Limit distribution of the least square estimator with observations sampled at random times driven by standard Brownian motion

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.

Keywords:

• Least squares estimator
• random times
• regression model
• asymptotic normality

2010 AMS Classification Numbers:

• 60G22
• 62J86
• 62M09

Additional information

Funding

This research was partially supported by Project REDES 150038, MATHAMSUD 19-MATH-06, Math AmSud 18-MATH-07 SaSMoTiDep, CONICYT - MATHAMSUD FANTASTIC 20-MATH-05. T. Roa was partially supported by Beca CONICYT-PFCHA/Doctorado Nacional/2018-21180298, S. Torres was partially supported by FONDECYT 1171335 and C. Tudor was partially supported by MEC PAI80160046.