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Local asymptotic normality of likelihood ratio in moderate deviation zone
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 71-85
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For logarithmic asymptotic we show that local asymptotic normality can be extended on moderate deviation zone if the same assumptions hold. We show that strong asymptotic of moderate deviation probabilities can be also obtained with rather mild assumptions. The extension on moderate deviation zone of second Le Cam Lemma for contiguous alternatives is proposed as well. 
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M. S. Ermakov. Local asymptotic normality of likelihood ratio in moderate deviation zone. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 34, Tome 525 (2023), pp. 71-85. http://geodesic.mathdoc.fr/item/ZNSL_2023_525_a5/

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