asymptoticVariance {robustlmm}

Compute Asymptotic Efficiencies

Description

asymptoticEfficiency computes the theoretical asymptotic efficiency for an M-estimator for various types of equations.

Usage

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),
  ...
)

Arguments

psi

object of class psi_func

equation

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

dimension for the multivariate location and scale problem.

desiredEfficiency

scalar, specifying the desired asymptotic efficiency, needs to be between 0 and 1.

interval

interval in which to do the root search, passed on to uniroot.

...

passed on to uniroot.

Details

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.

References

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)