Homebuying in New Orleans Before and After Katrina: Patterns by Space, Race and Income

Natural disasters can conceivably have significant impacts on the “neighborhood sorting” of different racial or economic groups across intrametropolitan space. Using Home Mortgage Disclosure Act data we examine mortgage-financed homebuying activity within the New Orleans MSA before and after Hurricane Katrina. We find that, while the total amount of homebuying in the 7-parish New Orleans MSA was relatively unchanged between 2004 and 2006, homebuying in the city declined significantly, and declined most in places experiencing severe storm damage. We also find that after Hurricane Katrina, the proportion of homebuyers in the region and the city who were African-American or low-income declined. Finally, we find that segregation levels of African-American and lower-income homebuyers f declined in the year following Katrina. However, some of this effect is likely due to smaller overall numbers of lower-income and African-American buyers in the region.New Orleans, housing after disasters, segregation

A convex pseudo-likelihood framework for high dimensional partial correlation estimation with convergence guarantees

Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either (1) parametric likelihoods, or, (2) regularized regression/pseudo-likelihoods, with the latter having the distinct advantage that they do not explicitly assume Gaussianity. As none of the popular methods proposed for solving pseudo-likelihood based objective functions have provable convergence guarantees, it is not clear if corresponding estimators exist or are even computable, or if they actually yield correct partial correlation graphs. This paper proposes a new pseudo-likelihood based graphical model selection method that aims to overcome some of the shortcomings of current methods, but at the same time retain all their respective strengths. In particular, we introduce a novel framework that leads to a convex formulation of the partial covariance regression graph problem, resulting in an objective function comprised of quadratic forms. The objective is then optimized via a coordinate-wise approach. The specific functional form of the objective function facilitates rigorous convergence analysis leading to convergence guarantees; an important property that cannot be established using standard results, when the dimension is larger than the sample size, as is often the case in high dimensional applications. These convergence guarantees ensure that estimators are well-defined under very general conditions, and are always computable. In addition, the approach yields estimators that have good large sample properties and also respect symmetry. Furthermore, application to simulated/real data, timing comparisons and numerical convergence is demonstrated. We also present a novel unifying framework that places all graphical pseudo-likelihood methods as special cases of a more general formulation, leading to important insights