Koenker and Basset Error (kb_err)
Contents
Koenker and Basset Error. Koenker and Bassett error of Linear Loss scenarios calculated with Matrix of Scenarios. Used for estimation of Value-at-Risk (i.e., percentile) in Linear Regression.
Syntax
kb_err(α, matrix) |
short call; |
kb_err_name(α, matrix) |
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.
is a parameter.
Output
When function Koenker and Basset 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
Koenker and Basset Error is calculated as follows:
,
where
is Loss Function defined by Matrix of scenarios matrix;
is parameter;
, 
are Partial Moment Penalty functions.
is an argument of function.
Example
Case Studies with Koenker and Basset 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, Rockafellar Error