The simple projection predictor in the general growth curve model

Yuan Quan-long · Fuzhou daxue xuebao. Ziran kexue ban · 2006

Considering the general growth curve model Y=XBZ+e,where E(Vec(e))=0,V(Vec(e))=σ~2ΔΣ,the unknown observation matrix Y_0=X_0BZ_0+e_0 is predicted using the known observation matrix Y.As to optimal predictor,on others' studies,for arbitrary linear predictable variable θ=tr(A′Y_0), its SPP is then defined by (θ)∧_(SPP)=Vec′(A)(Z′_0X_0)[(ZX′)T~-(Z′X)]~-(ZX′)T~-Vec(Y),where T=ΔΣ+(Z′ZXX′).A number of necessary and sufficient conditions where(θ)∧_(SPP) is also the best linear unbiased predictor are obtained,and the robustness of the(θ)∧_(SPP) on the covariance matrix is investigated,and thus the relevant results drawn Bolfarine H et al are widely used.

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