How to do multiple regression where all dependent and independent variables have uncertainties?

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klf
klf 2011-4-7
I have some data that I would like to run multiple regression on. The important thing here is that I would like the multiple regression to take into account the uncertainties in each of the data points -- something that mvregress doesn't do, as far as I can tell. What's more, each measurement in each of the variables has an uncertainty associated with it. For example, each measurement y(i) in the dependent variable y has its own uncertainty sy(i).
y = [y(1) y(2) ... y(n)]; % measured values of y
sy = [sy(1) sy(2) ... sy(n)] % uncertainties in measured values of y
The same goes for each of the independent variables x, w, z, etc.
x = [x(1) x(2) ... x(n)]
sx = [sx(1) sx(2) ... sx(n)]
When doing a single linear regression analysis, the function york_fit is able to handle data that have uncertainties in both the measured x- and y-values. I'd like to use something analogous to that -- just for multiple regression.
Anybody know how to do that? Is there a variant on mvregress that does that? Are there any canned functions that do that?
-Ken

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