Communications for Statistical Applications and Methods

  • 제24권3호
  • /
  • Pages.303-315
  • /
  • 2017
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

Intensive numerical studies of optimal sufficient dimension reduction with singularity

  • Yoo, Jae Keun (Department of Statistics, Ewha Womans University) ;
  • Gwak, Da-Hae (Department of Statistics, Ewha Womans University) ;
  • Kim, Min-Sun (Department of Statistics, Ewha Womans University)
  • 투고 : 2017.03.09
  • 심사 : 2017.05.15
  • 발행 : 2017.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Yoo (2015, Statistics and Probability Letters, 99, 109-113) derives theoretical results in an optimal sufficient dimension reduction with singular inner-product matrix. The results are promising, but Yoo (2015) only presents one simulation study. So, an evaluation of its practical usefulness is necessary based on numerical studies. This paper studies the asymptotic behaviors of Yoo (2015) through various simulation models and presents a real data example that focuses on ordinary least squares. Intensive numerical studies show that the $x^2$ test by Yoo (2015) outperforms the existing optimal sufficient dimension reduction method. The basis estimation by the former can be theoretically sub-optimal; however, there are no notable differences from that by the latter. This investigation confirms the practical usefulness of Yoo (2015).

키워드

참고문헌

  1. Chiaromonte F and Martinelli J (2002). Dimension reduction strategies for analyzing global gene expression data with a response, Mathematical Biosciences, 176, 123-144. https://doi.org/10.1016/S0025-5564(01)00106-7
  2. Cook RD (2003). Dimension reduction and graphical exploration in regression including survival analysis, Statistics in Medicine, 22, 1399-1413. https://doi.org/10.1002/sim.1503
  3. Cook RD and Ni L (2005). Sufficient dimension reduction via inverse regression: a minimum discrepancy approach, Journal of the American Statistical Association, 100, 410-428. https://doi.org/10.1198/016214504000001501
  4. Cook RD and Zhang X (2014). Fused estimators of the central subspace in sufficient dimension reduction, Journal of the American Statistical Association, 109, 815-827. https://doi.org/10.1080/01621459.2013.866563
  5. Li L (2006). Survival prediction of diffuse large-B-cell lymphoma based on both clinical and gene expression information, Bioinformatics, 22, 466-471. https://doi.org/10.1093/bioinformatics/bti824
  6. Shapiro A (1986). Asymptotic theory of overparameterized structural models, Journal of the American Statistical Association, 81, 142-149. https://doi.org/10.1080/01621459.1986.10478251
  7. Yoo JK (2009). Iterative optimal sufficient dimension reduction for the conditional mean in multivariate regression, Journal of Data Science, 7, 267-276.
  8. Yoo JK (2015). A theoretical note on optimal sufficient dimension reduction with singularity, Statistics and Probability Letters, 99, 109-113. https://doi.org/10.1016/j.spl.2015.01.004
  9. Yoo JK (2016a). Tutorial: dimension reduction in regression with a notion of sufficiency, Communications for Statistical Applications and Methods, 23, 93-103. https://doi.org/10.5351/CSAM.2016.23.2.093
  10. Yoo JK (2016b). Tutorial: Methodologies for sufficient dimension reduction in regression, Communications for Statistical Applications and Methods, 23, 105-117. https://doi.org/10.5351/CSAM.2016.23.2.105
  11. Yoo JK and Cook RD (2007). Optimal sufficient dimension reduction for the conditional mean in multivariate regression, Biometrika, 94, 231-242. https://doi.org/10.1093/biomet/asm003