Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Robust second-order rotatable designs invariably applicable for some lifetime distributions

  • Kim, Jinseog (Department of Big data and Applied Statistics, Dongguk University) ;
  • Das, Rabindra Nath (Department of Statistics, The University of Burdwan) ;
  • Singh, Poonam (Department of Statistics, University of Delhi) ;
  • Lee, Youngjo (Seoul National University and Dankook University)
  • Received : 2021.03.21
  • Accepted : 2021.09.10
  • Published : 2021.11.30
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Abstract

Recently a few articles have derived robust first-order rotatable and D-optimal designs for the lifetime response having distributions gamma, lognormal, Weibull, exponential assuming errors that are correlated with different correlation structures such as autocorrelated, intra-class, inter-class, tri-diagonal, compound symmetry. Practically, a first-order model is an adequate approximation to the true surface in a small region of the explanatory variables. A second-order model is always appropriate for an unknown region, or if there is any curvature in the system. The current article aims to extend the ideas of these articles for second-order models. Invariant (free of the above four distributions) robust (free of correlation parameter values) second-order rotatable designs have been derived for the intra-class and inter-class correlated error structures. Second-order rotatability conditions have been derived herein assuming the response follows non-normal distribution (any one of the above four distributions) and errors have a general correlated error structure. These conditions are further simplified under intra-class and inter-class correlated error structures, and second-order rotatable designs are developed under these two structures for the response having anyone of the above four distributions. It is derived herein that robust second-order rotatable designs depend on the respective error variance covariance structure but they are independent of the correlation parameter values, as well as the considered four response lifetime distributions.

Keywords

Acknowledgement

The authors are very much indebted to the referees who have provided valuable comments to improve this paper. The work of Youngjo Lee was supported by a grant from the National Research Foundation of Korea (NRF) that was funded by the Korea government (MSIT) (No 2019R1A2C1002408).

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