What is the H matrix?
H-matrix, a matrix whose comparison matrix is an M-matrix. Hadamard matrix, a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. Hasse–Witt matrix. Hat matrix. Hermitian matrix, a complex square matrix that is equal to its own conjugate transpose.
What is the significance of hat matrix H in regression?
Hat matrix only involves the observation in the predictor variable X as H = X ( X ′ X ) − 1 X ′ . It plays an important role in diagnostics for regression analysis. The hat matrix plays an important role in determining the magnitude of a studentized deleted residual and therefore in identifying outlying Y observations.
How is the hat matrix used in regression?
Analysis of elements of the projection hat matrix plays an important role in regression diagnostics because the diagonal elements of this matrix Hii = xi ( XTX) − 1 xTi indicate the presence of leverage points which are not detected by analysis of residuals.
What are the fitted values of the hat matrix?
The fitted values are Y ^ = X b = X ( X ′ X) − 1 X ′ Y = H Y. Like fitted values ( Y ^ ), the residual can be expressed as linear combinations of the response variable Yi.
Which is the extension of the hat matrix?
For more complex analysis, it is useful to form the extension of matrix X by a vector y to give matrix X* = ( X | y ). This matrix corresponds to the projection matrix Since the matrix H* contains information about all variables it can be used as the total measure of influential points.
When is the hat matrix close to zero?
If the diagonal elements are close to 1, Hii → 1, all nondiagonal elements are close to zero, Hij → 0, for j = 1, …, n. If the matrix X comes from the multivariate normal distribution, the quantity F = ( n − m) [ Hii − 1 / n ] [ (1 − Hii ) ( m − 1)] has the Fisher-Snedecor distribution F ( m — 1, n — m ).