Araya, HéctorBahamonde, NataliaFermín, Lisandro JavierRoa, TaniaTorres, Soledad2022-11-302022-11-302023http://repositoriobibliotecas.uv.cl/handle/uvscl/7223In this article, we prove the strong consistency of the least squares estimator in a random sampled linear regression model with long memory noise and an independent set of random times given by renewal process sampling. Additionally, we illustrate how to work with a random number of observations up to the time T = 1. A simulation study is provided to illustrate the behavior of the different terms involved and the performance of the estimator under different values of the Hurst parameter H.LONG-MEMORY NOISELEAST SQUARES ESTIMATORRANDOM TIMESRENEWAL MODELArticulo10.5705/ss.202020.0457