Maximum likelihood estimation for tensor normal models via castling transforms
Forum of Mathematics, Sigma, Tome 10 (2022)
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In this paper, we study sample size thresholds for maximum likelihood estimation for tensor normal models. Given the model parameters and the number of samples, we determine whether, almost surely, (1) the likelihood function is bounded from above, (2) maximum likelihood estimates (MLEs) exist, and (3) MLEs exist uniquely. We obtain a complete answer for both real and complex models. One consequence of our results is that almost sure boundedness of the log-likelihood function guarantees almost sure existence of an MLE. Our techniques are based on invariant theory and castling transforms.
@article{10_1017_fms_2022_37,
author = {Harm Derksen and Visu Makam and Michael Walter},
title = {Maximum likelihood estimation for tensor normal models via castling transforms},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {10},
year = {2022},
doi = {10.1017/fms.2022.37},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.37/}
}
TY - JOUR AU - Harm Derksen AU - Visu Makam AU - Michael Walter TI - Maximum likelihood estimation for tensor normal models via castling transforms JO - Forum of Mathematics, Sigma PY - 2022 VL - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.37/ DO - 10.1017/fms.2022.37 LA - en ID - 10_1017_fms_2022_37 ER -
%0 Journal Article %A Harm Derksen %A Visu Makam %A Michael Walter %T Maximum likelihood estimation for tensor normal models via castling transforms %J Forum of Mathematics, Sigma %D 2022 %V 10 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.37/ %R 10.1017/fms.2022.37 %G en %F 10_1017_fms_2022_37
Harm Derksen; Visu Makam; Michael Walter. Maximum likelihood estimation for tensor normal models via castling transforms. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.37
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