Behaviour of the least squares estimators of the linear model in a dependent context : asymptotic properties, implementation, examples

Abstract : In this thesis, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan (1973) who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and on the error process. Whatever the design and the error process satisfying Hannan’s conditions, we define an estimator of the asymptotic covariance matrix of the least squares estimator and we prove its consistency under very mild conditions. Then we show how to modify the usual tests on the parameter of the linear model in this dependent context. We propose various methods to estimate the covariance matrix in order to correct the type I error rate of the tests. The R package slm that we have developed contains all of these statistical methods. The procedures are evaluated through different sets of simulations and two particular examples of datasets are studied. Finally, in the last chapter, we propose a non-parametric method by penalization to estimate the regression function in the case where the errors are Gaussian and correlated.
Complete list of metadatas

Cited literature [79 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/tel-02354575
Contributor : Emmanuel Caron <>
Submitted on : Thursday, November 7, 2019 - 6:21:46 PM
Last modification on : Saturday, November 9, 2019 - 1:52:51 AM

File

Manuscrit_these.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : tel-02354575, version 1

Collections

Citation

Emmanuel Caron. Behaviour of the least squares estimators of the linear model in a dependent context : asymptotic properties, implementation, examples. Statistics [math.ST]. Ecole Centrale de Nantes (ECN), 2019. English. ⟨tel-02354575⟩

Share

Metrics

Record views

19

Files downloads

6