Principal fitted components for dimension reduction in regression
By R. Dennis Cook, Liliana Forzani. 2008
131 citations recorded by the source corpus.
We provide a remedy for two concerns that have dogged the use of principal components in regression: (i) principal components are computed from the predictors alone and do not make apparent use of the response, and (ii) principal components are not invariant or equivariant under full rank linear transformation of the predictors. The development begins with principal fitted components (Cook, 2007) and uses normal models for the inverse regression of the predictors on the response to gain reductive information for the forward regression of interest. This approach includes methodology for testing hypotheses about the number of components and about conditional independencies among
Subfields: Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/efb2a2d6dfc543812feaa0aa9271cfd9786d0758
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In Statistics and Probability
Citations in the corpus
- Gradient-based kernel method for feature extraction and variable selection (2012, methodology): “This is achieved by imposing the sparseness penalty of the group LASSO [29] in combination with an objective function of linear feature extraction written in the form of eigenproblem such as SIR and PFC [3].”
- Variable Selection in Predictive Regressions (2013, methodology): “See, for example, Li (1991) for sliced inverse regressions and the model based approach of Cook and Forzani (2008).”
- Fused Estimators of the Central Subspace in Sufficient Dimension Reduction (2014, methodology): “From Cook and Forzani (2008), we know that for this setting SY”
- Inner envelopes: Efficient estimation in multivariate linear regression (2012, background): “By a result of Cook & Forzani (2008), and with 0 replaced by its estimator ̂0, the estimator of the coefficients in this reduced rank regression has the form P B̂(̂ −1 0 ) ̂T0β̂sm.”