Properties of optimal regression designs under the second-order least squares estimator

Chi-Kuang Yeh and Julie Zhou ()
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Chi-Kuang Yeh: University of Victoria
Julie Zhou: University of Victoria

Statistical Papers, 2021, vol. 62, issue 1, No 5, 75-92

Abstract: Abstract We investigate properties of optimal designs under the second-order least squares estimator (SLSE) for linear and nonlinear regression models. First we derive equivalence theorems for optimal designs under the SLSE. We then obtain the number of support points in A-, c- and D-optimal designs analytically for several models. Using a generalized scale invariance concept we also study the scale invariance property of D-optimal designs. In addition, numerical algorithms are discussed for finding optimal designs. The results are quite general and can be applied for various linear and nonlinear models. Several applications are presented, including results for fractional polynomial, spline regression and trigonometric regression models.

Keywords: A-optimal design; Convex optimization; D-optimal design; Fractional polynomial; Generalized scale invariance; Peleg model; Spline regression; Number of support points; 62K05; 62K20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-018-01076-6

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