Functional sliced inverse regression analysis

By Louis Ferré, Anne-Françoise Yao, A. Machado. 2003

175 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/15eb259646731e2fcd1dac6d964d823bf1141339

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. H. Muller
2. Jeng-Min Chiou
3. Yehua Li
4. Jane-ling Wang
5. T. Hsing
6. Tommaso Cai
7. Peter Hall
8. Bing Li

In Control and Systems Engineering

1. H. Muller
2. T. Hsing
3. Bing Li
4. Francesca Chiaromonte
5. Jun Song
6. Haobo Ren
7. Peter Hall
8. Tommaso Cai

In Statistics and Probability

1. H. Muller
2. Yehua Li
3. Jeng-Min Chiou
4. Jane-ling Wang
5. Peter Hall
6. T. Hsing
7. Tommaso Cai
8. Bing Li

Citations in the corpus

• Nonlinear sufficient dimension reduction for functional data (2017, methodology): “In particular, the function-valued predictor and response do not have to be related through linear indices, as assumed by the recently-developed sufficient dimension reduction methods for functional data [Müller and Stadtmüller (2005), Ferré and Yao (2003, 2005), Hsing and Ren (2009)].”
• Functional Data Analysis (2016, methodology): “…which was first proposed for vector covariates as an off-shoot of sliced inverse regression (SIR) (Duan & Li 1991; Li 1991), and has been extended to functional data in Ferr´e & Yao (2003); Ferr´e & Yao (2005); Cook, Forzani & Yao (2010) and to longitudinal data in Jiang, Yu & Wang (2014).”
• Functional Modelling and Classification of Longitudinal Data * (2005, background): “A multitude of interesting combinations are conceivable and open to exploration, including additive regression models, multiple index models and sliced inverse regression (Ferr e & Yao, 2003).”
• Prediction in functional linear regression (2006, methodology): “This work was done while Tony Cai was visiting the Mathematical Sciences Institute of the Australian National University.”
• Smoothed Functional Inverse Regression (2005, methodology): “introduced by Ferré and Yao (2003).”
• DECIDING THE DIMENSION OF EFFECTIVE DIMENSION REDUCTION SPACE FOR FUNCTIONAL AND HIGH-DIMENSIONAL DATA (2010, methodology): “Ferré and Yao (2003, 2005) extended SIR to a functional-data setting, and showed that the EDR space can be consistently estimated under regularity conditions provided that the true dimension of the space is known; see also Forzani and Cook (2007) and Ferré and Yao (2007).”
• A general theory for nonlinear sufficient dimension reduction: Formulation and estimation (2013, methodology): “In this case Definition 1 is a generalization of the linear SDR for functional data introduced by Ferré and Yao (2003), and Hsing and Ren (2009).”
• Functional Modelling and Classification of Longitudinal Data. (2005, background): “Such approaches are discussed in Ferraty & Vieu ( 2004 ) and Rice ( 2004 ) and open up promising avenues for future research in FDA .”
• An RKHS formulation of the inverse regression dimension-reduction problem (2009, methodology): “At first glance, (5) might seem a straightforward extension of similar results for the multivariate case in Li (1991), or the functional case in Ferré and Yao (2003, 2005).”