Timeline for Bound for Large deviations of sums of independent (not identical) variables
Current License: CC BY-SA 4.0
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| Dec 12, 2019 at 4:19 | comment | added | Iosif Pinelis | Previous comment continued: If you want to ask another question, I think you should do it in a separate post. Also, after you changed your post, it has become only more confusing. In particular, now your $\Lambda^*_{X_i}$ is convex, rather than concave. Also, the function $\Lambda_X$ is still undefined in your post. | |
| Dec 12, 2019 at 4:17 | comment | added | Iosif Pinelis | @DJA : You are still saying that you are unsure about signs, but what you seemed to be sure about was that "[your] bound [was] in the direction that says that tails of the $X_i$ are very light". The definition of $\Lambda^*_{X_i}(t)$ in my answer implies that the inequality $\Lambda^*_{X_i}(t)\le f_i(t)$ in your original post means exactly that the right tails are light enough. So, I think your original question has been answered. | |
| Dec 11, 2019 at 22:27 | comment | added | DJA | Hi Iosef, thank you for the reply. I think we both had some signs flipped. My statement had some backwards inequalities that I have fixed. I think your definition of $\Lambda^*$ is also off by a negative sign. The bound you gave (i.e. that the inf of a sum is not smaller than the sum of infs) is of course true, but I am interested in the other direction. My guess after thinking more is that there should not be, in general, a good bound in the other direction. | |
| Dec 11, 2019 at 16:37 | vote | accept | DJA | ||
| Dec 11, 2019 at 20:57 | |||||
| Dec 11, 2019 at 1:49 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 151 characters in body
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| Dec 11, 2019 at 1:44 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |