Point Estimation Methods with Applications to Item Response Theory Models

Statistical inference is mainly concerned with providing some conclusions about the parameters which describe the distribution of a characteristic of interested. On the basis of a random sample drawn from a suitable population, point estimation methods assign a value to each unknown parameter of interest. In this paper we provide a summary of statistical methods for point estimation. Basic properties of an estimator are reviewed together with the main methods of finding estimators: method of moments, maximum likelihood and Bayesian methods. In particular, maximum likelihood estimation methods are discussed in the case of Rasch-type models for Item Response Theory, and illustrated through an example.