RobustMeans

Simple package implementing some Robust mean estimator.

mean(A::AbstractArray, Estimator::EmpiricalMean)

The usual empirical mean estimator. Nothing fancy.

LeeVal(x, δ; α₀ = 0.0)

Reference: Optimal Sub-Gaussian Mean Estimation in R by Lee et Valiant

MinskerNdaoud(x, k, p)

Reference: Robust and efficient mean estimation: an approach based on the properties of self-normalized sums

MedianOfMean(x::AbstractArray, k::Integer)

Compute the Median of Mean with k groups (it does not permute the samples)

TrimmedMean(x::AbstractArray, k::Integer)

Compute the Trimmed Mean thresolding data smaller α or larger than β

TrimmedMean(z, ε)

Z_estimator(x::AbstractArray, α, ψ::Function; ini = median(x))

Implement Z estimators given a

bound(estimator, δ, n::Int) Give the theoritical bound B such that for the estimator #TODO! correction math formula

\[\mathbb{P}( |X- \mathbb{E}(X)|/\sigma \leq B) \leq \delta\]

" sqrt(2log(1 / δ) / n) # Multiply by a factor (1 + o(1)) where o(1) = (1+O(sqrt(log(1/δ)/n)))*(1+log(log(1/δ))/log(1/δ)) goes to zeros with (log(1/δ)/n, δ)→ (0, 0) see https://www.youtube.com/watch?v=Kr0Kl_sXsJM Q&A

ψ_Catoni(x)

Catoni's influence function

ψ_Huber(x)

ψ_Huber's influence function

mean(A::AbstractArray, Estimator::MoM)

The Median of Mean estimator.

mean(A::AbstractArray, Estimator::Catoni, kwargs...)

Reference: Catoni

mean(A::AbstractArray, δ::Real, Estimator::EmpiricalMean)

The usual empirical mean estimator, for convenience, we authorize the extra dummy argument δ.

mean(A::AbstractArray, Estimator::Huber, kwargs...)

Reference: Huber

mean(A::AbstractArray, Estimator::δLeeValiant; kwargs...)

Reference: Optimal Sub-Gaussian Mean Estimation in R by Lee et Valiant

mean(A::AbstractArray, Estimator::MoM)

mean(A::AbstractArray, Estimator::δMinskerNdaoud; kwargs...)

Reference: Robust and efficient mean estimation: an approach based on the properties of self-normalized sums

 mean(A::AbstractArray, Estimator::TrimmedMean)

mean(A::AbstractArray, Estimator::TrimmedMean)

The Trimmed Mean estimator. (p)

mean(A::AbstractArray, Estimator::Z_Estimator)

A Z estimator given an influence function x->ψ(x) and a scaling parameter α.