### For Po-Ling Loh: Lepski's method

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How sensitive is the beta estimate to choice of sigma? This impacts how narrow your grid neads to be.
Since Lepski's method involves gridding according to powers of two, the procedure will succeed as long as the interval of values on which we grid is accurate even to an exponential approximation. So for instance, if an individual estimator is accurate with probability 1 - exp(-log n) and you grid an interval [sigma_min, 2^M * sigma_min] that contains the true sigma, the probability that the optimal error bound holds for the Lepski estimator is at least 1 - M*exp(-log n).

Community: WHOA-PSI 2017

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6 months ago by
Po-Ling Jog Loh

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