asymptoticEfficiency computes the theoretical asymptotic efficiency
for an M-estimator for various types of equations.
asymptoticVariance(
psi,
equation = c("location", "scale", "eta", "tau", "mu"),
dimension = 1
)asymptoticEfficiency(
psi,
equation = c("location", "scale", "eta", "tau", "mu"),
dimension = 1
)
findTuningParameter(
desiredEfficiency,
psi,
equation = c("location", "scale", "eta", "tau", "mu"),
dimension = 1,
interval = c(0.15, 50),
...
)
object of class psi_func
equation to base computations on. "location" and
"scale" are for the univariate case. The others are for a
multivariate location and scale problem. "eta" is for the shape of
the covariance matrix, "tau" for the size of the covariance matrix
and "mu" for the location.
dimension for the multivariate location and scale problem.
scalar, specifying the desired asymptotic efficiency, needs to be between 0 and 1.
interval in which to do the root search, passed on to
uniroot.
passed on to uniroot.
The asymptotic efficiency is defined as the ratio between the asymptotic variance of the maximum likelihood estimator and the asymptotic variance of the (M-)estimator in question.
The computations are only approximate, using numerical integration in the general case. Depending on the regularity of the psi-function, these approximations can be quite crude.
Maronna, R. A., Martin, R. D., Yohai, V. J., & Salibián-Barrera, M. (2019). Robust statistics: theory and methods (with R). John Wiley & Sons., equation (2.25)
Rousseeuw, P. J., Hampel, F. R., Ronchetti, E. M., & Stahel, W. A. (2011). Robust statistics: the approach based on influence functions. John Wiley & Sons., Section 5.3c, Paragraph 2 (Page 286)