Point estimation of autoregression parameters with an additional nuisance regression

Establish a point estimator for the autoregression parameters in a model whose errors follow an autoregressive process when an additional nuisance linear regression is present.

Background

The paper focuses on estimating the regression parameter vector in a linear model with stationary autoregressive errors while treating the autoregression coefficients as nuisance parameters. Its proposed rank-based RR-estimator is invariant to those nuisance autoregression parameters, but it does not estimate the autoregression parameters themselves.

Although point estimation of autoregression parameters has been studied for autoregressive models without an additional linear regression component, the corresponding problem in the presence of a nuisance regression remains unresolved. Solving it would support joint or complementary inference in applications where both regression effects and serial dependence are relevant.