# Statistical Estimation of Large Deviation Rates for i . i . d . Sub-exponential Random Walks

@inproceedings{Namkoong2017StatisticalEO, title={Statistical Estimation of Large Deviation Rates for i . i . d . Sub-exponential Random Walks}, author={Hongseok Namkoong and John C. Duchi and Peter W. Glynn}, year={2017} }

We study statistical inference of the rare event probability pm = P(Sm ≥ my) for fixed y > E[X] and Sm = ∑n i=1Xi where Xi’s are i.i.d. sub-exponential random variables. We consider the question “does large deviations theory help in nonparametric settings?” and answer it in the affirmative in our setup. Using the large deviations approximation pm ≈ e−mI where I := supλ{λy− logE[e ]} and estimating I from samples, we first show that a large deviations based estimator takes n = Θ̃((m −1… CONTINUE READING