ON THE CONSISTENCY OF THE LEAST SQUARES ESTIMATOR IN MODELS SAMPLED AT RANDOM TIMES DRIVEN BY LONG MEMORY NOISE: THE RENEWAL CASE

Héctor Araya; Natalia Bahamonde; Lisandro Fermín; Tania Roa; Soledad Torres

doi:10.5705/ss.202020.0457

ON THE CONSISTENCY OF THE LEAST SQUARES ESTIMATOR IN MODELS SAMPLED AT RANDOM TIMES DRIVEN BY LONG MEMORY NOISE: THE RENEWAL CASE

Héctor Araya, Natalia Bahamonde, Lisandro Fermín, Tania Roa, Soledad Torres

Research output: Contribution to journal › Article › peer-review

Abstract

In this study, 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 time T = 1. A simulation study is provided to illustrate the behavior of the different terms, as well as the performance of the estimator under various values of the Hurst parameter H.

Original language	English
Pages (from-to)	1-26
Number of pages	26
Journal	Statistica Sinica
Volume	33
Issue number	1
DOIs	https://doi.org/10.5705/ss.202020.0457
State	Published - Jan 2023
Externally published	Yes

Keywords

Least squares estimator
long-memory noise
random times
regression model
renewal process

Access to Document

10.5705/ss.202020.0457

Cite this

@article{b54735f94761464a86f5d3a5a07e1905,

title = "ON THE CONSISTENCY OF THE LEAST SQUARES ESTIMATOR IN MODELS SAMPLED AT RANDOM TIMES DRIVEN BY LONG MEMORY NOISE: THE RENEWAL CASE",

abstract = "In this study, 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 time T = 1. A simulation study is provided to illustrate the behavior of the different terms, as well as the performance of the estimator under various values of the Hurst parameter H.",

keywords = "Least squares estimator, long-memory noise, random times, regression model, renewal process",

author = "H{\'e}ctor Araya and Natalia Bahamonde and Lisandro Ferm{\'i}n and Tania Roa and Soledad Torres",

year = "2023",

month = jan,

doi = "10.5705/ss.202020.0457",

language = "English",

volume = "33",

pages = "1--26",

journal = "Statistica Sinica",

issn = "1017-0405",

publisher = "Institute of Statistical Science",

number = "1",

}

TY - JOUR

T1 - ON THE CONSISTENCY OF THE LEAST SQUARES ESTIMATOR IN MODELS SAMPLED AT RANDOM TIMES DRIVEN BY LONG MEMORY NOISE

T2 - THE RENEWAL CASE

AU - Araya, Héctor

AU - Bahamonde, Natalia

AU - Fermín, Lisandro

AU - Roa, Tania

AU - Torres, Soledad

PY - 2023/1

Y1 - 2023/1

N2 - In this study, 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 time T = 1. A simulation study is provided to illustrate the behavior of the different terms, as well as the performance of the estimator under various values of the Hurst parameter H.

AB - In this study, 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 time T = 1. A simulation study is provided to illustrate the behavior of the different terms, as well as the performance of the estimator under various values of the Hurst parameter H.

KW - Least squares estimator

KW - long-memory noise

KW - random times

KW - regression model

KW - renewal process

UR - http://www.scopus.com/inward/record.url?scp=85161630086&partnerID=8YFLogxK

U2 - 10.5705/ss.202020.0457

DO - 10.5705/ss.202020.0457

M3 - Article

AN - SCOPUS:85161630086

SN - 1017-0405

VL - 33

SP - 1

EP - 26

JO - Statistica Sinica

JF - Statistica Sinica

IS - 1

ER -

ON THE CONSISTENCY OF THE LEAST SQUARES ESTIMATOR IN MODELS SAMPLED AT RANDOM TIMES DRIVEN BY LONG MEMORY NOISE: THE RENEWAL CASE

Abstract

Keywords

Access to Document

Fingerprint

Cite this