REFERENCES
- Arcones, M.A., and Giné, E. (1992), “On the Bootstrap of M-Estimators and Other Statistical Functionals,” in Exploring the Limits of Bootstrap (East Lansing, MI, 1990), Wiley Series in Probability and Statistics , eds. R. LePage and L. Billard,New York: Wiley, pp. 13–47.
- Barrios, M.P., and Velilla, S. (2007), “A Bootstrap Method for Assessing the Dimension of a General Regression Problem,” Statistics and Probability Letters, 77, 247–255.
- Bentler, M.P., and Xie, J. (2000), “Corrections to Test Statistics in Principal Hessian Directions,” Statistics and Probability Letters, 47, 381–389.
- Bhattacharya, R.N., and Rao, R.R. (1976), Normal Approximation and Asymptotic Expansions (Wiley Series in Probability and Mathematical Statistics), New York-London-Sydney: Wiley.
- Boos, D.D. (1990), “On Generalized Score Tests,” The American Statistician, 46, 327–333.
- Bura, E., and Cook, R.D. (2001), “Extending Sliced Inverse Regression: The Weighted Chi-Squared Test,” Journal of the American Statistical Association, 96, 996–1003.
- Bura, E., and Yang, J. (2011), “Dimension Estimation in Sufficient Dimension Reduction: A Unifying Approach,” Journal of Multivariate Analysis, 102, 130–142.
- Cook, R.D., and 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., and Weisberg, S. (1991), Discussion of “Sliced Inverse Regression for Dimension Reduction,” by Ker-Chau Li, Journal of the American Statistical Association, 86, 28–33.
- Cragg, J.G., and Donald, S.G. (1996), “On the Asymptotic Properties of LDU-Based Tests of the Rank of a Matrix,” Journal of the American Statistical Association, 91, 1301–1309.
- Cragg, J.G., and Donald, S.G. (1997), “Inferring the Rank of a Matrix,” Journal of Econometrics, 76, 223–250.
- Eaton, M.L., and Tyler, D. (1994), “The Asymptotic Distribution of Singular Values With Applications to Canonical Correlations and Correspondence Analysis,” Journal of Multivariate Analysis, 50, 238–264.
- Feng, X., and He, X. (2009), “Inference on Low-Rank Data Matrices With Applications to Microarray Data,” Annals of Applied Statistics, 3, 1634–1654.
- Gill, L., and Lewbel, A. (1992), “Testing the Rank and Definiteness of Estimated Matrices With Applications to Factor, State-Space and ARMA Models,” Journal of the American Statistical Association, 87, 766–776.
- Hall, P. (1992), The Bootstrap and Edgeworth Expansion (Springer Series in Statistics), New York: Springer-Verlag.
- Hall, P., and Presnell, B. (1999), “Intentionally Biased Bootstrap Methods,” Journal of the Royal Statistical Society, Series B, 61, 143–158.
- Hall, P., and Wilson, S.R. (1991), “Two Guidelines for Bootstrap Hypothesis Testing,” Biometrics, 47, 757–762.
- Hu, F., and Kalbfleisch, J.D. (2000), “The Estimating Function Bootstrap” (with discussion and rejoinder by the authors), Canadian Journal of Statistics, 28, 449–499.
- Kalivas, J.H. (1997), “Two Data Sets of Near Infrared Spectra,” Chemometrics and Intelligent Laboratory Systems, 37, 255–259.
- Kleibergen, F., and Paap, R. (2006), “Generalized Reduced Rank Tests Using the Singular Value Decomposition,” Journal of Econometrics, 133, 97–126.
- Lee, J.M. (2003), Introduction to Smooth Manifolds (Graduate Texts in Mathematics) (Vol. 218). , ed. V. P. Godambe,New York: Springer-Verlag.
- Lele, S. (1991), “Resampling Using Estimating Equations,” in Estimating functions (Oxford Statistical Science Series) (Vol. 7), New York: Oxford University Press, pp. 295–304.
- Li, B., and 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.
- Li, K.-C. (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.
- Portier, F., and Delyon, B. (2013), “Optimal Transformation: A New Approach for Covering the Central Subspace,” Journal of Multivariate Analysis, 115, 84–107.
- Robin, J.-M., and Smith, R.J. (2000), “Tests of Rank,” Econometric Theory, 16, 151–175.
- van der Vaart, A.W. (1998), Asymptotic Statistics (Cambridge Series in Statistical and Probabilistic Mathematics) (Vol. 3), Cambridge: Cambridge University Press.
- Wellner, J.A., and Zhan, Y. (1996), “Bootstraping z-Estimators,” . Technical Report 308, University of Washington.
- Wood, A. T.A. (1989), “An f Approximation to the Distribution of a Linear Combination of Chi-Squared Variables,” Communications in Statistics—Simulation and Computation, 18, 1439–1456.
- 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.