Hat Matrix Diagonal

We givenecessary and sufficient conditions on the space of design matrix under which thecorresponding Hat matrix elements get desired extreme values.

Hat matrix diagonal. The hat matrix projection matrix P in econometrics is symmetric idempotent and positive definite. H XXX 1X Where hii are the diagonal elements of the hat matrix the HC2 variance estimator is VˆβHC2 XX 1Xdiag e2 i 1 hiiXXX 1. Calculating the diagonal-entries of Q only or else we would have a result matrix of NN 25e8 entries for your numbers i used this.

Then 6 3k - Ok JV 1Jp Jlk Vkk1k2I - k where rk Yk - fk. Note that Jp VJ1J is the expected Fisher information matrix at. So hii pii cii pii 1 n.

This matrix is shown to have many of the same properties and is seen to play the same role in the variances and covariances. Theconfidence interval estimate of the mean response. The matrix which transforms the data vector to the vector of fitted values for smoothing splines is termed the hat matrix.

The elements of the hat matrix may provide fur- ther information which is complementary to that re- suiting from the residuals. The hat matrix diagonal element for observation i denoted hi reflects the possible influ-ence of X. Any observation having a large hi is called a leverage point.

X-space is the data points associated diagonal element hiin the hat matrix. We did not call it hatvalues as R contains a built-in function with such a name. H i i 1 n x i x 2 x j x 2 where j 1 n.

So P is also a projection matrix. Data points that are far from the centroid of the X-space are potentially influentialA measure of the distance between a data point x i and the centroid of the X-space is the data points associated diagonal element h i in the hat matrix. The standard hat matrix is written.