How can I generate error for a minimum value from lsqcurvefit data?

I am using lsqcurvefit function to generate a fitting curve to a set of data. From this, I use the minimum value for a further calculation/result for which I used fminbnd. I also must identify the error in this calculation. Clearly, there must be some error associated with the fitting which thus causes error to appear in the minimum. Does anyone know how to get this error accurately?

Thank you so much for your help.

Answer 1

[Matt J]

When called with 3 outputs, LSQCURVEFIT will return the residual,

 [x,resnorm,residual] = lsqcurvefit(...)

You can apply any error metric you want to the residual, once you have it.

[Stacy]

I am aware that I can get the residual and in fact I use this in other aspects of my program with a separate use of lsqcurvefit. However, my problem is going from this residual to get an error for the x-axis location of the minimum value of the curve I get from lsqcurvefit. I guess I am just confused on how this residual will help me. Is it the actual error that I want or do I need to do some other calculation to get it?

[Matt J]

my problem is going from this residual to get an error for the x-axis location of the minimum value of the curve I get from lsqcurvefit.

Well, you wouldn't use the residual for that. Once you have your fitted curve, you should be able to get "the x-axis location of the minimum value of the curve" from fminsearch or fminbnd.

Once you have this x-axis location, you would need to compare it to something in order to define an "error" for it. Do you know the true location of the min. of the curve? If you do, you would just compare the estimate that FMINBND gives you to this known true value. If you don't know the true location, it's not clear how you wish to define the "error".

[Stacy]

Right. This is the problem. The curve the I have from lsqcurvefit is only a fit. Thus I do not know the true location of the minimum since the true minimum lies between two points of my data. Thus, I wanted to see if there was any way of figuring out how close this x-axis location that I get from fminbnd is to the true location of this minimum since there is error/uncertainty from a curve fit. So, if I have nothing concrete to actually compare it to, does this mean that I cannot actually get an error? I was thinking that I might be able to extract some sort of uncertainty or error in this minimum from lsqcurvefit since this is where the error (ie residuals) originally came from.

[Matt J]

I assume you know the statistical variation of your input data, or at least are prepared to assume that your residuals are Gaussian with some known standard deviation, sigma.

I think the only simple thing to do is to start with the fitted curve that lsqcurvefit gave you and add simulated random errors to that curve with standard deviation sigma. Repeat the fitting and the minimization of the curve for many random trials and observe the variance in the location of the minimum. That will be your uncertainty measure.

[Muthu Annamalai]

Is fmincon of use for discovering a global minimum in your data?

[Stacy]

Thank you Matt J. I will try to do this. It makes sense to do it that way. Yes, I do know my variation of the input data as well.

I am not familiar with fmincon, but looking at the documentation, I do not think it will be of use for my data.