A sequential design for estimating a nonlinear parametric function

A fully-sequential design for estimating a nonlinear function of the parameters in the simple linear regression model is proposed and its asymptotic behavior is investigated both theoretically and by simulation. The design requires that the observations be taken at x=±1 and specifies whether the nex...

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Vydané v:Applied mathematics and computation Ročník 138; číslo 1; s. 113 - 120
Hlavní autori: Rekab, Kamel, Tahir, Mohamed
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY Elsevier Inc 01.06.2003
Elsevier
Predmet:
Asymptotically optimal fixed design
Exact sciences and technology
Experimental design
Fisher information matrix
Fully-sequential design
Least squares estimator
Linear inference, regression
Mathematics
Probability and statistics
Sciences and techniques of general use
Second order approximation
Simple linear regression model
Statistics
Least squares estimator
Second order approximation
Simple linear regression model
Fully-sequential design
Asymptotically optimal fixed design
Fisher information matrix
Parameter estimation
Sequential design
Linear regression
Asymptotic behavior
Non linear function
Asymptotic optimality
Probability distribution
Linear model
Fisher information
Simulation
Regression model
Least squares method
Experimental design
Asymptotic approximation
Optimal design(statistics)
ISSN:0096-3003, 1873-5649
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Abstract A fully-sequential design for estimating a nonlinear function of the parameters in the simple linear regression model is proposed and its asymptotic behavior is investigated both theoretically and by simulation. The design requires that the observations be taken at x=±1 and specifies whether the next observation is to be taken at x=−1 or 1. It is shown that, under this design, the mean number of observations taken at x=1, m k , converges with probability one to an optimal value as k→∞, where k denotes the total number of design points. The simulation study indicates that m k converges in L 2 to the optimal value with the order of O( k −2).
AbstractList A fully-sequential design for estimating a nonlinear function of the parameters in the simple linear regression model is proposed and its asymptotic behavior is investigated both theoretically and by simulation. The design requires that the observations be taken at x=±1 and specifies whether the next observation is to be taken at x=−1 or 1. It is shown that, under this design, the mean number of observations taken at x=1, m k , converges with probability one to an optimal value as k→∞, where k denotes the total number of design points. The simulation study indicates that m k converges in L 2 to the optimal value with the order of O( k −2).
Author Rekab, Kamel
Tahir, Mohamed
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Issue 1
Keywords Least squares estimator
Second order approximation
Simple linear regression model
Fully-sequential design
Asymptotically optimal fixed design
Fisher information matrix
Parameter estimation
Sequential design
Linear regression
Asymptotic behavior
Non linear function
Asymptotic optimality
Probability distribution
Linear model
Fisher information
Simulation
Regression model
Least squares method
Experimental design
Asymptotic approximation
Optimal design(statistics)
Language English
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Ford, Titterington, Kitsos (BIB3) 1989; 31
Chaudhuri, Mykland (BIB1) 1993; 88
Ford (10.1016/S0096-3003(02)00113-3_BIB3) 1989; 31
Chaudhuri (10.1016/S0096-3003(02)00113-3_BIB1) 1993; 88
Ford (10.1016/S0096-3003(02)00113-3_BIB2) 1980; 67
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– volume: 67
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  ident: BIB2
  article-title: A sequentially constructed design for estimating a nonlinear parametric function
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  article-title: Nonlinear experiments: optimal design and inference based on likelihood
  publication-title: Journal of the American Statistical Association
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  article-title: A sequentially constructed design for estimating a nonlinear parametric function
  publication-title: Biometrika
  doi: 10.1093/biomet/67.2.381
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SubjectTerms Asymptotically optimal fixed design
Exact sciences and technology
Experimental design
Fisher information matrix
Fully-sequential design
Least squares estimator
Linear inference, regression
Mathematics
Probability and statistics
Sciences and techniques of general use
Second order approximation
Simple linear regression model
Statistics
Title A sequential design for estimating a nonlinear parametric function
URI https://dx.doi.org/10.1016/S0096-3003(02)00113-3
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