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RMSE plot of Monte Carlo simulation

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Sebsatien
Sebsatien 2020-12-2
评论： Sebsatien 2020-12-4
Hello
I would like your help for this problem that has been bothering me for quite some time.
So, I want to plot the Monte Carlo Simulation of the Root Mean Square Error (RMSE) between a parameter and an estimated parameter
I've written the attached code which was easy enough but the problem is that the plot seems off. From what I know RMSE is supposed to decrease with the number of simulations not oscillate like this.
What I am doing wrong ? And what to do to have a correct plot ?
Thanks in advance
Here's the code :
param = 1 ;
paramest = 1.2 ;
N = 1000;
for n = 1:N
y = param*rand(1,N);
yest = paramest*rand(1,N);
RMSE(n) = sqrt(mean((y - yest).^2));
end
plot(RMSE)
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Sebsatien
Sebsatien 2020-12-2
oh ok. Then I must have misunderstood MC simulation... I thought it was supposed to give the response of a given model in regards to random inputs.
So , I generated "N" random inputs and I wanted to find an output for each input before calculating the RMSE of all the outputs.
So what am I missing ?
Thanks for the reply
KSSV
KSSV 2020-12-2
You are missng the exact problem definition.

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采纳的回答

Jeff Miller
Jeff Miller 2020-12-2
RMSE is not supposed to decrease with the number of iterations, but it should stabilize.
Your plot oscillates because each point is based on a single estimate--the one generated at each value of n--nothing is being computed cumulatively across iterations. Try changing the end of your script to this:
cumRMSE = cumsum(RMSE) ./ [1:N];
plot(cumRMSE)

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