As the application period comes to an end, I realized I put as much thought into my application as a hefty class assignment. In fact, I would say that just putting the application together helped me to better understand the material that I hope to code for statsmodels this summer and taught me as much if not more than a typical class project usually does.
Briefly, I proposed to implement empirical likelihood estimation in python. Empirical likelihood is a non-parametric method of estimation that gives observed data a very loud voice. I am particularly drawn to this and nonparametric statistics in general for 2 (main) reasons.
First, it frees the researcher from many of the distributional assumptions that are typically found in standard econometrics and statistics textbooks. Although there are countless reasons to remove these assumptions, one is to predict movements in stock prices. Many classical models rely on assumptions or normality (or Brownian motion), when forecasting stock prices or pricing options. However, it has been shown that stock prices follow a distribution with heavy tails. Ignoring these fat tails (higher probabilities of large movements) can be problematic for researchers and practitioners alike.
The second reason I am attracted to empirical likelihood and nonparametric statistics is more pragmatical (or lazy, however you look at it). Statisticians spend plenty of resources deriving complicated analytical solutions that only apply "in the limit" and can often be very misleading when used in finite samples among people who are unsure of their worth. While these are sometimes helpful for practitioners or policy maker that only wants to "throw" a couple variables into a statistical software, it seems as though the derivation of these analytical solutions is somewhat of a mis-allocation of resources (brain power of some very smart people) since specific questions can be answered much more easily through other computational methods. Undoubtedly though, we will never stop developing these nice, pretty analytical solutions. It is in out nature.
"One reason comes from our wish, as theoreticians, to explore the source of the a priori practical principles that lie in our reason. " -Immanuel Kant, Groundwork of the Metaphysics of Morals.