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Freise F, Gaffke N, Schwabe R. The adaptive Wynn algorithm in generalized linear models with univariate response. Ann Stat 2021. [DOI: 10.1214/20-aos1974] [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)
- Fritjof Freise
- Department of Biometry, Epidemiology and Information Processing, University of Veterinary Medicine Hannover
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A Bayesian stochastic approximation method. J Stat Plan Inference 2021. [DOI: 10.1016/j.jspi.2020.07.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Convergence of least squares estimators in the adaptive Wynn algorithm for some classes of nonlinear regression models. METRIKA 2021. [DOI: 10.1007/s00184-020-00803-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Abstract
AbstractThe paper continues the authors’ work (Freise et al. The adaptive Wynn-algorithm in generalized linear models with univariate response. arXiv:1907.02708, 2019) on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper the asymptotics of adaptive least squares estimators under the adaptive Wynn algorithm is studied. Strong consistency and asymptotic normality are derived for two classes of nonlinear models: firstly, for the class of models satisfying a condition of ‘saturated identifiability’, which was introduced by Pronzato (Metrika 71:219–238, 2010); secondly, a class of generalized linear models. Further essential assumptions are compactness of the experimental region and of the parameter space together with some natural continuity assumptions. For asymptotic normality some further smoothness assumptions and asymptotic homoscedasticity of random errors are needed and the true parameter point is required to be an interior point of the parameter space.
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Affiliation(s)
- I-Chen Lee
- Department of Statistics, National Cheng Kung University, Tainan, Taiwan
| | - Yili Hong
- Department of Statistics, Virginia Tech, Blacksburg, VA
| | | | - Tirthankar Dasgupta
- Department of Statistics and Biostatistics, Rutgers University, Piscataway, NJ
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Hering P, Šimandl M. Sequential optimal experiment design for neural networks using multiple linearization. Neurocomputing 2010. [DOI: 10.1016/j.neucom.2010.04.004] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Guest T, Curtis A. Iteratively constructive sequential design of experiments and surveys with nonlinear parameter‐data relationships. ACTA ACUST UNITED AC 2009. [DOI: 10.1029/2008jb005948] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Chu PL, Lin Y, Shih WJ. Unifying CRM and EWOC designs for phase I cancer clinical trials. J Stat Plan Inference 2009. [DOI: 10.1016/j.jspi.2008.07.005] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Simulation-based designs for multiperiod control. Comput Stat Data Anal 2007. [DOI: 10.1016/j.csda.2007.04.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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