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Sufficient dimension reduction in regressions across heterogeneous subpopulations
Author(s) -
Ni Liqiang,
Dennis Cook R.
Publication year - 2006
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2005.00534.x
Subject(s) - sliced inverse regression , sufficient dimension reduction , mathematics , dimension (graph theory) , partial least squares regression , covariance , inverse , regression , statistics , dimensionality reduction , linear regression , regression analysis , computer science , combinatorics , artificial intelligence , geometry
Summary. Sliced inverse regression is one of the widely used dimension reduction methods. Chiaromonte and co‐workers extended this method to regressions with qualitative predictors and developed a method, partial sliced inverse regression, under the assumption that the covariance matrices of the continuous predictors are constant across the levels of the qualitative predictor. We extend partial sliced inverse regression by removing the restrictive homogeneous covariance condition. This extension, which significantly expands the applicability of the previous methodology, is based on a new estimation method that makes use of a non‐linear least squares objective function.