Asymptotic exponential bounds for MLE deviation under minimal conditions via classical and generic chaining methods

Abstract

In this paper non-asymptotic exact exponential estimates are derived (under minimal conditions) for the tail of deviation of the MLE distribution in the so-called natural terms: natural function, natural distance, metric entropy, Banach spaces of random variables, contrast function, majorizing measures or, equally, generic chaining.

References in corpus (3)

• Exact exponential bounds for the random field maximum distribution via the majoring measures (generic chaining)
• Bide - Side Exponential and Moment Inequalities for Tails of Distributions of Polynomial Martingales
• A penalized exponential risk bound in parametric estimation

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• Theory of approximation and continuity of random processes
• Uniform measures on the arbitrary compact metric spaces, with applications
• Exact exponential tail estimations in the Law of Iterated Logarithm for Bochner's mixed Lebesgue spaces
• Lower boundaries for parametric estimations in different norms
• Parametric density-based optimization of partition in cluster analysis, with applications
• Random processes and Central Limit Theorem in Besov spaces