Abstract

We consider regression analysis of longitudinal data when the temporal correlation is modeled by an autoregressive process. Robust R estimators of regression and autoregressive parameters are obtained. Our estimators are valid under censoring caused by detection limits. Efficient computation of the estimators is discussed. Theoretical and simulation studies of the estimators are presented. We analyze a real data set on air pollution using our methodology.

Highlights

  • We consider a time series {Xt : t ≥ 1} and an associated series of covariate vectors {Zt : t ≥ 1}, in q, for some q ≥ 1

  • We develop our methodology for the situation when the censoring is to the left which may occur when the values of the time series Xt fall below a detection limit Dt

  • The number of papers dealing with some form of censored time series data is limited (Vasudaven et al, 1996) Zeger and Brookmeyer (1986) argue that censoring may occur naturally in longitudinal studies when there are detection limits on the observation that are being collected in time

Read more

Summary

Introduction

We consider a time series {Xt : t ≥ 1} and an associated series of covariate vectors {Zt : t ≥ 1}, in q, for some q ≥ 1. The number of papers dealing with some form of censored time series data is limited (Vasudaven et al, 1996) Zeger and Brookmeyer (1986) argue that censoring may occur naturally in longitudinal studies when there are detection limits on the observation that are being collected in time. They took a fully parametric approach to the above problem and fitted a Gaussian error model using the maximum likelihood approach via an EM type algorithm.

The estimators
The complete data case
Modification for censored data
Computation of the estimator
Computation of the weights
Bootstrap inference
Simulation studies
An application
Discussion

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.