Mean Square Error (meansquare)
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.
,
, 
,
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 Square Root Quadratic function.
is an argument of Mean Square Error function.
Example
See also
Root Mean Squared Error, Root Mean Squared Error Normal Independent, Root Mean Squared Error Normal Dependent, Standard Risk, Standard Gain, Standard Risk Normal Independent, Standard Gain Normal Independent, Standard Risk Normal Dependent, Standard Gain Normal Dependent, Standard Deviation, Mean Square Error Normal Independent, Mean Square Error Normal Dependent, Variance