Non Parametric methods are statistical techniques that do not require to specify functional forms for objects being estimated. Instead, they let the data itself plays and informs the resulting model in a particular manner. Such methods are becoming increasingly popular for applied data analysis, they are best suited to situations involving large data sets for which the number of variables involved is manageable. These methods are often deployed after common parametric specifications are found to be unsuitable for the problem at hand, particularly when formal rejection of a parametric model based on specification tests yields no clues as to the direction in which to search for an improved parametric model.
The job market understood the importance of the non/semi-parametric methods and almost any serious software contains the principal techniques in this area. We illustrate the different models and techniques with R and Matlab. First, R because of the huge number of packages from CRAN, and secondly Matlab because is the easiest environment for programming arrays in econometrics (and typically all objects are arrays in applied econometrics). Both are very representative for the job market. Each lecture will be accompanied by numerical examples and small programming tutorials.
Course outline:
- Brief Review of Statistics and Probability Concepts used in the course (pre-requisites)
- Empirical non parametric estimators: histogram, empirical distribution, regressogram
- Kernel-based methods in Non Parametric Econometrics: Parzen-Rosenblatt, Nadaraya-Watson
- Semi-parametric methods : Single index and Additive models
- Splines-based methods in Non Parametric Econometrics: Smoothing splines and Least-Squares splines
- Series-based methods in Non Parametric Econometrics: Wavelets, Laguerre and Hermite Polynomials