We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This enables us to study the efficiency of estimators, such as regular estimators and minimax leading a universal tight lower bound beyond i.i.d. assumption. formulation complements theory contiguity developed in previous paper [Fujiwara Yamagata, Bernoulli 26 (2020) 2105–2141]...

Abstract In this paper, we study sample size thresholds for maximum likelihood estimation tensor normal models. Given the model parameters and number of samples, determine whether, almost surely, (1) function is bounded from above, (2) estimates (MLEs) exist, (3) MLEs exist uniquely. We obtain a complete answer both real complex One consequence our results that sure boundedness log-likelihood g...

Examination of the available ignition delay time data and correlations in the case of methane, butane, heptane, decane, kerosene, Jet-A and <span style="font-size: 12pt; color: #000000; font-style: nor...