Detection and Estimation of Block Structure in Spatial Weight Matrix

In many economic applications, it is often of interest to categorize, classify, or label individuals by groups based on similarity of observed behavior. We propose a method that captures group affiliation or, equivalently, estimates the block structure of a neighboring matrix embedded in a Spatial Econometric model. The main results of the Least Absolute Shrinkage and Selection Operator (Lasso) estimator shows that off-diagonal block elements are estimated as zeros with high probability, property defined as “zero-block consistency.” Furthermore, we present and prove zero-block consistency for the estimated spatial weight matrix even under a thin margin of interaction between groups. The tool developed in this article can be used as a verification of block structure by applied researchers, or as an exploration tool for estimating unknown block structures. We analyzed the U.S. Senate voting data and correctly identified blocks based on party affiliations. Simulations also show that the method performs well.     

Penalized multidimensional fitting for protein movement detection

The three-dimensional structure of a given protein can take different conformations depending upon the reaction it undergoes and its substrate/cofactor/partners binding state. Various methods exist to study these conformational changes but only one, called DynDom, is clearly focused on movement detection. An alternative method is proposed, making use of multivariate data analysis, called ‘penalized Multidimensional Fitting (penalized MDF)’ based on penalized movements of points in order to approach the distances between points after movement to the distances given by the reference matrix. The objective is to detect the amino acids that undergo an important movement by fitting the distances of one conformation to the distances of the second one by modifying only the coordinates of the first one. This method is applied to three different proteins.