Effect of imprecisely known nuisance parameters on estimates of primary parameters

Abstract

Let the model under consideration have two types of parameters, α and θ, where α represents the nuisance parameters and θ represents the primary parameters (or parameters of interest). We will suppose that θ is estimated after α has been fixed at some value , and that is determined from information other than that used to form the estimate for θ . This paper examines the properties of in the presence of uncertainty in the assumed value for ∝. In particular, we consider: (1) the effect of the uncertainty in on the dispersion matrix, and hence confidence intervals, for ; and (2) the effect of on the asymptotic properties of . The results of this paper are developed in a multivariate setting and apply to a broad class of estimators, including maximum likelihood, maximum a posteriori, and least squares.