kappa_and_c: Constants for tau-scale estimator
In meszre/tauPFC: Computes Robust Estimators for the PFC Model

Description Usage Arguments Details Value Note References Examples

This function computes the constants to define the rho-functions (in the rho quasi-optimal family) and expectations in order to obtain high efficiency and the maximum possible breakdown point (0.5). The values are obtained by solving the equations that relate the rho-functions with these characteristics of robustness

1	kappa_and_c(p, efficiency)

`p`	dimension of the vector of the response variable
`efficiency`	efficiency required, values between 0 and 1, excluding extremes

For more details about the way the constants are chosen, see Bergesio et al. (2020). For the definition of rho quasi optimal family of functions, see Muler and Yohai (2002) and Salibian-Barrera et al. (2016).

The result is returned as a list containing

`c1`	tuning parameter such that ρ₁ is strictly increasing in [0; c₁] and constant for values greater than c₁.
`c2`	tuning parameter such that ρ₂ is strictly increasing in [0; c₂] and constant for values greater than c₂.
`k1`	constant value involved in the ρ₁ expectation.
`k2`	constant value involved in the ρ₂ expectation.

It is not an efficient procedure, so it can take some seconds.

Bergesio, A., Szretter Noste, M. E. and Yohai, V. J. (2020). A robust proposal of estimation for the sufficient dimension reduction problem.

Muler, N. and Yohai, V. J. (2002). Robust estimates for arch processes. Journal of Time Series Analysis, 23(3):341-375.

Salibian-Barrera, M., Van Aelst, S. and Yohai, V. J. (2016). Robust tests for linear regression models based on τ-estimates. Computational Statistics & Data Analysis 93:436-455.