The paper considers the estimation problem of the autoregressive parameter in the first-order autoregressive process with Gaussian noises when the noise variance is un-known. We propose a non-asymptotic technique to compensate the unknown variance, and then, to construct a point estimator with any prescribed mean square accuracy. Also a fixed-width confidence interval with any prescribed coverage accuracy is proposed. The results of Monte-Carlo simulations are given.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics