Variance misspecification in Gaussian mixtures creates a phase diagram: correct specification recovers true means independent of SNR, under-smoothing biases means with SNR^{-1} error in low SNR, and over-smoothing collapses clusters above an SNR-dependent threshold.
Model-based clustering, discriminant analysis, and density estimation.Journal of the American statistical Association, 97(458):611–631
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The interplay of signal-to-noise ratio and variance misspecification in Gaussian mixtures
Variance misspecification in Gaussian mixtures creates a phase diagram: correct specification recovers true means independent of SNR, under-smoothing biases means with SNR^{-1} error in low SNR, and over-smoothing collapses clusters above an SNR-dependent threshold.