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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.
