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|Title:||Dependence and the dimensionality reduction principle|
Additive and multiplicative regression model
Minimum distance estimation
Rates of convergence
|Citation:||Yatracos, Y. (2004). Dependence and the dimensionality reduction principle. Annals of the Institute of Statistical Mathematics 56 (2) : 265-277. ScholarBank@NUS Repository.|
|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.|
|Source Title:||Annals of the Institute of Statistical Mathematics|
|Appears in Collections:||Staff Publications|
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