RMSE plot of Monte Carlo simulation

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)

[KSSV]

There is no simulation in your code...you are creating two sets of random numbers and finding the RMSE, offcourse you will end up with the same plot what you got.

[Sebsatien]

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]

You are missng the exact problem definition.

Answer 1

[Jeff Miller]

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)

[Sebsatien]

Thank you very much my good sir, you saved my life. =)