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Information in a two-stage adaptive optimal design.

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Title: Information in a two-stage adaptive optimal design.
Authors: Lane, Adam1 adam.lane@cchmc.org, Yao, Ping2 pyao@niu.edu, Flournoy, Nancy3 flournoyn@missouri.edu
Source: Journal of Statistical Planning & Inference. Jan2014, Vol. 144, p173-187. 15p.
Subjects: Information theory, Optimal designs (Statistics), Adaptive control systems, Maximum likelihood statistics, Cumulative distribution function, Approximation theory
Abstract: Abstract: In adaptive optimal designs, each stage uses a locally optimal design evaluated at the maximum likelihood estimates derived using cumulative data from all prior stages. This dependency on prior stages affects Fisher's information, the asymptotic covariance matrix of the maximum likelihood estimates. Fisher's information is motivated for use in adaptive designs with small samples by deriving the Cramèr–Rao lower bound for such experiments. Then the usefulness of Fisher's information is shown from both a design and an analysis perspective. From a design perspective, the locally optimal stage one sample size is defined in terms of Fisher's information and a procedure to approximate it is suggested. From an analysis perspective, Fisher's information is compared to a commonly used information measure derived by ignoring the stage dependencies and to the observed information. To make the analysis explicit, a two stage design with fixed first stage is examined in the context of a general nonlinear regression model. [Copyright &y& Elsevier]
Copyright of Journal of Statistical Planning & Inference is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 92514059
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Information in a two-stage adaptive optimal design.
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  Data: <searchLink fieldCode="AR" term="%22Lane%2C+Adam%22">Lane, Adam</searchLink><relatesTo>1</relatesTo><i> adam.lane@cchmc.org</i><br /><searchLink fieldCode="AR" term="%22Yao%2C+Ping%22">Yao, Ping</searchLink><relatesTo>2</relatesTo><i> pyao@niu.edu</i><br /><searchLink fieldCode="AR" term="%22Flournoy%2C+Nancy%22">Flournoy, Nancy</searchLink><relatesTo>3</relatesTo><i> flournoyn@missouri.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Statistical+Planning+%26+Inference%22">Journal of Statistical Planning & Inference</searchLink>. Jan2014, Vol. 144, p173-187. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Information+theory%22">Information theory</searchLink><br /><searchLink fieldCode="DE" term="%22Optimal+designs+%28Statistics%29%22">Optimal designs (Statistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Adaptive+control+systems%22">Adaptive control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+likelihood+statistics%22">Maximum likelihood statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Cumulative+distribution+function%22">Cumulative distribution function</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink>
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  Data: Abstract: In adaptive optimal designs, each stage uses a locally optimal design evaluated at the maximum likelihood estimates derived using cumulative data from all prior stages. This dependency on prior stages affects Fisher's information, the asymptotic covariance matrix of the maximum likelihood estimates. Fisher's information is motivated for use in adaptive designs with small samples by deriving the Cramèr–Rao lower bound for such experiments. Then the usefulness of Fisher's information is shown from both a design and an analysis perspective. From a design perspective, the locally optimal stage one sample size is defined in terms of Fisher's information and a procedure to approximate it is suggested. From an analysis perspective, Fisher's information is compared to a commonly used information measure derived by ignoring the stage dependencies and to the observed information. To make the analysis explicit, a two stage design with fixed first stage is examined in the context of a general nonlinear regression model. [Copyright &y& Elsevier]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Statistical Planning & Inference is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jspi.2013.07.010
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      – Code: eng
        Text: English
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        PageCount: 15
        StartPage: 173
    Subjects:
      – SubjectFull: Information theory
        Type: general
      – SubjectFull: Optimal designs (Statistics)
        Type: general
      – SubjectFull: Adaptive control systems
        Type: general
      – SubjectFull: Maximum likelihood statistics
        Type: general
      – SubjectFull: Cumulative distribution function
        Type: general
      – SubjectFull: Approximation theory
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      – TitleFull: Information in a two-stage adaptive optimal design.
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            NameFull: Lane, Adam
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            NameFull: Yao, Ping
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            NameFull: Flournoy, Nancy
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            – D: 01
              M: 01
              Text: Jan2014
              Type: published
              Y: 2014
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              Value: 144
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            – TitleFull: Journal of Statistical Planning & Inference
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