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Zhang B, Gramacy RB, Johnson LR, Rose KA, Smith E. Batch-sequential design and heteroskedastic surrogate modeling for delta smelt conservation. Ann Appl Stat 2022. [DOI: 10.1214/21-aoas1521] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | | | | | - Kenneth A. Rose
- University of Maryland Center for Environmental Science, Horn Point Laboratory
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Idais O, Schwabe R. Equivariance and Invariance for Optimal Designs in Generalized Linear Models Exemplified by a Class of Gamma Models. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2021. [DOI: 10.1007/s42519-021-00221-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
AbstractThe main intention of the present work is to outline the concept of equivariance and invariance in the design of experiments for generalized linear models and to demonstrate its usefulness. In contrast with linear models, pairs of transformations have to be employed for generalized linear models. These transformations act simultaneously on the experimental settings and on the location parameters in the linear component. Then, the concept of equivariance provides a tool to transfer locally optimal designs from one experimental region to another when the nominal values of the parameters are changed accordingly. The stronger concept of invariance requires a whole group of equivariant transformations. It can be used to characterize optimal designs which reflect the symmetries resulting from the group actions. The general concepts are illustrated by models with gamma distributed response and a canonical link. There, for a given transformation of the experimental settings, the transformation of the parameters is not unique and may be chosen to be nonlinear in order to fully exploit the model structure. In this case, we can derive invariant maximin efficient designs for the D- and the IMSE-criterion.
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Li Y, Deng X. On Efficient Design of Pilot Experiment for Generalized Linear Models. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2021. [DOI: 10.1007/s42519-021-00222-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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