TY - JOUR
T1 - On directional regression for dimension reduction
AU - Li, Bing
AU - Wang, Shaoli
N1 - Funding Information:
Bing Li is Professor, Department of Statistics, Pennsylvania State University, University Park, PA 16802 (E-mail: [email protected]). Shaoli Wang is Postdoctoral Researcher, Department of Epidemiology and Public Health, Yale University School of Medicine, New Haven, CT 06520. This work was supported in part by National Science Foundation grants DMS-0204662 and DMS-0405681. The authors thank two anonymous referees, an associate editor, and the joint editors for their many useful suggestions that helped us improve both the presentation and the substance of this article.
PY - 2007/9
Y1 - 2007/9
N2 - We introduce directional regression (DR) as a method for dimension reduction. Like contour regression, DR is derived from empirical directions, but achieves higher accuracy and requires substantially less computation. DR naturally synthesizes the dimension reduction estimators based on conditional moments, such as sliced inverse regression and sliced average variance estimation, and in doing so combines the advantages of these methods. Under mild conditions, it provides exhaustive and √n-consistent estimate of the dimension reduction space. We develop the asymptotic distribution of the DR estimator, and from that a sequential test procedure to determine the dimension of the central space. We compare the performance of DR with that of existing methods by simulation and find strong evidence of its advantage over a wide range of models, Finally, we apply DR to analyze a data set concerning the identification of hand-written digits.
AB - We introduce directional regression (DR) as a method for dimension reduction. Like contour regression, DR is derived from empirical directions, but achieves higher accuracy and requires substantially less computation. DR naturally synthesizes the dimension reduction estimators based on conditional moments, such as sliced inverse regression and sliced average variance estimation, and in doing so combines the advantages of these methods. Under mild conditions, it provides exhaustive and √n-consistent estimate of the dimension reduction space. We develop the asymptotic distribution of the DR estimator, and from that a sequential test procedure to determine the dimension of the central space. We compare the performance of DR with that of existing methods by simulation and find strong evidence of its advantage over a wide range of models, Finally, we apply DR to analyze a data set concerning the identification of hand-written digits.
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U2 - 10.1198/016214507000000536
DO - 10.1198/016214507000000536
M3 - Article
AN - SCOPUS:35348849313
SN - 0162-1459
VL - 102
SP - 997
EP - 1008
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 479
ER -