Matlab函数：极大似然估计

1、functionpara,standard_deviation,fv=my_mle(fun,para0,varargin)%estimateparametersandstandarderrorswhenusingmaximiumlikelihoodestimation(MLE)%input%fun:afunctiondefinedbyusersforcalculatinglogprobabilitydensityfunction(pdf)andnegativesumoflogarithmofpdf%para0:giveninitialparameters%varargin:otherneede

2、dparametersrequiredbyfun%output%para:estimatedparameters%standard_deviation:standarddeviationsofestimatedparameters%fv:maximizedlikelihoodfunctionvalue%example1:estimatemeanandstandarddeviationbyrealizationsofa%randomvariablewhichisnormallydistributed%functionf=mynormpdfsum(x,num,y)%yy=l/sqrt(2*pi)/

3、x(2)*exp(-(y-x(l).人2/2/x(2)人2);%ifnum=1%(note:itmustbesetto1)%f=log(yy);%elsef=-sum(log(yy);end%y=2+3*randn(5000,1);%para,standard_deviation=my_mle(mynormpdfsum,0;2,y)%example2:estimatecoefficientsinalinearregression%clear%x=randn(500,1);%y=2+3*x+randn(500,1);%para,standard_deviation,fv=my_mle(mynor

4、mpdfsum001,1;2;3,y,x)%functionf=mynormpdfsum001(para,num,y,x)%yy=l/sqrt(2*pi)/para(3)*exp(-(y-para(l)-para(2)*x).人2/2/para(3)人2);%ifnum=1%(note:itmustbesetto1)%f=log(yy);%elsef=-sum(log(yy);endpara0=para0(:);para,fv=fminsearch(fun,para0,2,varargin:);fv=-fv;d=numericalfirstderivative(fun,para,1,varar

5、gin:);standard_deviation=sqrt(diag(pinv(d*d);%functionf=numericalfirstderivative(fun,parameter,varargin)%input:%fun:thenameofafunction%parameter:givenparameterwithrespecttowhichfirst-orderderivativeiscalculated%varargin:otherneededparametersrequiredbyfun%output:%f:numericalfirstorderderivativeoffunatparametern=length(parameter);fori=1:na=zeros(n,1);a(i)=min(parameter(i)*1e-6,1e-5);y1(:,i)=feval_r(fun,parameter+a,var