The EIVE-CGA Estimator

eive(;
dirtyx::Vector{T},
y::Vector{T},
otherx::Union{Nothing, Matrix{T}, Vector{T}},
popsize::Int = 50,
numdummies::Int = 10,
rng::RNGType = MersenneTwister(1234))::SimpleEiveResult where {T<:Real, RNGType<:AbstractRNG}

Description:

The method searches for a set of dummy (binary) variables that separates the erroneous independent variable into clean part and error part. The clean part is then used in the main regression estimation. Those dummy variables minimize the sum of squares of residuals of the main regression. In other terms the methods searches for a set of proxy variables that do not exist in real. Please see the reference for details.

Arguments:

• dirtyx: Independent variable measured with some error
• y: Dependent variable
• otherx: Matrix of other independent variables
• popsize: Number of individuals in the population (optional)
• numdummies: Number of dummy variables to use (optional)
• rng: Random number generator (optional)

Examples

julia> import Random
julia> using ErrorsInVariables
julia> rng = Random.MersenneTwister(1234)
julia> n = 30
julia> deltax = randn(rng, n) * sqrt(3.0)
julia> cleanx = randn(rng, n) * sqrt(7.0)
julia> e = randn(rng, n) * sqrt(5.0)
julia> y = 20.0 .+ 10.0 .* cleanx .+ e
julia> dirtyx = cleanx + deltax
julia> eive(dirtyx = dirtyx, y = y, otherx = nothing) 

EiveResult([20.28458307772922, 9.456757289676714])

julia> X = hcat(ones(n), dirtyx);

julia> # Biased OLS estimates:
julia> X \ y
2-element Vector{Float64}:
 17.94867860059858
  5.8099584879737876

References

Satman, M. Hakan, and Erkin Diyarbakirlioglu. "Reducing errors-in-variables bias in linear regression using compact genetic algorithms." Journal of Statistical Computation and Simulation 85.16 (2015): 3216-3235.