Matlab函数：极大似然估计

-function para,standard_deviation,fv=my_mle(fun,para0,varargin)%estimate parameters and standard errors when using maximium likelihood estimation(MLE)%input%fun: a function defined by users for calculating log probability density function (pdf) and negative sum of logarithm of pdf%para0 : given initial parameters% varargin: other needed parameters required by fun%output%para: estimated parameters% standard_deviation: standard deviations of estimated parameters% fv: maximized likelihood function value%example1: estimate mean and standard deviation by realizations of a%random variable which is normally distributed%function f=mynormpdfsum(x,num,y)%yy=1/sqrt(2*pi)/x(2)*exp(-(y-x(1).2/2/x(2)2);%if num=1 %(note: it must be set to 1)%f=log(yy);%else f=-sum(log(yy);end%y=2+3*randn(5000,1);%para,standard_deviation=my_mle(mynormpdfsum,0;2,y)% example2:estimate coefficients in a linear regression% clear% x=randn(500,1);% y=2+3*x+randn(500,1);% para,standard_deviation,fv=my_mle(mynormpdfsum001,1;2;3,y,x)% % function f=mynormpdfsum001(para,num,y,x)% yy=1/sqrt(2*pi)/para(3)*exp(-(y-para(1)-para(2)*x).2/2/para(3)2);% if num=1 %(note: it must be set to 1)% f=log(yy);% else f=-sum(log(yy);endpara0=para0(:);para,fv=fminsearch(fun,para0,2,varargin:);fv=-fv;d=numericalfirstderivative(fun,para,1,varargin:);standard_deviation=sqrt(diag(pinv(d*d);%function f=numericalfirstderivative(fun,parameter,varargin)% input:% fun: the name of a function% parameter: given parameter with respect to which first-order derivative is calculated% varargin: other needed parameters required by fun% output:% f: numerical first order derivative of fun at parametern=length(parameter);for i=1:na=zeros(n,1);a(i)=min(parameter(i)*1e-6,1e-5);y1(:,i)=feval_r(fun,parameter+a,v