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NON‐PARAMETRIC ESTIMATION OF DIRECTION IN SINGLE‐INDEX MODELS WITH CATEGORICAL PREDICTORS
Author(s) -
Yin Xiangrong
Publication year - 2005
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2005.00380.x
Subject(s) - sliced inverse regression , mathematics , sufficient dimension reduction , categorical variable , dimension (graph theory) , subspace topology , index (typography) , dimensionality reduction , inverse , parametric statistics , single index model , statistics , regression , econometrics , artificial intelligence , computer science , mathematical analysis , combinatorics , geometry , world wide web
Summary This paper proposes a general dimension‐reduction method targeting the partial central subspace recently introduced by Chiaromonte, Cook & Li. The dependence need not be confined to particular conditional moments, nor are restrictions placed on the predictors that are necessary for methods like partial sliced inverse regression. The paper focuses on a partially linear single‐index model. However, the underlying idea is applicable more generally. Illustrative examples are presented.