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Combining Error Terms into a General Error Term

Lets say I have 4 error terms:

$$e_1,e_2,e_3,e_4$$

Each of these error terms come from different simulations of data using different classification methods.

Let $gamma$ be the number of empirical data and $delta$ be the number of simulated data and $d$ is the difference of the two. The error terms are $frac{d}{gamma}$. An example is as follows (in this case the difference $d$ is always 5):

$$gamma = 500, delta = 505 implies e_1 = frac{5}{500} =1% $$
$$gamma = 50, delta = 45 implies e_2 = frac{5}{50} = 10% $$
$$gamma = 30, delta = 35 implies e_3 = frac{5}{30} =16% $$
$$gamma = 1, delta = 6 implies e_4 = frac{5}{1} = 500% $$

I want to combine these error terms into one general error term, however I want to make an emphasis on certain error terms. Because, using the average of these terms would make an error result that is too susceptible to outliers. $e_3$ is the most accurate in my opinion. Is it suitable to create a linear combination of these error terms to define a general error term?

If so, it would look like this:
$$ E = alpha_1 e_1 + alpha_2 e_2 + alpha_3 e_3 + alpha_4 e_4 , forall alpha_iinmathbb{R}$$

If this is allowable, what would be the best way to define alpha values s.t. $0<=E<=1$ OR $0%<=E<=100%$ ?

(Note: This is not the same as using a regression model).

Cross Validated Asked on January 1, 2021

1 Answers

One Answer

A common error calculation is MAPE (Mean Absolute Percent Error) which is often used in demand forecasting.

$$frac{sum|(actuals-forecasts)|}{sum(actuals)}$$

In your case it seems that the simulations are the forecasts and the empirical data are the actuals.

It is similar to what you are doing except all the numerators are summed up and all the denominators are summed up before dividing so that your last error term won't have such a dramatic effect. There are also several variations of MAPE such as weighted MAPE which you may find helpful if you have another variable such as sales that you want to weight your error terms with.

Answered by Kristen Bystrom on January 1, 2021

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