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• W1574204554 abstract "Dimension reduction for regression analysis has been one of the most popular topics in the past two decades. It sees much progress with the introduction of the inverse regression, centered around the two key methods, sliced inverse regression (SIR) and sliced average variance estimation (SAVE). It is well known that SIR works poorly when the inverse conditional expectation is close to being nonrandom. SAVE and its many generalizations, which do not suffer from this drawback, lag behind SIR in many other circumstances. Usually a certain weighted hybrid of SIR and SAVE is necessary to improve overall performance. However, it is difficult to find the optimal mixture weights in a hybrid, and most such hybrid methods, as well as SAVE, require the restrictive constant (conditional) variance condition. We propose a much weaker condition and a new accompanying algorithm. This enables us to create several new central matrices that perform very favourably to existing central matrix based methods without referring to hybrids. The Canadian Journal of Statistics 41: 421–438; 2013 © 2013 Statistical Society of CanadaResumeLa reduction de la dimension en analyse de regression a ete un sujet de predilection au cours des deux dernieres decennies. D'importants progres ont ete realises grâce a l'introduction de la regression inverse, axee sur les deux methodes principales, soient la regression inverse par tranches (SIR) et l'estimation de la variance moyenne par tranches (SAVE). Il est bien connu que la methode SIR fonctionne mal lorsque l'esperance conditionnelle inverse est presque non aleatoire. La methode SAVE et ses nombreuses generalisations ne presentent pas cet inconvenient, mais elles comportent des lacunes a bien d'autres egards par rapport a SIR. Une methode ponderee hybride de SIR et SAVE est generalement necessaire afin d'ameliorer la performance globale. Cependant, il est difficile d’etablir les poids de melanges optimaux dans une methode hybride, et la plupart de ces hybrides, de meme que SAVE, necessitent une condition restrictive de constance de la variance (conditionnelle). Les auteurs proposent une condition beaucoup moins contraignante et un nouvel algorithme. Cette approche permet de creer de nouvelles matrices centrales qui donnent de tres bons resultats par rapport aux methodes existantes fondees sur les matrices centrales sans toutefois se referer aux methodes hybrides. La revue canadienne de statistique 41: 421–438; 2013 © 2013 Societe statistique du Canada" @default.
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• W1574204554 date "2013-05-23" @default.
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• W1574204554 title "On central matrix based methods in dimension reduction" @default.
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• W1574204554 doi "https://doi.org/10.1002/cjs.11181" @default.
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