Exponential deficiency of convolutions of densities
Iosif Pinelis (2012)
ESAIM: Probability and Statistics
Similarity:
If a probability density () ( ∈ ℝ) is bounded and := ∫e ()d < ∞ for some linear functional and all ∈ (01), then, for each ∈ (01) and all large enough , the -fold convolution of the -tilted density := e ()/ is bounded. This is a corollary of a general, “non-i.i.d.” result, which is also shown to enjoy a certain optimality property. Such results and their corollaries stated in terms of the absolute integrability of the corresponding characteristic...