Two examples in the theory of large deviations

Dmitry Ioffe

Statistics & Probability Letters, 1993, vol. 18, issue 4, 297-300

Abstract: We consider the usual approach to large deviations via the convex conjugate to log-moment generating function. Our first example shows that in the absence of exponential tightness the procedure may lead to correct results but no point on the graph of the rate function will have a supporting hyperplane. The second example implies that if in addition the condition of strict convexity is dropped, then the lower large deviation bound may fail everywhere.

Keywords: Fenchel; transform; large; deviations (search for similar items in EconPapers)
Date: 1993
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