Rockafellar Error (ro_err)
Contents
Rockafellar Error. Rockafellar error of Linear Loss scenarios calculated with Matrix of Scenarios. Used for estimation of Mixed Value-at-Risk in Linear Regression. Conditional Value-at-Risk approximately equals the discrete Mixed Value-at-Risk and it can be estimated using Rockafellar error in Linear Regression.
Syntax
ro_err(matrix, matrix_coef) |
short call; |
ro_err_name(matrix, matrix_coef) |
call with optional name. |
Parameters
matrix is a Matrix of Scenarios:
where the header row contains names of variables (except scenario_probability, and scenario_benchmark). Other rows contain numerical data. The scenario_probability, and scenario_benchmark columns are optional.
matrix_coef is a PSG matrix:
where the header row contains names of variables: 
. Other rows contain numerical data.
Output
When function Rockafellar Error is used in optimization or calculation problems PSG automatically calculates and includes in the solution report two outputs:
pseudo_R2_function_name |
|
contributions(function_name) |
Mathematical Definition
Rockafellar Error is calculated as follow:
subject to
where
is Loss Function defined by matrix;
are parameters defined by matrix_coef which should satisfy conditions:
,
, 
.
is an argument of function.
Example
Case Studies with Rockafellar Error
See also
Mean Absolute Error, Mean Absolute Error Normal Independent, Mean Absolute Error Normal Dependent, Mean Square Error, Mean Square Error Normal Independent , Mean Square Error Normal Dependent, Root Mean Squared Error, Root Mean Squared Error Normal Independent, Root Mean Squared Error Normal Dependent, Koenker and Basset Error