Robust estimation in structural equation models using Bregman divergences

摘要: Structural equation models seek to find causal relationships between latent variables by analysing the mean and covariance matrix of some observable indicators variables. Under a multivariate normality assumption on distribution errors, maximum likelihood estimators are asymptotically efficient. The significantly influenced violation hence there is need robustify inference procedures. We propose minimise Bregman divergence or its variant, total divergence, robust estimator model matrix, with respect parameters interest. Our approach robustification different from standard approaches in that we achieve two levels: firstly, choosing matrix; secondly, using measure estimator. focus (total) von Neumann particular estimate structural model. tested simulation study shows significant advantages estimating contaminated data sets seems perform better than other well known models. References E. G. Baranoff, S. Papadopoulos T. W. Seger. Capital Risk Revisited: A Equation Model Approach for Life Insurers. Journal Insurance, 74:653–681, 2007. doi:10.1111/j.1539-6975.2007.00229.x K. Bollen. Equations Latent Variables . Wiley, New York, 1989. I. Dhillon J. A. Tropp. Matrix Nearness Problems Divergences. SIAM Analysis Applications , 29:1120–1146, 2008. doi:10.1137/060649021 F. Nielsen Boltz. Burbea–Rao Bhattacharyya Centroids. IEEE transactions information theory 57:5455–5466, 2011. doi:10.1109/TIT.2011.2159046 B. C. Vemuri, M. Liu, S.-I. Amari Nielsen. Total Divergence Its DTI Analysis. Transactions medical imaging 30:475–483, doi:10.1109/TMI.2010.2086464 Verboven Hubert. LIBRA: MATLAB library analysis, Chemometrics intelligent laboratory systems 75:127–136, 2005. doi:10.1016/j.chemolab.2004.06.003 K.-H. Yuan P. Bentler. modeling covariances. Sociological Methodology 28:363–396, 1998. doi:10.1111/0081-1750.00052 Robust structure British Mathematical Statistical Psychology 51:63–88, doi:10.1111/j.2044-8317.1998.tb00667.x Yuan, Bentler Chan. Modeling Heavy Tailed Distributions, Psychometrika 69:421–436, 2004. doi:10.1007/BF02295644 X. Zhong Yuan. Bias Efficiency Modeling: Maximum Likelihood Versus Methods. Multivariate Behavioral Research, 46:229–265, doi:10.1080/00273171.2011.558736 Matlab Library http://wis.kuleuven.be/stat/robust/LIBRA/LIBRA-home