A General Overview of Parametric Estimation and Inference Techniques

In parametric statistical inference, which we will be primarily concerned with in this course, the underlying distribution of the population is taken to be parametrized by a Euclidean parameter. In other words, there exists a subset Θ of k-dimensional Euclidean space such that the class of dsitributions P of the underlying population can be written as {Pθ : θ ∈ Θ}. One key assumption made at this stage is that of identifiability; namely that the map θ 7→ Pθ is one-one. Thus knowing θ is equivalent to knowing the underlying distribution.