Confidence Sets for General Parameters

Let X₁,…, X _n denote a realization of a stationary time series. Suppose the infinite dimensional distribution of the infinite sequence is denoted P. The problem we consider is inference for a parameter θ(P). The focus of the present chapter is the case when the parameter space Θ is a metric space. The reason for considering such generality is to be able to consider the case when the parameter of interest is an unknown function, such as the marginal distribution of the process or the spectral distribution function of the process. Here, we need to extend the arguments of previous chapters to cover the more general case.