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D-optimal design for the heteroscedastic Berman model on an arc

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  • Liu, Xin
  • Yue, Rong-Xian
  • Wong, Weng Kee

Abstract

There are various methods for fitting data to circles or ellipses in many different types of applied problems. However, the design of such studies is rarely discussed and for the few that do, model errors are commonly assumed to be homoscedastic and uncorrelated. This paper provides an analytic description of the D-optimal designs for estimating parameters in the bivariate Berman model on an arc when errors are correlated and heteroscedastic. We evaluate D-efficiencies and relative efficiencies of the commonly used equidistant sampling methods and show that such designs can be inefficient.

Suggested Citation

  • Liu, Xin & Yue, Rong-Xian & Wong, Weng Kee, 2018. "D-optimal design for the heteroscedastic Berman model on an arc," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 131-141.
    • Handle: RePEc:eee:jmvana:v:168:y:2018:i:c:p:131-141
    DOI: 10.1016/j.jmva.2018.07.003
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    References listed on IDEAS

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    1. Mark Berman, 1983. "Estimating the Parameters of a Circle When Angular Differences are Known," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(1), pages 1-6, March.
    2. Chernov, N. & Sapirstein, P.N., 2008. "Fitting circles to data with correlated noise," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5328-5337, August.
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