how do one weight lsqcurvefit with standard error from dependent data?

Question

Arbol 2017-10-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/361650-how-do-one-weight-lsqcurvefit-with-standard-error-from-dependent-data

I ran into this post about weighted lsqcurvefit:

https://www.mathworks.com/matlabcentral/answers/48802-nonlinear-fit-with-constraints-in-r2012b

Shouldn't the weight from:

Weights = 1./(N.*SE.^2);
nonlinmodelW = @(B,t) Weights .* nonlinearmodel(B,t);
x = lsqcurvefit(nonlinmodelW,x0,xdata,ydata,lb,ub);

Be:

Weights = 1./(N.*SE);
nonlinmodelW = @(B,t) Weights .* nonlinearmodel(B,t);
x = lsqcurvefit(nonlinmodelW,x0,xdata,ydata.*Weights,lb,ub);

I noticed it did mentioned earlier in the post the weight ydata as well. The reason I don't square SE is because the function value return:

sum([(nonlinmodelW(B,xdata) - ydata)/(N*SE)].^2);
so if you weight with Weights = 1./SE it will returns the above equation, rather than:
the quadrature of the weight:
sum([(nonlinmodelW(B,xdata) - ydata)/((N*SE).^2)].^2);

Also, on the standard error of the fitted parameters, I found other source that it can be found by:

v=residuals from nonlinear least squares;
J=jacobian;
Q_xx = resnorm*inv(J'*J)/length(ydata);
% Precision measures ,i.e. the standard deviation of each parameter
Precision_of_solved_parameters = sqrt(diag(Q_xx));

Can anyone confirm this standard deviation? The code Star Strider provided will give error.