Adaptive estimation of mixed discrete-continuous distributions under smoothness and sparsity

Brown University, Providence RI

Investigators

Abstract

Economists often analyze questions such as whether a consumer will buy a car or not (yes or no) and if so how much to spend on the car (an amount that takes any value). Economists do not have a good method to analyze these questions. This research project will develop a new and efficient method to analyze data that has these characteristics. The results will give social science researchers an important tool to analyze problems that involve complicated data structures. With ever increasing sophisticated data collection and the availability of powerful computing power, a method that can be used to efficiently analyze such complicated data sets will be extremely valuable to researchers and policy makers in all fields. The methods developed in this research will be programmed and be freely available to all researchers. The results of this research will allow researchers to give more accurate advice to policy makers and thus improve decision making and economic growth. This research project develops a framework for estimating mixed discrete-continuous distributions where the multivariate discrete part of the distribution can have either a large or a small number of support points; may be smooth or not, and these characteristics can differ from one discrete coordinate to another. The optimal convergence rates for estimation of discrete-continuous distributions will be derived in these settings. Preliminary results suggest that smoothing is beneficial only for a subset of discrete variables with a quickly growing number of support points or sufficiently high level of smoothness. The proposed estimation procedures are based on Bayesian mixtures of multivariate normal distributions with covariate dependent mixing weights. The proposed methods will deliver practical and optimal adaptive nonparametric alternatives to standard econometric models such as ordered probit and Poisson regression, and first stage estimators in two stage estimation procedures for structural discrete choice models. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.