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 ($\alpha N$) 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 simulation results to illustrate our theoretical results.