Adolfo J. Quiróz

Adolfo Quiroz, Simón Ramírez-Amaya, Álvaro Riascos

High quality risk adjustment in health insurance markets weakens insurer incentives to engage in inefficient behavior to attract lower-cost enrollees. We propose a novel methodology based on Markov Chain Monte Carlo methods to improve risk adjustment by clustering diagnostic codes into risk groups optimal for health expenditure prediction. We test the performance of our methodology against common alternatives using panel data from 500 thousand enrollees of the Colombian Healthcare System. Results show that our methodology outperforms common alternatives and suggest that it has potential to improve access to quality healthcare for the chronically ill.

R. Bárcenas, M. D. Gónzalez--Lima, A. J. Quiroz

An importance sampling and bagging approach to solving the support vector machine (SVM) problem in the context of large databases is presented and evaluated. Our algorithm builds on the nearest neighbors ideas presented in Camelo at al. (2015). As in that reference, the goal of the present proposal is to achieve a faster solution of the SVM problem without a significance loss in the prediction error. The performance of the methodology is evaluated in benchmark examples and theoretical aspects of subsample methods are discussed.

Mateo Díaz, Adolfo J. Quiroz, Mauricio Velasco

For data living in a manifold $M\subseteq \mathbb{R}^m$ and a point $p\in M$ we consider a statistic $U_{k,n}$ which estimates the variance of the angle between pairs of vectors $X_i-p$ and $X_j-p$, for data points $X_i$, $X_j$, near $p$, and evaluate this statistic as a tool for estimation of the intrinsic dimension of $M$ at $p$. Consistency of the local dimension estimator is established and the asymptotic distribution of $U_{k,n}$ is found under minimal regularity assumptions. Performance of the proposed methodology is compared against state-of-the-art methods on simulated data.