> -----Original Message----- > From: [EMAIL PROTECTED] [SMTP:[EMAIL PROTECTED] On Behalf Of Mark Miller > Sent: Thursday, November 17, 2005 10:16 AM > To: [email protected] > Subject: [R] Standard Error > > I have worked out that when I fit data I get an estimate and a standard > error, > but all the definitions I can find describe the standard error of a sample as > the standard deviation over the square root of the sample size, so if I am > fitting to a log-normal distribution, what is the standard error associated > with the standard deviation and why is it different from the standard error > of the mean. ------------ One thing is the standard error of the estimate_of_a_mean_ from a random_sample_from_a_population, whose formula you mentioned. Another thing, though related of course, is the standard error of a parameter_estimate from a model.
The standard error of a parameter estimate from a model is a measure of the precision with which the parameter was estimated. The standard lognormal distribution is a model with two parameters (there is another with three parameters): the mean and the standard deviation. When you fit that model -the lognormal distribution- to a sample, you are estimating these two parameters. If you maximise the likelihood for your data as a function of the two parameters the estimation process, if successful, will produce the two estimates and the corresponding standard errors of those estimates (plus the estimated covariance between the estimates). Both parameters, the lognormal mean and the lognormal standard deviation, are unknown and are estimated so that each one has its corresponding measure of precision. You can think of the standard error of a parameter estimate from a model at least in two ways. (1) Because maximum likelihood estimates tend to distribute normally, then the standard errors of parameter estimates are the standard deviation parameter estimates in a normal distribution whose mean is estimated by the maximum likelihood estimate itself. For example the output report from the ADMB statistical system simply put the header Standard Deviation in the column for standard errors of parameter estimates. Presumably this is because the ADMB's author subscribe to this interpretation. (2) You can also think of standard error of parameter estimates as measuring the curvature of the likelihood function about the maximum likelihood estimate. In the pure-likelihood theory of inference this is the preferred interpretation. So A.W.F. Edwards (1972, Likelihood, Cambridge UP) has renamed the standard errors calling them "the span". I hope this makes sense to you. Ruben ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
