Barcelona Microeconometrics Summer School 

Applied Non-Parametric Methods

Instructor: Franco Peracchi

The purpose of this course is to introduce participants to basic nonparametric methods for data description and regression analysis. The course is divided in three parts. The first deals with nonparametric density estimation. After introducing the kernel method for univariate density estimation and discussing its statistical properties, other methods for univariate and multivariate density estimation are presented and discussed. The second part introduces several methods for estimating regression functions: regression splines, kernel and nearest neighbor methods, cubic smoothing splines, and local polynomial regression. It then discusses the statistical properties of the proposed estimators, and methods for high dimensional data. The third part deals with estimation of distribution and quantile functions, both unconditionally and conditionally on regressors. It also discusses the relationship between the two approaches and various generalizations. Each of the three parts ends with a discussion of relevant Stata commands.

Course Outline

1. Nonparametric density estimators
   • Empirical densities
   • The kernel method
   • Statistical properties of the kernel method
   • Other methods for density estimation
   • Multivariate density estimation
   • Stata commands
     
     
2. Linear nonparametric regression estimators
   • Regression splines
   • The kernel method
   • The nearest neighbor method
   • Cubic smoothing splines
   • Local polynomial regression
   • Statistical properties of linear smoothers
   • Methods for high dimensional data
   • Stata commands
     
     
3. Distribution function and quantile function estimators
   • The empirical distribution function
   • The empirical quantile function
   • Estimating the conditional quantile function
   • Estimating the conditional distribution function
   • Relationships between the two approaches
   • Generalizations
   • Stata commands

References