Likelihood-based inference with singular information matrix

By Andrea Rotnitzky, D. R. Cox, Matteo Bottai, James M. Robins. 2000

173 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/eca1e888fa145e70b43aa81a7cc8feec950e143d

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In Statistics and Probability

Citations in the corpus

The centred parametrization for the multivariate skew-normal distribution (2008, background): “[16], where it is shown that in these circumstances the rate of convergence of the estimates is slower than the usual Op(n) and that the limiting distribution of the estimates can be bimodal.”
A Bayesian information criterion for singular models (2013, methodology): “Keywords: Bayesian information criterion; Factor analysis; Mixture model; Model selection; Reduced rank regression; Schwarz information criterion; Singular learning theory”
Bimodal extension based on the skew‐normal distribution with application to pollen data (2011, methodology): “Finally, making use of Theorem 3 in Rotnitzky et al. (2000) with the above re-parametrization we can conclude that:”
The Skew‐normal Distribution and Related Multivariate Families * (2005, background): “The phenomenon of singularity at a ¼ 0 of the expected Fisher information matrix is special case of the problem studied in great generality by Rotnitzky et al. (2000), but motivated by a problem closely related to the present one.”
Skewed distributions in finance and actuarial science: a review (2015, background): “As a direct consequence of the above arguments, the rank of the information matrix is at least two less than its order, thus preventing application of results in Rotnitzky et al. (2000).”
Inferential Aspects of the Skew Exponential Power Distribution (2004, methodology): “Rotnitzky et al. (2000) derived the asymptotic distribution of the MLE Oµ D .”
Testing the Number of Components in Normal Mixture Regression Models (2015, methodology): “…analyze the LRT statistic for testing H01 : (θ1, σ1) = (θ2, σ2) by developing a higher-order approximation of the log-likelihood function that can be expressed in a quadratic form, when α ∈ (0, 1), through a judiciously designed reparameterization by extending the result of Rotnitzky et al. (2000).”
Statistical applications of the multivariate skew normal distribution (2009, background): “Such an unusual distribution of the MLE is in qualitative agreement with the ®ndings of Rotnitzky et al. (1999).”