Timeline for What is a strict definition of U-shaped relationship?
Current License: CC BY-SA 3.0
14 events
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| Jul 19, 2019 at 11:23 | comment | added | scottkosty | @Parseltongue unfortunately I've made zero progress directly on that package. I would like to work on better non-parametric methods before that general package. It's only indirectly related, but I've been working on a paper for a new quasi-convexity restriction method (arxiv.org/abs/1809.01038). However, it will take time for that work to translate into U-shapes. Probably I won't work on the general R package still for another couple of years. | |
| Jul 19, 2019 at 0:25 | comment | added | Parseltongue | @scottkosty, any progress on the package you reference at the bottom of your post? | |
| Nov 29, 2017 at 16:07 | history | bounty ended | Neznajka | ||
| Nov 29, 2017 at 16:07 | vote | accept | Neznajka | ||
| Nov 25, 2017 at 22:05 | comment | added | scottkosty | @amoeba As an example, see the function labeled "sin" in Figure 2 of my paper. I believe (although I have not checked) that the two lines test would give asymptotic inference suggesting that "sin" is a U-shape, even though it has three turning points. | |
| Nov 25, 2017 at 21:56 | comment | added | scottkosty | @amoeba When I use "U-shape" I'm referring to definition 4 above (a function with exactly one turning point). For my test, the null is U-shapedness. What I mean is that asymptotically the null of U-shapedness will be rejected if there is any violation of U-shapedness in the underlying regression function (e.g. there are two turning points). This is not the case for Uri's test because the two lines test is about the average derivative. So there can be wiggles without necessarily leading to asymptotic inference against U-shapes. | |
| Nov 25, 2017 at 20:41 | comment | added | amoeba | I am sorry I still don't understand this bit that I quoted above: "Do you want a test that rejects the null hypothesis because of a small violation of U-shapedness?" Can you please explain what this means? Are you asking if one wants a test that rejects the null [of no U-shape; i.e. a test that concludes that there is a U-shape] if there is "a small violation of U-shapedness" i.e. if there actually is no U-shape but almost a U-shape? I am pretty confused by what you mean here. | |
| Nov 25, 2017 at 18:17 | comment | added | whuber♦ | (+1) Very nice, thoughtful, authoritative overview. Welcome to our site! | |
| Nov 25, 2017 at 16:48 | comment | added | scottkosty |
@amoeba the nulls of the qmutest package are quasi-convexity and monotonicity (corresponding to the R functions cbquasi and cbmono). Combined, the tests give inference about U-shapes. Indeed this is different from the OLS quadratic specification and Uri's two lines test. I made edits to add information on the null hypotheses.
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| Nov 25, 2017 at 16:41 | history | edited | scottkosty | CC BY-SA 3.0 |
discuss quasi-convex-but-not-monotone
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| Nov 25, 2017 at 11:33 | comment | added | amoeba | (I am glad to see that you favourably mention Uri's paper: I mentioned it in my answer here and it was heavily criticized in the comments.) | |
| Nov 25, 2017 at 11:32 | comment | added | amoeba | +1. I am a bit confused by this sentence: "Do you want a test that rejects the null hypothesis because of a small violation of U-shapedness?" I assume that the null is that there is no U-shapedness, so that a sufficiently small p-value were an evidence of U-shapedness, is that correct? | |
| Nov 25, 2017 at 10:02 | review | First posts | |||
| Nov 25, 2017 at 10:35 | |||||
| Nov 25, 2017 at 10:00 | history | answered | scottkosty | CC BY-SA 3.0 |