SIAM REVIEWVol. 34, No. 2, pp. 325-349, June 1992
() 1992 Society for Industrial and Applied MathematicsO08
BOOK REVIEWS
EDITED BY NICHOLAS D. KAZARINOFF
Subset Selection in Regression. ByA. J. MillerChapman &
Hall, New York, 1990. x + 229pp. $47.50. ISBN 0-412-35380-6.
Mono-graphs on Statistics and Applied Probability,Vol. 40.
This monograph is unique in its coverage.There is no other book
on the subject, al-though there are some survey articles,
mostnotably Millers article [1].
After an introductory chapter there is achapter on least squares
computations. Milleremphasizes orthogonalization procedures,
es-pecially planar rotations, and not the Gauss-Jordan approach
that is prominent in Amer-ican statistical packages. The
Gauss-Jordanalgorithm is often given in the form called thesweep
algorithm, which is described by Miller,but the name "sweep" is not
used by him. Hegives an excellent explanation of why the
or-thogonalization method gives better accuracy,but gives no
evidence of the need for the in-creased accuracy over what is
obtainable indouble precision from Gauss-Jordan. Thischapter also
has algorithms for computing theregressions on all subsets of a set
ofpredictors.
Chapter 3 begins with some of the standardprocedures for
variable selection, such as for-ward selection, backward
elimination, and thecombination of these two called stepwise
re-gression. Then Miller describes more sophis-ticated procedures
for generating the subsetsofpredictors that are "best" by some
criterion.He also describes ridge regression and its usein subset
selection. The final section consistsof four examples, including
one with 20 vari-ables and only 14 cases and another examplewith 11
variables and 13 cases. Based on theseand other examples, Miller
makes the generalobservation that the best subset proceduresare
advantageous over the sequential proce-dures mainly in these
examples with few casescompared to the number of variables. On
theother hand, the reader might wonder if theapparent advantage is
usually just a matter ofrandom error. Do 14 cases have sufficient
in-formation to enable choice from all subsets of20 predictors?
325
Next is a chapter on significance testing.Miller suggests
including entirely random pre-dictors, and seeing how well they
competewith the variables in the data. If the ran-dom predictors
are chosen, then there are toomany predictors. After mentioning
that theusual F-test is not valid, he presents othermethods,
including some based on simulationand random permutation, and some
for simul-taneous confidence intervals based on the
F-distribution.
Chapter 5 emphasizes the bias in regres-sion coefficients that
results when predictorsubsets are selected based on error sums
ofsquares. Several cures are given for this dis-ease, including
Millers new maximum likeli-hood method. Unfortunately, this method
iscomplicated, it is limited to special cases, andit may increase
the variance while decreasingthe bias.The following chapter gives a
variety of
stopping rules, criteria for deciding how manypredictors to
retain. It concludes with a verygood discussion of the
relationships amongthe various criteria.
Finally, Chapter 7 is a summary in the formof seven questions
that Miller poses and an-swers. Question 6 asks whether subset
re-gression can be justified, and Millers answermentions the case
in which the predictors areexpensive to measure. The reader who
hasworked through the book to this point may bedisappointed that
the author does not make astronger case for subset selection.
Even though the bibliography runs toaround 200 entries, it does
not include all re-search on subset selection. One could wonderif
there were space constraints, because thedata for only one of the
examples are given,and there are not many figures. On page83 Miller
advocates the use of graphical andother methods of residual
analysis, but thereis not much of this in the book, perhaps
againbecause of space limitations. Another reasonmight be that, as
he points out on page 14,the properties of residuals are unknown
whenpredictors have been selected based on thesesame residuals.
Dow
nloa
ded
12/0
2/14
to 1
29.1
20.2
42.6
1. R
edis
trib
utio
n su
bjec
t to
SIA
M li
cens
e or
cop
yrig
ht; s
ee h
ttp://
ww
w.s
iam
.org
/jour
nals
/ojs
a.ph
p
326 BOOK REVIEWS
Miller does a fine job of summarizing mostof the research in
this field, and he givesclear explanations of some complicated
pro-cedures. Those who use subset selection andthose who teach it
should read at least Chap-ters 3 and 6. Millers survey [1] is
useful, too,because it has material not in the book, andthe
accompanying discussion gives the viewsofothers.
REFERENCE
[1] A. J. MILLER, Selection of subsets and regres-sion
variables, J. Roy. Statist. Soc., A, 147(1984), pp. 389-425.
KENNETH N. BERKIllinois State University
Computer Networks and Systems: Queue-ing Theory and Performance
Evaluation. ByThomas G. Robertazzi. Springer-Verlag, NewYork, 1990.
xii + 306 pp. $49.50. ISBN 0-387-97393-1.
Various models of computer communica-tion networks capture
different aspects of net-work performance. For example, a graph
the-oretic representation provides information onconnectivities and
path capacities, whereas aqueueing model deals with message
delays,buffer occupancies and overflows, character-istics of
traffic among work stations, and thelike. Because it has been
generally recog-nized that queueing models are essential tothe
effective analysis of networks, electricaland computer engineers
have become famil-iar with queueing theory, while queueing
the-orists have applied their skills to networks.
Accordingly, it comes as no surprise thatseveral recent texts on
networks devote a largefraction of their contents to applicable
aspectsof queueing theory. The book under reviewgoes a step
further; queueing analysis of net-works is its central theme. Since
the book isintended for beginning graduate students,
it(intentionally) contains no original material,and should be
judged on the basis of its peda-gogic quality.
This text is not directed at a mathematicalaudience. The level
of rigor is perhaps wellillustrated by the statement (page 18):
It turns out that random splits of a Pois-son process are
Poisson and that ajoining of
independent Poisson processes is also Pois-son. A little thought
with the coin flippinganalogy will show that this is true.
This statement appears in reference to theintroduction of the
M/M/1 queue, which withvariations such as the M/M/m/m queue,
occu-pies sixty-five pages early in the book. The ar-guments on
equilibrium probabilities for suchqueues are based on deriving the
usual dif-ferential equations, and setting the derivativeto zero;
one finds no reference to the transi-tion matrix, recurrent states,
reducibility, Kol-mogorov equations, or any of the other termsdear
to those familiar with Markov processes.The same chapter contains a
simplified
treatment of the embedded M/G/1 queue, areference to
reversibility and its implications,and Littles formula. None of the
three(!)proofs or ensuing exposition of Littles for-mula give any
indication that this result is notmerely applicable to queues, but
is actuallya systems theorem of broad interest. Indeed,the whole
chapter suffers from a narrow focus,and is almost entirely
derivative of (but less lu-cid than) the standard texts [1]-[4]
repeatedlyreferenced by the author.
Next is a chapter dealing with queueingnetworks. The emphasis is
on Markov sys-tems having product form equilibrium solu-tion. The
author attempts to explain globaland local balance intuitively in
terms of prob-ability flows, rather than in the context of
theinfinitesimal generator. His exposition is lesssuccessful than
that found in earlier books[5], which yield similar results with
consid-erable elegance but no greater mathematicalcomplexity. There
are also examples, at leastone ofwhich is borrowed directly from a
well-established text [6].
Following this chapter on networks ofqueues is another long
chapter (about sixtypages), covering numerical methods. Theserelate
almost entirely to the calculation ofproduct form solutions.
Algorithms are de-scribed, and some numerical examples offered.
There is virtually no error analysis, noris attention given to
relative computationalrequirements of alternative methods. In
thelatter portion of the chapter, "guest authors"discuss
simulation, but without any specificswhatsoever. In the opinion of
the reviewer,the chapters focus on product form is exces-sively
restrictive (especially for a first course
Dow
nloa
ded
12/0
2/14
to 1
29.1
20.2
42.6
1. R
edis
trib
utio
n su
bjec
t to
SIA
M li
cens
e or
cop
yrig
ht; s
ee h
ttp://
ww
w.s
iam
.org
/jour
nals
/ojs
a.ph
p
