Likelihood-Based Sufficient Dimension Reduction

By R. Dennis Cook, Liliana Forzani, Bing Li. 2009

169 citations recorded by the source corpus.

We obtain the maximum likelihood estimator of the central subspace under conditional normality of the predictors given the response. Analytically and in simulations we found that our new estimator can preform much better than sliced inverse regression, sliced average variance estimation and directional regression, and that it seems quite robust to deviations from normality.

Subfields: Control and Systems Engineering, Statistics and Probability

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Citations in the corpus

Supervised Dimensionality Reduction via Distance Correlation Maximization (2016, methodology): “…28.16 27.39 27.24 27.18 gKDR [Fukumizu and Leng, 2014] 29.72 27.62 27.29 26.91 26.81 SCA [Yamada et al., 2011] 28.53 27.31 26.60 26.32 26.30 LAD [Cook and Forzani, 2009] 30.42 30.39 30.20 30.04 29.99 SAVE [Shao et al., 2009] 31.93 31.27 30.72 30.53 30.31 SIR [Li, 1991] 33.63 32.65 31.39 31.16…”
Principal fitted components for dimension reduction in regression (2008, background): “Investigations into extensions that address these limitations are in progress (Cook and Forzani, 2009).”
Sufficient Dimension Reduction via Distance Covariance (2016, methodology): “Furthermore, we compare our method DCOV with four competitors: SIR, SAVE, PHD, and LAD.”
Fused Estimators of the Central Subspace in Sufficient Dimension Reduction (2014, methodology): “A good choice of slicing scheme may become more crucial in second-order methods such as SAVE (Cook and Weisberg 1991), DR (Li and Wang 2007), and LAD (Cook and Forzani 2009).”
ldr: An R Software Package for Likelihood-Based Su?cient Dimension Reduction (2014, methodology): “Likelihood-based sufficient dimension reduction We describe the following three sufficient dimension reduction methods: covariance reduction (Cook and Forzani 2008a), likelihood acquired directions (Cook and Forzani 2009), and principal fitted components (Cook 2007; Cook and Forzani 2008b).”
Model checking for parametric single‐index models: a dimension reduction model‐adaptive approach (2016, background): “…(SAVE) (Cook and Weisberg, 1991), contour regression (Li et al., 2005), directional regression (Li and Wang, 2007), likelihood acquired directions (Cook and Forzani, 2009), discretization–expectation estimation (DEE) (Zhu et al., 2010a) and average partial mean estimation (Zhu et al., 2010b).”