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|Title:||Dependence and the dimensionality reduction principle||Authors:||Yatracos, Yannis G.||Keywords:||Mathematical models;Parameter estimation;Statistical methods;Problem solving||Issue Date:||2004||Publisher:||Springer Link||Source:||Annals of the Institute of Statistical Mathematics, 2004, Volume 56, Issue 2, Pages 265-277||Abstract:||Stone's dimensionality reduction principle has been confirmed on several occasions for independent observations. When dependence is expressed with φ-mixing, a minimum distance estimate θ̂n is proposed for a smooth projection pursuit regression-type function θ ∈, that is either additive or multiplicative, in the presence of or without interactions. Upper bounds on the L1-risk and the L 1-error of θ̂n are obtained, under restrictions on the order of decay of the mixing coefficient. The bounds show explicitly the additive effect of φ-mixing on the error, and confirm the dimensionality reduction principle.||URI:||http://ktisis.cut.ac.cy/handle/10488/6667||ISSN:||0020-3157 (print)
|DOI:||10.1007/BF02530545||Rights:||© 2004 The Institute of Statistical Mathematics||Type:||Article|
|Appears in Collections:||Άρθρα/Articles|
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