(New page: MATLAB has a "[http://www.mathworks.com/access/helpdesk/help/toolbox/stats/mle.html mle]" function for maximum likelihood estimation. I think that this function is useful to verify the re...) |
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MATLAB has a "[http://www.mathworks.com/access/helpdesk/help/toolbox/stats/mle.html mle]" function for maximum likelihood estimation. I think that this function is useful to verify the result of hw2 if you have MATLAB. I try to find the effect of the sample size in MLE using "mle" function because the number of samples is critical for estimation. To do this, I generate samples from normal distribution with mean as 0 and std as 5. The below graph shows the results of MLE according to the number of samples. | MATLAB has a "[http://www.mathworks.com/access/helpdesk/help/toolbox/stats/mle.html mle]" function for maximum likelihood estimation. I think that this function is useful to verify the result of hw2 if you have MATLAB. I try to find the effect of the sample size in MLE using "mle" function because the number of samples is critical for estimation. To do this, I generate samples from normal distribution with mean as 0 and std as 5. The below graph shows the results of MLE according to the number of samples. | ||
[[Image:mle_samples.jpg]] | [[Image:mle_samples.jpg]] | ||
| + | |||
| + | The code for this graph is like below. | ||
| + | |||
| + | samples_step = 3; | ||
| + | num_samples = samples_step:samples_step:10000; | ||
| + | len = length(num_samples); | ||
| + | mu = 0; | ||
| + | sigma = 5; | ||
| + | muhat = zeros(1, len); | ||
| + | sigmahat = zeros(1, len); | ||
| + | for x = num_samples | ||
| + | data = mu + sigma * randn(1, x); | ||
| + | phat = mle(data(1, :)); | ||
| + | muhat(1, x/samples_step) = phat(1); | ||
| + | sigmahat(1, x/samples_step) = phat(2); | ||
| + | end | ||
| + | plot(num_samples, muhat); | ||
| + | hold on; | ||
| + | plot(num_samples, sigmahat); | ||
--[[User:Han84|Han84]] 22:49, 2 April 2010 (UTC) | --[[User:Han84|Han84]] 22:49, 2 April 2010 (UTC) | ||
Revision as of 19:00, 2 April 2010
MATLAB has a "mle" function for maximum likelihood estimation. I think that this function is useful to verify the result of hw2 if you have MATLAB. I try to find the effect of the sample size in MLE using "mle" function because the number of samples is critical for estimation. To do this, I generate samples from normal distribution with mean as 0 and std as 5. The below graph shows the results of MLE according to the number of samples.
The code for this graph is like below.
samples_step = 3; num_samples = samples_step:samples_step:10000; len = length(num_samples); mu = 0; sigma = 5; muhat = zeros(1, len); sigmahat = zeros(1, len); for x = num_samples
data = mu + sigma * randn(1, x); phat = mle(data(1, :)); muhat(1, x/samples_step) = phat(1); sigmahat(1, x/samples_step) = phat(2);
end plot(num_samples, muhat); hold on; plot(num_samples, sigmahat);
--Han84 22:49, 2 April 2010 (UTC)
