permutation Invariant Covariance Estimation, Electronic Journal of Statistics, 2, 494–515.
  • Setodji, C., Cook, R.D. (2004), K-Means Inverse Regression, Technometrics, 46, 421–429.
  • Shapiro, A. (1986), Asymptotic Theory of Overparameterized Structural Models, Journal of the American Statistical Association, 81, 142–149.
  • Timmermann, A.G. (2006), “Forecast Combinations,” in Handbook of Economic Forecasting, eds. G. Elliott, C. W. J. Granger, and A. Timmerman, Amsterdam: North-Holland.
  • Varin, C., Reid, N., Firth, D. (2011), An Overview of Composite Likelihood Methods, Statistica Sinica, 21, 5–42.
  • Ye, Z., 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.
  • Zhu, L., Ng, K.W. (1995), Asymptotics of Sliced Inverse Regression, Statistica Sinica, 5, 727–736.
  • Zhu, L., Zhu, L., Feng, Z. (2010), Dimension Reduction in Regressions Through Cumulative Slicing Estimation, Journal of the American Statistical Association, 105, 1455–1466.

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