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
Summary
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.
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