Root Mean Squared Error.  Root Squared of Linear Loss scenarios calculated with Matrix of Scenarios or Expected Matrix of Products. By definition, it is an average of squared  loss scenarios.

 

Syntax

 
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 Root Mean Squared Error is used in optimization or calculation problems PSG automatically calculates and includes in the solution report two outputs:

 

 

Mathematical Definition

Root Mean Squared Error is calculated on the matrix of scenarios matrix as follows:

,

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).

 

Root Mean Squared Error is calculated on expected matrix of products matrix_cov as follows:

where

is a Square Root Quadratic function.

 

is an argument of Root Mean Squared Error function.

 

Example

 

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 Normal Independent, Root Mean Squared Error Normal Dependent, Koenker and Basset Error, Rockafellar Error