Optimal designs for regression models with autoregressive errors structure
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.
Cite
@article{arxiv.1602.03794,
title = {Optimal designs for regression models with autoregressive errors structure},
author = {Holger Dette and Andrey Pepelyshev and Anatoly Zhigljavsky},
journal= {arXiv preprint arXiv:1602.03794},
year = {2016}
}
Comments
Keywords and Phrases: linear regression; correlated observatio ns; signed measures; optimal design; BLUE; AR processes; continuous autoregressive model AMS Subject classification: Primary 62K05; Secondary 31A10