Limit distribution of the least square estimator with observations sampled at random times driven by standard Brownian motion. Issue 11 (3rd June 2023)

• Record Type: Journal Article
• Authors: Roa, Tania; Torres, Soledad; Tudor, Ciprian
• Is Part Of: Communications in statistics. Volume 52:Issue 11(2023)
• Page Start: 3730
• Page End: 3750
• Publication Date: 2023-06-03
• Subjects: Least squares estimator -- random times -- regression model -- asymptotic normality; 60G22 -- 62J86 -- 62M09; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2021.1980044
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this article, we study the limit distribution of the least square estimator, properly normalized, from a regression model in which observations are assumed to be finite ( αN ) and sampled under two different random times. Based on the limit behavior of the characteristic function and convergence result we prove the asymptotic normality for the least square estimator. We present simulations results to illustrate our theoretical results.