RSAVS_Get_Psi: Compute psi_vec

In fenguoerbian/RSAVS: Robust Subgroup Analysis and Variable Selection

Compute psi_vec

Description

This function computes the psi_vec needed by the algorithm.

Usage

RSAVS_Get_Psi(y_vec, l_type = "L1", l_param = NULL)

Arguments

y_vec	numeric vector
l_type	character string, type of loss function. "L1": l-1 loss(absolute value loss) "L2": l-2 loss(squared error loss) "Huber": Huber loss. Its parameter is given in l_param. Default value is "L1".
l_param	numeric vector containing necessary parameters of the corresponding loss function. The default value is NULL.

Details

In the algorithm, when all \mu are shrinked to the same value, we have

\mu_0 = \mathrm{argmin}_{\mu} \sum_i\rho(y_i - \mu)

and

psi\_vec = (\psi(y_1 - \mu_0), \cdots, \psi(y_n - \mu_0))

where \psi = \partial \rho.

Value

the psi_vec

Note

there is a SIGN different between this psi_vec and \partial \rho w.r.t \mu

for non-differential loss like L1 at 0, the derivative at 0+ is returned.

fenguoerbian/RSAVS documentation built on Oct. 25, 2024, 3:16 p.m.