Abstract
Recent sufficient dimension reduction methodologies in multivariate regression do not have direct application to a categorical predictor. For this, we define the multivariate central partial mean subspace and propose two methodologies to estimate it. The first method uses the ordinary least squares. Chi-squared distributed statistics for dimension tests are constructed, and an estimate of the target subspace is consistent and efficient. Moreover, the effects of continuous predictors can be tested without assuming any model. The second method extends Iterative Hessian Transformation to this context. For dimension estimation, permutation tests are used. Simulated and real data examples for illustrating various properties of the proposed methods are presented.
Original language | English |
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Pages (from-to) | 1825-1839 |
Number of pages | 15 |
Journal | Journal of Multivariate Analysis |
Volume | 99 |
Issue number | 8 |
DOIs | |
State | Published - Sep 2008 |
Keywords
- 62G08
- 62H05
- Categorical predictor
- Conditional mean
- Multivariate regression
- Partial dimension reduction
- Predictor effect test