Nonparametric Statistics
Objectifs
A parametric statistical model involves a family of laws characterized by a small number of unknown real parameters. Such a framework may be perfectly appropriate when the family of probability laws chosen appears to be imposed by the random phenomenon to be described.
In practice, however, the choice of a parametric model is often no more than a convenient simplification, leading to identification errors. The alternative approach is to define a broader, "non-parametric" model, where a possible law is characterized by a function (rather than an element of k). Identifying the law then boils down to estimating this function, an approach that has seen vigorous development in recent years, and will be the focus of this course.
Plan
Non-parametric and semi-parametric models; basic principles of functional estimation.
Density estimation using the kernel method.
Regression estimation using the kernel method.
Non-parametric propensity score estimation.
Generalized method of moments and optimal instruments.
Prérequis
probability theory, inferential statistics, linear regression