Challenging the empirical mean and empirical variance: a deviation study

Details Challenging the empirical mean and empirical variance: a deviation study Challenging the empirical mean and empirical variance: a deviation study

2010-09-10

arxiv.org/abs/1009.2048v2

Mathematics

Statistics Theory

Second version presents an improved variance estimate in section 4.1

Scientific paper

We present new M-estimators of the mean and variance of real valued random variables, based on PAC-Bayes bounds. We analyze the non-asymptotic minimax properties of the deviations of those estimators for sample distributions having either a bounded variance or a bounded variance and a bounded kurtosis. Under those weak hypotheses, allowing for heavy-tailed distributions, we show that the worst case deviations of the empirical mean are suboptimal. We prove indeed that for any confidence level, there is some M-estimator whose deviations are of the same order as the deviations of the empirical mean of a Gaussian statistical sample, even when the statistical sample is instead heavy-tailed. Experiments reveal that these new estimators perform even better than predicted by our bounds, showing deviation quantile functions uniformly lower at all probability levels than the empirical mean for non Gaussian sample distributions as simple as the mixture of two Gaussian measures.

Affiliated with

Also associated with

No associations

Rating

Challenging the empirical mean and empirical variance: a deviation study does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Challenging the empirical mean and empirical variance: a deviation study, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Challenging the empirical mean and empirical variance: a deviation study will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-672642