Robust methods for heteroskedastic regression

Heteroskedastic regression data are modelled using a parameterized variance function. This procedure is robustified using a method with high breakdown point and high efficiency, which provides a direct link between observations and the weights used in model fitting. This feature is vital for the application, the analysis of international trade data from the European Union. Heteroskedasticity is strongly present in such data, as are outliers. A further example shows that the new method outperforms ordinary least squares with heteroskedasticity robust standard errors, even when the form of heteroskedasticity is mis-specified. A discussion of computational matters concludes the paper. An appendix presents the new scoring algorithm for estimation of the parameters of heteroskedasticity. Generalizes the standard model for heteroskedasticity in non-robust regression.Flexibility of the robust model shown on complex international trade data.Outperforms conventional "heteroskedastic robust" standard errors.Linked graphics provide insight into importance of individual observations.Provides publicly available Matlab code for very robust heteroskedastic regression.

[1]  R. Carroll,et al.  Variance Function Estimation , 1987 .

[2]  Francesca Torti,et al.  FSDA: A MATLAB toolbox for robust analysis and interactive data exploration , 2012 .

[3]  David Ruppert,et al.  Transformation and Weighting , 2014 .

[4]  Tsung-Chi Cheng,et al.  Robust diagnostics for the heteroscedastic regression model , 2011, Comput. Stat. Data Anal..

[5]  D. Ruppert,et al.  A comparison between maximum likelihood and generalized least squares in a heteroscedastic linear model , 1982 .

[6]  G. M. Tallis.  Elliptical and Radial Truncation in Normal Populations , 1963 .

[7]  Bent Nielsen,et al.  Corrigendum: Analysis of the forward search using some new results for martingales and empirical processes , 2016, Bernoulli.

[8]  A. Harvey.  Estimating Regression Models with Multiplicative Heteroscedasticity , 1976 .

[9]  Anthony C. Atkinson,et al.  Monitoring robust regression , 2014 .

[10]  Anthony C. Atkinson,et al.  The forward search: theory and data analysis , 2010 .

[11]  A. Atkinson,et al.  Finding an unknown number of multivariate outliers , 2009 .

[12]  Anthony C. Atkinson,et al.  A Parametric Framework for the Comparison of Methods of Very Robust Regression , 2014, 1405.5040.

[13]  V. Yohai,et al.  Robust Statistics: Theory and Methods , 2006 .

[14]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[15]  Valerii V. Fedorov,et al.  Optimal Design for Nonlinear Response Models , 2013 .

[16]  Alessio Farcomeni,et al.  Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter , 2014, J. Multivar. Anal..

[17]  Peter Filzmoser,et al.  Robust joint modeling of mean and dispersion through trimming , 2012, Comput. Stat. Data Anal..

[18]  Peter J. Rousseeuw,et al.  Robust regression and outlier detection , 1987 .

[19]  Anthony C. Atkinson,et al.  Exploratory tools for clustering multivariate data , 2007, Comput. Stat. Data Anal..

[20]  Bent Nielsen,et al.  Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models , 2016 .

[21]  David Ruppert,et al.  Fitting heteroscedastic regression models , 1994 .

[22]  Stanley P. Azen,et al.  Computational Statistics and Data Analysis (CSDA) , 2006 .

[23]  P. Rousseeuw.  Least Median of Squares Regression , 1984 .

[24]  D. Ruppert,et al.  Transformation and Weighting in Regression , 1988 .