Timeline for Is a spline interpolation considered to be a nonparametric model?
Current License: CC BY-SA 4.0
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| Dec 27, 2022 at 2:19 | history | edited | Alexis | CC BY-SA 4.0 |
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| Sep 23, 2021 at 15:54 | history | edited | Alexis | CC BY-SA 4.0 |
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| Apr 21, 2021 at 11:35 | vote | accept | John Doe | ||
| Apr 2, 2021 at 18:27 | comment | added | usεr11852 | @AdamO: Sure, I don't disagree. | |
| Apr 2, 2021 at 17:29 | comment | added | Alexis | +1 @AdamO and when the variances of those distributions are equal, I think? | |
| Apr 2, 2021 at 17:22 | comment | added | AdamO | @usεr11852 assumptions != parametric modeling. Even the famed Wilcoxon test, widely touted as a test of medians, is only a test of median when the distributions are symmetric. | |
| Apr 2, 2021 at 17:07 | history | edited | Alexis | CC BY-SA 4.0 |
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| Apr 2, 2021 at 16:50 | comment | added | Acccumulation | @COOLSerdash Any output of a computer can be described as a vector consisting of a finite number of real components. | |
| Apr 2, 2021 at 16:17 | comment | added | Alexis | @COOLSerdash Thank you! I think it is pretty clear that smoothing function indeed have a finite vector of $\theta$ real components that define the smoothing function. That said, my lack of pwn-level certainty on the topic around this exact point is why I begged for whuber's wisdom. :) | |
| Apr 2, 2021 at 7:11 | comment | added | COOLSerdash | +1. You write: "On the other hand, these models are parametric, in the mathematical sense that they indeed involve parameters". But this is not the definition of parametric as nonparametric models also involve parameters. To give a very concise (and possibly incomplete) definition: Parametric models can be represented in terms of a vector $\theta$ consisting of a finite number of real components. All other problems are called nonparametric. So it's still unclear to me if splines are parametric or not because for a fixed number of knots, the weights for the basis functions are of finite length. | |
| Apr 1, 2021 at 23:08 | comment | added | Alexis | @StephanKolassa I adore nitpicky pedantry, and have modified my language. :D <3 | |
| Apr 1, 2021 at 23:08 | history | edited | Alexis | CC BY-SA 4.0 |
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| Apr 1, 2021 at 20:37 | comment | added | Stephan Kolassa | Micro-nitpick: you can use splines in quantile regression just fine, so the centrality of $y$ is irrelevant. So here is my +1. | |
| Apr 1, 2021 at 18:14 | history | edited | Alexis | CC BY-SA 4.0 |
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| Apr 1, 2021 at 17:38 | history | edited | Alexis | CC BY-SA 4.0 |
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| Apr 1, 2021 at 17:00 | comment | added | usεr11852 | I like this answer (+1). Probably with the exception of Kaplan-Meier I can't think something that doesn't have some reasonable but core underlying statistical assumption. Realistically most smoothers assume some notion of local linearity. | |
| Apr 1, 2021 at 16:54 | history | edited | Alexis | CC BY-SA 4.0 |
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| Apr 1, 2021 at 16:45 | comment | added | Alexis | @whuber I would love your insight on how my answer works… and if you think I can improve it. My answer is informed by my understanding of a comment or two you have made over the years. | |
| Apr 1, 2021 at 16:43 | history | answered | Alexis | CC BY-SA 4.0 |