In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced observations and the residuals under which the estimator is strongly consistent. In particular, we consider observation instances that are negatively superadditive dependent within each other, while for the residuals we merely assume that they are generated by some continuous function. In addition, we prove that the rate of convergence is proportional to the sampling rate $N$, and we complement our findings with a simulation study providing insights on finite sample properties.
翻译:在本文中,我们在随机观测实例的基础上,研究线性回归模型中最平方估计者的无症状行为;对随机间距观测的时间和依赖结构以及估计者非常一致的残留物提供温和的假设;特别是,我们考虑相互之间有负超常依赖性的观测情况,而对于剩余物,我们仅仅假设它们是由某种连续功能产生的。此外,我们证明,汇合率与抽样率成比例,我们用模拟研究来补充我们的调查结果,就有限的抽样特性提供洞察力。