Question on Finding the Least Squares Estimate (Under Certain Conditions)

[chrishello]

The answer to b(-i.) is easy to find (i.e. when the ith observation is omitted). It is just the answer to the least squares estimate of b for the normal case but with a slight adjustment (as shown below).


However, Im having some trouble finding b* (when the ith observation is fitted.) Could someone help me with this?

Thanks

[chiro]

Hey chrishello.

Did you try creating a partition where you have your design matrix to be X = [X* | x(i) | X**] and then express your least squares in terms of these partitions?

For example: If you have a simple partition X = [X* | v] then you calculate Xy (where y is a vector), then if y* = y without last element then Xy = X*y* + v*y' where y' is the last element.

Now you can generalize this to different partitions and different kinds of vectors/matrices but the idea is the same.

If you relate the partitions to the general model, then'll you get an expression.