Timeline for Optimal bandwidth selection in conditional density estimation
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| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| Mar 15, 2017 at 14:08 | comment | added | Henry.L | @jbowman You are just using a basis consisting of kernels with different parameters to approximate a functional form. I think all inference is done on the space of measures on the sample space. By assuming an exact functional form you just assume a better loss function which does not penalize a specific parametric family...If you really want, you can also call regression models semi-parametrics to impress your friends. I do not think this thread is relevant to OP and we can start another POST if you want to discuss, thanks. | |
| Mar 15, 2017 at 14:02 | comment | added | jbowman | Can't agree with that; the sample mean is a nonparametric estimator of the population mean, and there's only one thing being estimated. "Nonparametric", writing loosely, implies you aren't assuming that you know the true functional form, in this case the true distribution, so are fitting a more general function whose parameterization allows you to "get close to" a broader region of function space than you could if you just assumed, e.g., the data followed a MV Gaussian.. It does not imply"no parameters" or "infinite parameters". | |
| Mar 15, 2017 at 13:52 | comment | added | Henry.L | There is really NO definition of nonparametric from my perspective, finally you must reduce to parametric cases in order to make any meaningful inference, the only difference is that nonparametrics do NOT impose restrictions on numbers of parameters and thus more flexible. Consider those "classical nonparametric tests(say Mann-Whitney)" may be easier for you to see what is my point here. But thanks for the clarification. | |
| Mar 15, 2017 at 13:48 | history | edited | Henry.L | CC BY-SA 3.0 |
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| Mar 15, 2017 at 13:47 | comment | added | Henry.L | @Adrien I did not mean KDE is NOT nonparametric, I just want to distinguish KDE from Dirichlet/Gaussian processes methods. And it is well accepted that kernel smoothing is more like polynomial smoothing rather than more recent Bayesian nonparametric methods like Dirichlet/Gaussian processes, I really do not see what is your point here... | |
| Mar 15, 2017 at 13:01 | comment | added | Adrien | (4) I don't know what you call a basis in kernel density estimation, but anyway that is not the definition of nonparametric. If you don't believe me, check the first sentence of the wikipedia article: en.wikipedia.org/wiki/Kernel_density_estimation | |
| Mar 15, 2017 at 12:12 | comment | added | Henry.L | @Adrien (4)Personally I treat every procedure with an explicit basis as parametric(You can also call it nonparametric, but what I have for non parametric in mind is sth like bayesian nonparametrics). Here the basis is kernels and the dimension of the space may or may not be infinite. | |
| Mar 15, 2017 at 12:10 | comment | added | Henry.L | @Adrien (1,2)I am asking for the same kernel with different procedures(in different dimensions the optimal bandwidth selection varies, so if we choose the bandwidth stepwisely then the resulting bandwidth may or may not be the same as the optimal bandwidth we choose simultaneously for every dimension). It is not related with product kernel or not; | |
| Mar 15, 2017 at 10:20 | comment | added | Adrien | (4) Kernel density estimation is totally nonparametric, why are you saying it's a parametric method? | |
| Mar 15, 2017 at 10:17 | comment | added | Adrien | (2) I would say the fact that true optimal kernels and bandwidths are not product of 1D kernels and 1D bandwidths, but full d-Dimensional kernels and bandwidths. You can of course restrict yourself to product kernels, but it comes with a price. | |
| Mar 15, 2017 at 10:14 | comment | added | Adrien | (1) I'm not sure I understand the question. You are computing "optimal" bandwidths w.r.t different criteria. If you're using different methods,it's only logical to assume they will produce different results. | |
| Mar 14, 2017 at 23:13 | history | edited | Henry.L |
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| Mar 14, 2017 at 18:10 | history | edited | Henry.L | CC BY-SA 3.0 |
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| Mar 14, 2017 at 17:05 | history | edited | Henry.L | CC BY-SA 3.0 |
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| Mar 14, 2017 at 16:56 | history | edited | Henry.L |
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| Mar 14, 2017 at 16:50 | history | asked | Henry.L | CC BY-SA 3.0 |