Dimension Reduction for Multivariate Response Data

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Inner envelopes: Efficient estimation in multivariate linear regression (2012, methodology): “Following Li et al. (2003), we took the monthly measurements of precipitation or temperature as responses, and the longitude, latitude of the stations and year as predictors, giving r = 12 and p = 3.”
ENVELOPE MODELS FOR PARSIMONIOUS AND EFFICIENT MULTIVARIATE LINEAR REGRESSION (2010, background): “Many of these, ranging from various versions of principal components to a multivariate implementation of sliced inverse regression (Li et al. (2003)) are algorithmic in nature, making it difficult to determine postapplication standard errors and other inference-related quantities.”
Estimation for a partial-linear single-index model (2009, methodology): “When the dimension q of Z is greater than 1, a multivariate extension of SIR [Li et al. (2003)] can be employed conceptually in Step 1 of the algorithm.”
On a Projective Resampling Method for Dimension Reduction With Multivariate Responses (2008, methodology): “For MS, we use the slicing scheme proposed by Li et al. (2003): The first slicing is made on the first variable, yielding h slices of equal length, each of which is then further sliced into h subslices according to the second variable, and so on.”
Asymptotics for pooled marginal slicing estimator based on SIRα approach (2005, methodology): “[17] andAragon [1] considered several estimation methods in this multivariate context.”