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Extrapolation designs with constraints
Author(s) -
Fang Zhide
Publication year - 2003
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315856
Subject(s) - extrapolation , bounding overwatch , mathematics , norm (philosophy) , minimax , variance (accounting) , mathematical optimization , mean squared error , space (punctuation) , statistics , computer science , artificial intelligence , accounting , political science , law , business , operating system
The author considers (asymptotically) minimax extrapolation designs for an approximately multiple linear model with the model contaminant f being restricted only by its L 2 norm. He splits the integrated mean squared prediction error (IMSPE) of the fitted value over the extrapolation space into two parts, namely the integrated prediction variance (IPV) and the integrated prediction bias (IPB). For a spherical design space and an annular extrapolation space, he constructs the design that minimizes the maximum value, over f, of IPB subject to bounding IPV. He also constructs the design that minimizes IPV subject to bounding the maximum IPB.