Let var, std, cor take a CovarianceEstimator

[tpgillam]

Currently StatsBase.jl defines CovarianceEstimator here, and defines methods of cov that take one as the first argument.

I think it would be convenient to allow similar dispatches for related methods. These could have fairly simple default implementations, something like the following (untested) sketch:

var(ce::CovarianceEstimator, x::AbstractVector; kwargs...) = cov(ce, x; kwargs...)

std(ce::CovarianceEstimator, args...; kwargs...) = sqrt(var(ce, args...; kwargs...))

cov2cor!(x::AbstractMatrix) = cov2cor!(x, sqrt.(diag(x)))

cor(ce::CovarianceEstimator, x::AbstractVector, y::AbstractVector) = cov2cor!(cov(ce, x, y))
cor(ce::CovarianceEstimator, X::AbstractMatrix; kwargs...) = cov2cor!(cov(ce, X; kwargs...))
cor(ce::CovarianceEstimator, X::AbstractMatrix, w::AbstractWeights; kwargs...) = cov2cor!(cov(ce, X, w; kwargs...))

Any thoughts or objections to this? I'm happy to make a PR for more concrete discussion if this seems reasonable :)

[nalimilan]

Why not, but I guess you'd also expect CovarianceEstimation.jl (or another package) to define the corresponding functions? Otherwise it wouldn't be super useful.

@mateuszbaran Any opinion?

[tpgillam]

I’d propose including something like the default implementations above in StatsBase.

At that point, so long as the first dispatch of cov is available (since that is effectively var), it might not generally be necessary to override for specific estimators, I would hope?

[nalimilan]

Ah, got it. Yes, makes sense. Let's hear what @mateuszbaran says though.

[mateuszbaran]

I think this definitely makes sense for cor but so far I haven't seen the need for fancy methods of estimating variance and standard deviation.

[tpgillam]

the need for fancy methods of estimating variance and standard deviation.
For example, my current case would be mateuszbaran/CovarianceEstimation.jl#80 - specifically, I would like to provide equivalent functions for biweight_midvariance and biweight_scale](https://docs.astropy.org/en/stable/api/astropy.stats.biweight.biweight_scale.html).

To me, it seems nice to just implement a Biweight (or similar name) covariance estimator, and then be able to get these things with var(Biweight(), ...) and std(Biweight(), ...).

[I would be surprised if there aren't other regularisation techniques that would also fit this pattern - winsorising might be one off the top of my head]

[mateuszbaran]

Sure, if you have a use for that, don't mind my comment 🙂

[nalimilan]

OK feel free to make a PR @tpgillam then.