最大似然法在matlab中估计均值和协方差的应用

Question

我试图用matlab中的最大似然法计算估计均值和协方差.我是Matlab的新手，有一些问题我喜欢在这里被解决。

我使用以下代码：

clear all;
%Visualization of 2D Gaussian Distribution
% Mean of the distribution
mu = [1 -1]; 
% Covariance matrix (Must be symetric)
sigma = [ 2 1 ; 1 3 ];

% Samples
X = mvnrnd(mu,sigma,1000);

analytical_mean = mean(X);
analytical_cov = cov(X);

N = size(X,1);

estimated_mean = sum(X)/N;
summation = 0;
for i=1:N,
 row = X(i,:);
 tmp1= (row - estimated_mean);
 tmp2 =  tmp1';
 summation = summation + tmp2;
end  

covar = summation/N;

现在analytical_mean和estimated_mean是相等的，但是我计算出来的协方差covar不是像analytical_cov这样的矩阵。好的，我需要知道如何正确计算covar。

我所用的方程式如下：

​

​

Answer 1

你可以试试这个

[m,n] = size(X);
estimated_mean = sum(X)/m;
tmp=zeros(m,n);
for i=1:n
tmp(:,i)= ((X(:,i) - estimated_mean(i)));
end
covar = (tmp.'*tmp)/m;