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Singular information matrix
Theory and mehtods related to the nonregular scenario in likelihoodbased inference when the Fisher information matrix is singular at some points in the parameter space. 

Papers
Rotnitzky A, Cox DR, Bottai M, Robins JM. Likelihoodbased asymptotic inference with singular information. Bernoulli, 6(2): 243284, 2000 Bottai M. Confidence regions when the Fisher information is zero. Biometrika, 90(1): 7384, 2003 Bottai M, Orsini N. Confidence intervals for the variance component of randomeffects linear models. The Stata Journal, 4(4): 429435, 2004 Bottai M, Geraci M, Lawson A. Testing for Unusual Aggregation of Health Risk in Semiparametric Models. Statistics in Medicine, 27(15): 29022921, 2008 Ekvall KO, Bottai M. Confidence regions near singular information and boundary points with applications to mixed models. Annals of Statistics, 50(3): 18061832, 2022 
Presentations
Bottai M. Local level of the Wald test when the information is zero. Proceedings of the Annual National Conference of the Italian Statistical Society, Cleup, Padua, Italy, 361364, 2002 Software Download software in Stata: net install st0077, from(http://www.statajournal.com/software/sj44/) Download software and a worked out example in R from:
https://github.com/koekvall/lmmstest

Unit of Biostatistics, Nobels väg 13, Karolinska Institutet, 17177 Stockholm, Sweden 