Optimal designs for comparing several regression curves

This article is concerned with the optimal design problem of efficient statistical inference for comparing several regression curves estimated from samples of independent measurements. The objective is to find the mu pc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu <^>c_{p}$$\end{document}-optimal designs that minimize an Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_p$$\end{document}-norm of the asymptotic variance of the prediction for the contrasts of k regression curves. General equivalence theorems are established to verify the mu pc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu <^>c_p$$\end{document}-optimality in the set of all approximate designs. Invariant property with respect to model reparameterization are also obtained. The results obtained for the linear models are extended to the situation of generalized linear models. Three examples are presented to illustrate the applications of the obtained results.