Examinando por Autor "Roa, Tania"

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  • Miniatura
    Ítem
    On the consistency of least squares estimator in models sampled at random times driven by long memory noise: the Jittered case.
    (Institute Of Statistical Science, Academia Sinica, 2023) Araya, Héctor; Bahamonde, Natalia; Fermín, Lisandro Javier; Roa, Tania; Torres, Soledad
    In numerous applications, data are observed at random times. Our main purpose is to study a model observed at random times that incorporates a long-memory noise process with a fractional Brownian Hurst exponent H. We propose a least squares estimator in a linear regression model with long-memory noise and a random sampling time called “jittered sampling”. Specifically, there is a fixed sampling rate 1/N, contaminated by an additive noise (the jitter) and governed by a probability density function supported in [0, 1/N]. The strong consistency of the estimator is established, with a convergence rate depending on N and the Hurst exponent. A Monte Carlo analysis supports the relevance of the theory and produces additional insights, with several levels of long-range dependence (varying the Hurst index) and two different jitter densities.
  • Miniatura
    Ítem
    On the consistency of the least squares estimator in models sampled at random times driven by long memory noise: the renewal case.
    (Institute Of Statistical Science, Academia Sinica, 2023) Araya, Héctor; Bahamonde, Natalia; Fermín, Lisandro Javier; Roa, Tania; Torres, Soledad
    In 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.