Mean Square Error (meansquare_err)
Contents
Mean Square Error. Mean Square of Linear Loss scenarios calculated with Matrix of Scenarios or Expected Matrix of Products.
Syntax
meansquare(matrix) |
short call for case of matrix of scenarios; |
quadratic(matrix_cov) |
short call for case of expected matrix of products; |
meansquare_name(matrix) |
call with optional name; |
quadratic_name(matrix_cov) |
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_cov is a PSG matrix:
where the header row contains names of variables. Other rows contain numerical data.
,
, 
.
Output
When function Mean Square 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
Mean Square Error is calculated on the matrix of scenarios matrix as follows::
,
where
random vector 
has components 
and J vector scenarios, 
,
random value 
, which is the i-th component of the random vector, 
, has J discrete scenarios 
,
is probability of the scenario 
.
is Loss Function (See section Loss and Gain Functions).
Mean Square Error is calculated on expected matrix of products matrix_cov as follows:
,
where
is a Quadratic function.
is an argument of Mean Square Error function.
Example
See also
Mean Absolute Error, Mean Absolute Error Normal Independent, Mean Absolute Error Normal Dependent, 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, Rockafellar Error