quantile / median / depth methods

[fabian-s]

... not feasible for feval_irreg

... for feval_reg: use MBD? (see roahd:::MBD.default, e.g.), other depths as in rainbow:::fdepth, ddalpha::depthf?

... for fbase: could use multivariate depths on coefs directly (but consider scaling of basis functions)

[fabian-s]

@jeff-goldsmith : any preferences / any experience which depths work well and should be the default?

[jeff-goldsmith]

i'd vote roahd::MBD.default of these options, although i haven't used it much myself.

i guess we'll trust users to compute quantile / median curves for smooth feval_reg data?

[fabian-s]

Even cheaper and more intuitive alternative: half region depth

[jeff-goldsmith]

I think there’s a super-computationally efficient implementation of MBD, but I’d have to dig around for it. Or by “cheaper” do you mean “fewer dependencies”? On Mar 14, 2018, at 10:54 AM, Fabian Scheipl <[email protected]<mailto:[email protected]>> wrote: Even cheaper and more intuitive alternative: half region depth<https://www.sciencedirect.com/science/article/pii/S0167947310004123> — You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub<https://github.com/fabian-s/tidyfun/issues/19#issuecomment-373050311>, or mute the thread<https://github.com/notifications/unsubscribe-auth/AH_3hxsSTzspOqLsKHv2cp0Lno7d_Wduks5teS9CgaJpZM4SVFLu>.

[fabian-s]

yeah, I know, roahd uses the trick you probably mean. I did mean cheaper computationally, but come to think about it this might not actually be true....

[fabian-s]

Serfling, R., & Wijesuriya, U. (2017). Depth-based nonparametric description of functional data, with emphasis on use of spatial depth. Computational Statistics & Data Analysis, 105, 24-45.
seems like a good resource for this

• add more depths (MBD specifically does NOT detect spike outliers)
• figure out quantile method from above paper / other lit (or simply use MEI?)
• use quantiles to define rank/order and proper min/max methods?

More Lit:

Center-Outward Distribution Functions, Quantiles, Ranks, and Signs: https://arxiv.org/abs/1806.01238

Nadja&Thomas seem to have used some of this stuff in https://arxiv.org/pdf/1906.03151.pdf, ask them?

depths for irregular funs/ functional fragments: https://www.tandfonline.com/doi/abs/10.1080/10618600.2022.2070171

"random" depth: solid theory + comp. efficient (?)
https://www.ma.imperial.ac.uk/~hbattey/STS532.pdf
https://arxiv.org/pdf/2206.13897.pdf

[fabian-s]

see also experiments in attic/dev-quantile.Rmd