Large-scale computation of pseudospectra using ARPACK and eigs

ARPACK and its MATLAB counterpart, eigs, are software packages that calculate some eigenvalues of a large non-symmetric matrix by Arnoldi iteration with implicit restarts. We show that at a small additional cost, which diminishes relatively as the matrix dimension increases, good estimates of pseudospectra in addition to eigenvalues can be obtained as a by-product. Thus in large-scale eigenvalue calculations it is feasible to obtain routinely not just eigenvalue approximations, but also information as to whether or not the eigenvalues are likely to be physically significant. Examples are presented for matrices with dimension up to 200,000

Robust methods of building regression models : an application to the housing sector.

This article studies robustification strategies for the linear model in the presence of outliers. The advantages of an internal analysis of the robustness of least squares for a given sample are pointed out. The application of this methodology is illustrated by building an explicit model of the determinants of rental housing values in the Madrid Metropolitan Area.Outliers; Influential observations; Robust regression; Cook distance; Hedonic price function; Housing market;

Instrumental Variable Quantile Estimation of Spatial Autoregressive Models

We propose an instrumental variable quantile regression (IVQR) estimator for spatial autoregressive (SAR) models. Like the GMM estimators of Lin and Lee (2006) and Kelejian and Prucha (2006), the IVQR estimator is robust against heteroscedasticity. Unlike the GMM estimators, the IVQR estimator is also robust against outliers and requires weaker moment conditions. More importantly, it allows us to characterize the heterogeneous impact of variables on different points (quantiles) of a response distribution. We derive the limiting distribution of the new estimator. Simulation results show that the new estimator performs well in finite samples at various quantile points. In the special case of median restriction, it outperforms the conventional QML estimator without taking into account of heteroscedasticity in the errors; it also outperforms the GMM estimators with or without considering the heteroscedasticity.Spatial Autoregressive Model; Quantile Regression; Instrumental Variable; Quasi Maximum Likelihood; GMM; Robustness.

Testing the equality of central tendency measures using T1 statistic with different trimming strategies

When the assumptions of normality and homoscedasticity are met, researchers should have no doubt in using classical test such as t-test and ANOVA to test for the equality of central tendency measures for two and more than two groups respectively.However, in real life we do not often encounter with this perfect situation.T1 statistic was proposed as an alternative robust method that could handle the problem of nonnormality when using trimmed mean with 15% symmetric trimming as the central tendency measures, but their study only focused on the condition of homogeneous variances.Motivated by the good performance of the method, in this study we propose using T1 statistic with three different trimming strategies, namely, i) predetermined 15% symmetric trimming ii) predetermined asymmetric trimming based upon hinge estimators and iii) empirically determined asymmetric trimming based on robust scale estimators, MADn, Tn and LMSn to handle simultaneously the problem of nonnormality and heteroscedasticity.To test for the robustness of the procedures towards the violation of the assumptions, several variables will be manipulated.The variables are types of distributions, heterogeneity of variances, sample sizes, nature of pairings of group sample sizes and group variances, and number of groups.Type I error for each procedures will then be calculated.This study will be based on simulated data with each procedure will be simulated 5000 times and each set of data will be bootstrapped 599 times.The proposed procedures, generally, generated good Type I error control.The combination of T1 statistic with HQ1 produced promising procedures that are capable of addressing the problem of testing the equality of central tendency measures especially for skewed distributions