Timeline for Statistical test for boundedness of Expectation
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 5, 2018 at 1:55 | comment | added | Iosif Pinelis | @Bombyxmori : In a paper with A. Kontorovich, we obtain exact lower bounds on the excess risk in a certain model of machine learning (arxiv.org/abs/1606.08920); upper bounds are also known (but not with exact constants). Of course, all that is for finite samples. For finite samples, the question of the existence of a good test on the finiteness of the mean does have a meaning, even though the answer to it is negative, as I showed. However, the infinite sample assumption simply makes testing unnecessary. | |
| Apr 5, 2018 at 1:40 | comment | added | Bombyx mori | This is not true, problems in statistical learning often have no effective sample size and no good effective error estimates. This is why we need a computational learning theory in real life data analysis. I think infinite sample assumption here is necessary, for small sample the question is meaningless to me. But I have not read your answer. | |
| Apr 5, 2018 at 1:35 | comment | added | Iosif Pinelis | @Bombyxmori : If you say "Let assume for convenience that you can have as many sample of unknown distribution as you wanted", then basically there is no problem. Statistical tests are only needed for real-life, finite samples (which may sometimes be large, but still finite). | |
| Apr 5, 2018 at 1:32 | history | edited | Bombyx mori | CC BY-SA 3.0 |
edited body
|
| Apr 5, 2018 at 1:31 | comment | added | Bombyx mori | @IosifPinelis: "Let assume for convenience that you can have as many sample of unknown distribution as you wanted. " (just fixed the typo). I think if the sample size is finite (<10, say), there is no way we can ever check if the mean is finite. It would simply does not make sense. | |
| Apr 5, 2018 at 1:30 | comment | added | Iosif Pinelis | @Bombyxmori : How do you "generate one million sample of $X$"? (Of course, taking the square roots is no problem.) | |
| Apr 5, 2018 at 1:25 | history | edited | Bombyx mori | CC BY-SA 3.0 |
added 34 characters in body
|
| Apr 5, 2018 at 1:23 | comment | added | Bombyx mori | @MattF. You do not take the mean of $W_{i}$, which has already been normalized. You use the equivalence of $t$-test to normalize $W_{i}$ by dividing $\sigma/1000$, then compare it with the normal distribution via something like QQ plot, etc. | |
| Apr 5, 2018 at 1:20 | comment | added | Bombyx mori | @IosifPinelis: You just generate one million sample of $X$ and take the square root. | |
| Apr 5, 2018 at 1:17 | comment | added | Iosif Pinelis | A number of questions here. The first one: how do you "Generate one million random sample of $\sqrt{X}$"? The distribution of $X$ is unknown -- otherwise there is no need for any statistical tests. | |
| Apr 5, 2018 at 1:15 | comment | added | user44143 | With this setup, the mean of W’s will be 0, so the t-statistic will be 0 too. | |
| Apr 5, 2018 at 0:48 | history | answered | Bombyx mori | CC BY-SA 3.0 |