Parameter estimation for random sampled Regression Model with Long Memory Noise

2019/02/22 by Héctor Araya, Araya, Héctor, Natalia Bahamonde +7
Decision Sciences · Engineering · Mathematics · #60G22 #62J86 #62M09 #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Methodology (stat.ME) #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST) #math.ST #msc:60G22 #msc:62J86 #msc:62M09 #stat.ME #stat.TH

paper · pdf · doi:10.48550/arxiv.1902.08590

19 pages, 4 figures

arxiv created 2019/02/22 · openalex publication_date 2019/02/22 · arxiv updated 2019/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we present the least squares estimator for the drift parameter in a linear regression model driven by the increment of a fractional Brownian motion sampled at random times. For two different random times, Jittered and renewal process sampling, consistency of the estimator is proven. A simulation study is provided to illustrate the performance of the estimator under different values of the Hurst parameter H.

Citations

• Fractional Brownian Motions, Fractional Noises and Applications

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