Optimal designs for regression models with autoregressive errors structure
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Date
2016
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Abstract
In the one-parameter regression model with AR(1) and AR(2) errors we find explicit
expressions and a continuous approximation of the optimal discrete design for the signed
least square estimator. The results are used to derive the optimal variance of the best
linear estimator in the continuous time model and to construct efficient estimators and
corresponding optimal designs for finite samples. The resulting procedure (estimator and
design) provides nearly the same efficiency as the weighted least squares and its variance
is close to the optimal variance in the continuous time model. The results are illustrated
by several examples demonstrating the feasibility of our approach.
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Keywords
linear regression, continuous autoregressive model, AR processes, BLUE, optimal design, signed measures, correlated observations