Combining standard errors of fit parameters

Hi, I have fitted a 3 parameter (mean, sigma & tau) model to my data and have also computed the standard error for each of them. The statistic of interest for my data is the sum of mean and tau. My question is how do I estimate the total error for this new statistic? I know I can't simply add up the errors for mean and tau. Any help would be greatly appreciated. Thanks in advance.

Answer 1

[Tom Lane]

The standard error is an estimate of the standard deviation of the estimator in repeated sampling. The square of the standard deviation is the variance, so you can compute that using what you have. What you need to do is compute

var(mean+tau) = var(mean) + var(tau) + 2*cov(mean,tau)

where for each parameter listed I mean its estimate. So you need to be able to compute the covariance between your mean and tau estimates. Can you get that from whatever gave you the original estimates and standard errors?

Answer 2

[Robert Alvarez]

The bootstrap is a great method for computing estimates of statistics. Most formulas you will see assume normal statistics but the bootstrap will work if the data are not normally distributed or are of unknown distribution.

The statistics toolbox has the bootstrp function that makes implementing it easy. See the help.

If you do not have the toolbox, there are free versions of bootstrap routines on the internet for example in the stixbox toolbox (although I have not used that implementation).

It is not hard to implement your own from the description of the method. It basically involves using random samples with replacement of your data.