Timeline for Kernel Density Estimate for Cauchy
Current License: CC BY-SA 4.0
12 events
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| Feb 2, 2022 at 16:11 | comment | added | Xi'an | @Greenparker: The only characterisation of the target density $f$ that matters in the mean integrated square error (MISE) and the choice of an optimal bandwidth is$$\int (f")^2(x)\,\text dx$$which is well-defined for the Cauchy density. | |
| Feb 2, 2022 at 8:30 | comment | added | Greenparker | Thanks @BruceET. From here it dependents on the norm of the second derivative of the target density, which for gaussian densities, depends on the variance. This naturally assumes that the target density exhibits a finite variance, and I think that is the issue. | |
| Feb 2, 2022 at 8:18 | comment | added | BruceET | The optimal choice of bandwidth depends on the standard deviation. I may be crawling out on a limb here, but I think other parts of the theory of kernel density estimation may also depend on the existence of the population standard deviation. For now, I'll leave that for users who know more about KDE than I to clarify. | |
| Feb 2, 2022 at 7:59 | history | edited | BruceET | CC BY-SA 4.0 |
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| Feb 2, 2022 at 7:58 | comment | added | Greenparker | Thanks @BruceET. Certainly, I can understand how the code may be modified to make visually acceptable KDEs. I am more curious as to where the theory of KDEs brings down in the practical implementation for Cauchy. That is, why is it "usually necessary to disregard more than a few values in the tails of the sample" | |
| Feb 2, 2022 at 7:24 | history | edited | BruceET | CC BY-SA 4.0 |
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| Feb 2, 2022 at 7:18 | history | edited | BruceET | CC BY-SA 4.0 |
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| Feb 2, 2022 at 7:12 | comment | added | BruceET | Yes, I changed the wording a bit before I saw your comment. | |
| Feb 2, 2022 at 7:10 | history | edited | BruceET | CC BY-SA 4.0 |
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| Feb 2, 2022 at 7:07 | comment | added | Xi'an | Strictly speaking, there are no "outliers" in a Cauchy sample, all points within the sample are from the same Cauchy distribution. | |
| Feb 2, 2022 at 7:04 | history | edited | BruceET | CC BY-SA 4.0 |
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| Feb 2, 2022 at 6:59 | history | answered | BruceET | CC BY-SA 4.0 |