Non-asymptotic confidence estimation of the parameters in stochastic regression models with Gaussian noises. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Konev, Victor V.; Vorobeychikov, Sergey E.
• Is Part Of: Sequential analysis. Volume 36:Issue 1(2017)
• Page Start: 55
• Page End: 75
• Publication Date: 2017-01-02
• Subjects: Autoregressive models -- confidence estimation -- non-asymptotic distribution -- prescribed coverage probability -- regression with Gaussian noises -- sequential interval estimators -- threshold first-order autoregression; 60G40 -- 62F25 -- 62J05 -- 62L12; Sequential analysis -- Periodicals; 519.54
• DOI: 10.1080/07474946.2016.1275421
• Languages: English
• ISSNs: 0747-4946

Abstract

ABSTRACT: The article considers the problem of estimating linear parameters in stochastic regression models with Gaussian noises, such as an autoregression of the first order, threshold autoregression, and some others. We propose the non-asymptotic technique for constructing a fixed-size confidence region for unknown parameters with any prescribed coverage probability. The construction makes use of some new properties of the sequential point estimates known in the literature. The results of Monte Carlo simulations for AR(1) and TAR(1) models are given. A new version of the sequential point estimate is proposed.