Summary: Computational Statistics and Statistical Modelling:
Mathematical Tripos, Part IIA, questions from 1997 onwards
P.M.E.Altham, Statistical Laboratory, University of Cambridge.
July 5, 2005
I/12M
i) Assume that the n­dimensional observation vector Y may be written
Y = X# + #,
where X is a given n × p matrix of rank p, # is an unknown vector, and
# # Nn (0, # 2 I).
Let Q(#) = (Y -X#) T (Y -X#). Find “
#, the least­squares estimator of #, and show that
Q( “
#) = Y T (I -H)Y
where H is a matrix that you should define.
If now X# is written as X# = X 1 # 1 +X 2 # 2 , where X = (X 1 : X 2 ), # T = (# T
1 : # T
2 ), and # 2 is
of dimension p 2 , state without proof the form of the F-test for testing H 0 : # 2 = 0.
ii) The data in the GLIM analysis shown were obtained as part of a health survey in the
US investigating cholesterol levels in women from two states, Iowa and Nebraska (denoted by 1,2

Source: Altham, Pat - Statistical Laboratory, Centre for Mathematical Sciences, University of Cambridge

Collections: Mathematics