This dissertation, "On Sliced Methods in Dimension Reduction" by Yingxing, Li, 李迎星, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author.
Abstract:
Abstract of thesis entitled \ON SLICED METHODS IN DIMENSION REDUCTION" submitted by LI Yingxing for the Degree of Master of Philosophy at The University of Hong Kong in August 2005 Due to the problem of data sparseness in predictor space caused by high di- mensional covariates, dimension reduction becomes more and more important in regression analysis. Among all dimension reduction methods, two new methods are promising: Sliced Inverse Regression (SIR) and Sliced Average Variance Es- timation (SAVE). By using the inverse regression, they can nd out a few linear combinations of the components of the covariates so that the dimension of the covariates is reduced while all the information is still captured to predict the response. In this study, the pros and cons of both these two methods were inves- tigated. TomaintaintheadvantagesofboththeSIRandtheSAVE, somehybrid methods were proposed. The performance of the hybrid methods was examined through simulations. Furthermore, to assess the usefulness of the sliced methods, the asymptotic behavior of the SAVE was systematically examined. The ndings show that though the SAVE and the SIR are both based on slicing estimations, theirpropertiesaretotallydi(R)erent. TheSAVEislessrobustagainstthenumber of data in every slice. Moreover, if the response is continuous, the SAVE is notroot n consistent and is even not convergent if the number of data in each slice is independent of n, where n is the sample size. Taking this into account, a bias corrected SAVE is recommended, which can achieve the root n consistency and asymptotic normality.
DOI: 10.5353/th_b3155925
Subjects:
Data reduction
Regression analysis