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Constrained design strategies for improving normal approximations in nonlinear regression problems

Publication ,  Journal Article
Clyde, M; Chaloner, K
Published in: Journal of Statistical Planning and Inference
May 1, 2002

In nonlinear regression problems, the assumption is usually made that parameter estimates will be approximately normally distributed. The accuracy of the approximation depends on the sample size and also on the intrinsic and parameter-effects curvatures. Based on these curvatures, criteria are defined here that indicate whether or not an experiment will lead to estimates with distributions well approximated by a normal distribution. An approach is motivated of optimizing a primary design criterion subject to satisfying constraints based on these nonnormality measures. The approach can be used either to I) find designs for a fixed sample size or to II) choose the sample size for the optimal design based on the primary objective so that the constraints are satisfied. This later objective is useful as the nonnormality measures decrease with the sample size. As the constraints are typically not concave functions over a set of design measures, the usual equivalence theorems of optimal design theory do not hold for the first approach, and numerical implementation is required. Examples are given, and a new notation using tensor products is introduced to define tractable general notation for the nonnormality measures. © 2002 Elsevier Science B.V. All rights reserved.

Duke Scholars

Published In

Journal of Statistical Planning and Inference

DOI

ISSN

0378-3758

Publication Date

May 1, 2002

Volume

104

Issue

1

Start / End Page

175 / 196

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics
 

Citation

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Clyde, M., & Chaloner, K. (2002). Constrained design strategies for improving normal approximations in nonlinear regression problems. Journal of Statistical Planning and Inference, 104(1), 175–196. https://doi.org/10.1016/S0378-3758(01)00239-7
Clyde, M., and K. Chaloner. “Constrained design strategies for improving normal approximations in nonlinear regression problems.” Journal of Statistical Planning and Inference 104, no. 1 (May 1, 2002): 175–96. https://doi.org/10.1016/S0378-3758(01)00239-7.
Clyde M, Chaloner K. Constrained design strategies for improving normal approximations in nonlinear regression problems. Journal of Statistical Planning and Inference. 2002 May 1;104(1):175–96.
Clyde, M., and K. Chaloner. “Constrained design strategies for improving normal approximations in nonlinear regression problems.” Journal of Statistical Planning and Inference, vol. 104, no. 1, May 2002, pp. 175–96. Scopus, doi:10.1016/S0378-3758(01)00239-7.
Clyde M, Chaloner K. Constrained design strategies for improving normal approximations in nonlinear regression problems. Journal of Statistical Planning and Inference. 2002 May 1;104(1):175–196.
Journal cover image

Published In

Journal of Statistical Planning and Inference

DOI

ISSN

0378-3758

Publication Date

May 1, 2002

Volume

104

Issue

1

Start / End Page

175 / 196

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 0104 Statistics