Parametric Inference

For parametric models of the form

where is the parameter space and is the parameter.

Info

The problem of inference is the problem of estimating the parameter .

Often, we are only interested in some function . For example, if then the parameter is . If our goal is to estimate , then is called the parameter of interest, and is called a nuisance parameter.

Example

Let . The parameter is and the parameter space is . Suppose that is the outcome of a blood test and suppose we are interested in , the fraction of the population whose test score is larger than . Let denote a standard Normal variable. Then

The parameter of interest is .

Sources

• Wasserman, L. (2010). All of Statistics: A concise Course in Statistical Inference. Chapter 9.