Timeline for Statistical test for boundedness of Expectation
Current License: CC BY-SA 3.0
14 events
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| Apr 9, 2018 at 5:17 | comment | added | san | @IosifPinelis Agreed. In fact with thick tails (unbounded variance) I would surprised if one would get even a $1/\sqrt n$ convergence. | |
| Apr 5, 2018 at 23:39 | comment | added | Iosif Pinelis | I think statistical inference is usually substantially weaker than it is made it out to be. Even in the most perfect one-dimensional iid models, the rate of convergence to normality is only $\asymp1/\sqrt n$, and this is especially unhelpful in tail areas (which are usually of interest), especially when the tails are thick, as it is oftentimes the case. So, unless $n$ is infinite :-), one should not expect much. | |
| Apr 5, 2018 at 19:46 | comment | added | san | I wonder if one can use Markov inequality to demonstrate that no matter where you 'place' the mean there is much more mass in the tail than Markov inequality would indicate. These infinitely many hypohesis needs to be accounted for, perhaps with VC dimension arguments. | |
| Apr 5, 2018 at 19:34 | comment | added | san | @IosifPinelis Thanks a lot for adding the citations. I have been reading up on Hill estimators and their likes the past few months. It seems the question of how best to estimate where the tail starts (needed in the computation of the estimators) hasn't been satisfactory settled yet. | |
| Apr 5, 2018 at 19:31 | vote | accept | san | ||
| Apr 5, 2018 at 12:28 | comment | added | Iosif Pinelis | @san : I have added pointers to what I think is relevant literature. | |
| Apr 5, 2018 at 12:23 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Apr 5, 2018 at 5:54 | comment | added | san | I understood this intuitively at the time of posing the question, so I appreciate your time to make it rigorous. I should have framed it better. What I had in mind was -- given that I need to distinguish between the bounded and unbounded expectations how much can one weaken the setting from the easy case of a distinguishing between two parametric distributions of finite and infinite expectations. For example growth rate on $E[X^\alpha]$ for $\alpha \uparrow1$, or unimodality, or monotonicity or smoothness etc. There must be literature on such criteria, would appreciate pointers | |
| Apr 5, 2018 at 2:25 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Apr 5, 2018 at 2:20 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Apr 5, 2018 at 1:27 | comment | added | Iosif Pinelis | @MattF. : I wanted to explain details of statistical testing to people who may not be quite familiar with it. That took some space. Also, it is usually not so easy to prove nonexistence; cf. e.g. the paper "The Nonexistence of Certain Statistical Procedures in Nonparametric Problems" by Bahadur projecteuclid.org/euclid.aoms/1177728077 | |
| Apr 5, 2018 at 1:21 | comment | added | user44143 | I agree with the result, but this seems more than the question warrants. | |
| Apr 5, 2018 at 1:19 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Apr 5, 2018 at 1:09 | history | answered | Iosif Pinelis | CC BY-SA 3.0 |