Timeline for Convergence of an orthormal expansion of the density
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 29, 2021 at 14:21 | comment | added | lrnv | For my problem i do need the full sum, although yes people usually truncate the estimator. So there is no convergence at all that i an obtain for these kind of estimators ? | |
| Jan 29, 2021 at 14:16 | comment | added | mike | I think you can't take the obvious estimate for f, it's probably not an L^2 function, and you probably need to truncate the sum ($ \hat{f}(x) = \sum\limits_{i}^{u(n)} \widehat{a_i} g_i(x)$ where u(n) some upper bound) to get a good estimate. I believe I've seen this issue, but don't recall the details. | |
| Jan 29, 2021 at 13:01 | comment | added | lrnv | Never mind my previous comment, now i get what you mean. Ok the walsh basis is quite peculiar. Maybe we could restrict to basis of continuous functions ? The functions in my basis are even integrable, derivable, etc.. What i mean is: Is there some condition on the basis we could express that would make my assumption true ? EDIT: Fundamentally, i dont think i am summing the squares of the basis functions... I'm summing the square distances between them and the empirical ones ! | |
| Jan 29, 2021 at 12:53 | comment | added | lrnv | I'm not quite getting your point. I started by saying that $f$ belong to L_2, which means that $f$ converges. If i read you correctly, you propose a case where coefficients are infinite, which means that the function is not even analytic, and certainly not square-integrable. So this is different. Did i read you correctly ? | |
| Jan 29, 2021 at 12:46 | history | answered | mike | CC BY-SA 4.0 |