Locally optimal designs for comparing curves in generalized linear models

Chang-Yu Liu, Xin Liu and Rong-Xian Yue ()
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Chang-Yu Liu: Shanghai Normal University
Xin Liu: Donghua University
Rong-Xian Yue: Shanghai Normal University

Statistical Papers, 2024, vol. 65, issue 5, No 21, 3201 pages

Abstract: Abstract This article is concerned with the optimal design problem of efficient statistical inference for comparing regression mean curves in two generalized linear models (GLMs) estimated from two samples of independent measurements. The main objective is to find the locally $$\mu _p$$ μ p -optimal designs for given values of the model parameters that minimize an $$L_p$$ L p -norm of the asymptotic variance of the difference between the two estimated regression curves. Two equivalence theorems are given to verify the locally $$\mu _p$$ μ p -optimality of the designs in the set of all approximate designs for the comparison of regression curves in two GLMs. Several numerical examples are presented to illustrate the superiorities of the locally $$\mu _p$$ μ p -optimal designs ( $$p=1,\infty $$ p = 1 , ∞ ) by comparing them with equidistant designs and individual D-optimal designs for the comparison of regression curves in different scenarios.

Keywords: Generalized linear model; Logistic model; Poisson model; Comparison of curves; Optimal design; Equivalence theorem; 62K05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01514-0

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