Lecture Series Description:
In this lecture series, I will cover techniques for estimating semiparametric and nonparametric statistical models. These techniques allow us to relax restrictive assumptions (such as linearity, independence, etc.) that are required by parametric estimators. I will focus on understanding these estimators, implementing these estimators in stata and r, and using these estimators in political science applications.
Lecture 1 (March 26) – Semiparametric Methods (Slides and References)
Semiparametric models offer a superior alternative to parametric models for dealing with heteroskedasticity (in the linear model), over and under-dispersion (in count data models), time-series dependence, unit interdependence (in panel data models), and spatial dependence. Correcting for any one of these problems is difficult in the parametric context because selecting a specification presents a difficult problem. Semiparametric methods get around this problem by postulating a statistical model that is general enough to include any reasonable specification. Moreover, parametric approaches to dealing with these problems offer computational challenges and are therefore often absent from statistical packages. Semiparametric approaches for dealing with these problems are often very easy to apply.
Lecture 2 (April 2) – Density Estimation (Slides and References)
Nonparametric models allow the researcher to relax assumptions (such as linearity) that are often employed by conventional estimators. While linearity is often a reasonable assumption, there exist situations where it is too restrictive. In such situations, one may be tempted to abandon multivariate analysis and proceed using graphical methods (for example, histograms or LOESS) which don't impose restrictive assumptions on the data. In doing so, one would be giving up that ability to assess sampling variability in the data and to control for additional variables. Nonparametric methods provide a framework for applying graphical methods while retaining the ability to conduct statistical inference and to include control variables. In the second lecture, I will cover density estimation in detail. The basic techniques used for density estimation are applicable to a wide class of nonparametric problems.
Lecture 3 (April 9) – Multivariate Nonparametric Methods (Slides and References)
In the third lecture, I will cover nonparametric regression and nonparametric binary choice models, building on our understanding of the density estimation problem. These techniques extend multivariate models such as OLS, logit, and probit, while relaxing restrictive linearity assumptions.