Browse > Article
http://dx.doi.org/10.5351/CKSS.2012.19.1.107

Effect of Dimension in Optimal Dimension Reduction Estimation for Conditional Mean Multivariate Regression  

Seo, Eun-Kyoung (Department of Education, Sungkyunkwan University)
Park, Chong-Sun (Department of Statistics, Sungkyunkwan University)
Publication Information
Communications for Statistical Applications and Methods / v.19, no.1, 2012 , pp. 107-115 More about this Journal
Abstract
Yoo and Cook (2007) developed an optimal sufficient dimension reduction methodology for the conditional mean in multivariate regression and it is known that their method is asymptotically optimal and its test statistic has a chi-squared distribution asymptotically under the null hypothesis. To check the effect of dimension used in estimation on regression coefficients and the explanatory power of the conditional mean model in multivariate regression, we applied their method to several simulated data sets with various dimensions. A small simulation study showed that it is quite helpful to search for an appropriate dimension for a given data set if we use the asymptotic test for the dimension as well as results from the estimation with several dimensions simultaneously.
Keywords
Multivariate regression; conditional mean model; optimal dimension reduction;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Cook, R. D. and Nachtsheim, C. J. (1994). Reweighting to achieve Elliptically Contoured Covariates in Regression, Journal of the American Statistical Association, 89, 592-600.   DOI   ScienceOn
2 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.   DOI   ScienceOn
3 Cook, R. D. and Setodji, C. M. (2003). A model-free test for reduced rank in multivariate regression, Journal of the American Statistical Association, 98, 340-351.   DOI   ScienceOn
4 Ferguson, T. (1958). A method of generating best asymptotically normal estimates with application to the estimation of bacterial densities, Annals of Mathematical Statistic, 29, 1046-1062.   DOI   ScienceOn
5 Li, K. C. (1991). Sliced inverse regression for dimension reduction, Journal of the American Statistical Association, 86, 316-342.   DOI   ScienceOn
6 Rao, C. R. (1965). Linear Statistical Inference and Its Application, Wiley, New York.
7 Shapiro, A. (1986). Asymptotic theory of overparameterized structural models, Journal of the American Statistical Association, 81, 142-149.   DOI   ScienceOn
8 Yoo, J. K. and Cook, R. D. (2007). Optimal sufficient dimension reduction for the conditional mean in multivariate regression, Biometrika, 94, 231-242.   DOI   ScienceOn
9 Cook, R. D. and Li, B. (2002). Dimension reduction for the conditional mean, Annals of Statistics, 30, 455-474.   DOI   ScienceOn