|
Items in cart [0] |
Questions? Call 888-624-8373 |
PAPERBACK Free Resources |
||||||||||||||||
|
||||||||||||||||
|
||||||||||||||||
| ||||||||||||||||||||||||||||||
|
||||||||||||||||||||||||||||||
| Copyright © 2009. National Academy of Sciences. All rights reserved. Terms of Use and Privacy Statement |
Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 90
CHAPTER 5
CLOSING PERSPECTIVE
Discriminant analysis and cluster analysis must be
"classified" as among the most useful statistical techniques for
somety's problems. This report has-attempted to summarize and
assess their status in terms of methodology, theory, and software.
The material, it is hoped, will be informative both to users of these
techniques, who may want an update on the state-of-the-art, and
to professional statisticians, who may be more interested in
current research and what remains to be done.
Even casual readers of this report will have noticed tremen-
dous differences between the conditions of discriminant analysis
and cluster analysis. The former is a well developed subject with a
variety of effective methods and supporting theory. The latter is
lacking in film foundations and agreed-upon methodology.
Perhaps it is only along the software coordinate that there is
approximate parity. Indeed, there may be more software for clus-
ter analysis simply because of the proliferation of ad hoc methods
for this purpose.
In spite of its relatively advanced state, there are still many
interesting problems to be worked on in discriminant analysis.
Specific mention was maple in Chapters 2 and 3 of the promising
new areas of projection pursuit classification and additive logistic
regression analysis; the need for more study of biases associated
with the use of the bootstrap in estimating error rates and of the
tradeoffs between bias and mean square error performance of dif-
ferent estimates of error rates; and, generally, the opportunities
for additior~al development and experimentation with the variety
of non parametric and semiparametnc methods that are now avail-
able.
However, the greatest needs appear to be in the cluster
analysis arena. Unless significant breakthroughs in theory and
insights into the behavior of procedures are produced, cluster
analysis is likely to remain a largely descriptive technique whose
90
OCR for page 91
results are too dependent upon the vagaries of particular methods
A list of research problems, some of which were discussed in
Chapters 2 and 3, includes
.
.
.
developing a stronger base of inferential and diagnostic tools
(a high priority should be placed on the development of sam-
ple reuse techniques that will work in the clustering con-
text);
closing the gap between theory and practice (the need is
illustrated by the attractiveness of single linkage clustering
from a theoretical point of view in spite of its frequent poor
performance in practice);
compensating for the lack of adequate theory with empirical
development of new insights about existing algorithms
(clever and extensive simulation studies may be the only
way around the mathematical and theoretical difficulties in
this field);
finding tools for selection, scaling, and transformation of
variables that are effective at bringing out cluster structure
(iterative schemes may be required because the clusters are
unknown in advance);
learning how to make clustering algorithms robust to data
idiosyncrasies (the payoff may prove to be in the 'local"
application of the robustness concept rather than a crude
global attack that is insensitive to fine cluster structure)
Another area that is ripe for more research concerns prob-
lems that fall between discriminant analysis and cluster analysis
A fair amount of work has been done near the discriminant end of
the spectrum, e g, dealing with the situation where errors are
present in the group labels of the training sample Little is known
about how to do cluster analysis in the presence of limited prior
information on the composition of clusters
91
OCR for page 92
ElEFERENCES
ANDERBERG, M. R. (1973~. Cluster Analysis for Applications.
Academic Press, New York.
ANDERSON, E. (19571. A semi-graphical method for the analysis
of complex problems. Proc. Nat. Acad. Sci. USA 43 923-927.
ANDERSON, T. W. (1958~. An Introduction to Multivariate Sta-
tistical Analysis. Wiley, New York.
ANDERSON, T. W., and BAHADUR, R. R. (19621. Classification
into two multivanate normal distributions with different
covanance matrices. Ann. Math. Statist. 33 420-431.
ANDREWS, D. F. (1972~. Plots of high-dimensional data.
Biometrics 28 125-136.
ARABIE, P. (1977~. Clustering representations of group overlap.
J. Math. Sac. 5112-128.
ARABIE, P. and CARROLL, J. D. (1980~. MAPCLUS: A
mathematical programming approach to fitting to ADCLUS
model. Psychometrika 45 211-235.
ART, D., GNANADESIKAN, R., and KE11ENRING, J. R. (19821.
Data-based metrics for cluster analysis. Utilitas Mathematica
31A 75-99.
ASIMOV, D. (19851. The grand tour. SIAM e7. Sci. Statist. Com-
put. 6 128-143.
BAKER, F. B. (19741. Stability of two hierarchical grouping tech-
niques, Case I: Sensitivity to data errors. cl. Amer. Statist.
Assoc. 69 440-445.
92
OCR for page 93
BECKER, P. (1968). Recognitions of Patterns. Polyte~isk,
Copenhagen.
BELL, P. A. and KOREY, J. L. (1975~. QUICLSTR: A FORTRAN
program for hierarchical cluster analysis with a large number
of subjects. Behavioral Research Methods and Instrumenta-
tion 7 575.
BINDER, D. A. (1978~. Comment on 'Estimating mixtures of nor-
mal distributions and switching regressions'. J. Amer. Statist.
Assoc. 73 746-747.
BLASHFIELD, R. K., ALDENDERFER, M. S. and MOREY, L. C.
(1982~. Cluster analysis literature on validation. In Classify-
ing Social Data. (H. Hudson, ea.) 167-176. Jossey-Bass, San
Francisco.
BOCK, H. H. (19851. On significance tests in cluster analysis. d.
Classification 2 77-108.
BRIEMAN, L., FRIEDMAN, J. H., OLSHEN, R. A., and STONE,
C. J. (19841. Classification and Regression Trees. Wadsworth,
Belmont, CA.
BREIMAN, L. MEISEL, W. S., and PURCELL, E. (1977~. Vari-
able kerned estimates of multivanate densities and their cali-
bration. Technometrics 19135-144.
BROADBENT, S. R. and HAMMERSLEY, J. M. (19571. Percola-
tion Processes, I: Crystals and Mazes. Proc. Cambridge Phi-
[os. Soc. 53 629-641
BUdA, A., HURLEY, C. and MCDONALD, J. A. (19861. A data
viewer for multivariate data. Computer Science arm Statistics:
Proceedings fifths 18th Symposium on the Interface 171-174.
CACOULLOS, T. (1966~. Estimation of a multivariate density.
Ann. Math. Statist. 18179-189.
CElE:N, H., GNANADESIKAN, R., and KE:1YENRING, J. R.
(1974~. Statistical methods for grouping corporations. San-
kEya B 36 1-28.
93
OCR for page 94
CHE:RNOFF, H. (19721. The selection of effective attributes for
deciding between hypotheses using linear discriminant func-
tions. In Frontiers of Pattern Recognition. (S. Watanabe, ea.)
55-60. Academic Press,NewYorl`.
CEIE:RNOFF, H. (1973a). Some measures for discriminating
between normal multivariate distributions with unequal
covariance matrices. In Multivariate Analysis III. (P. R.
i . .
Krishnaiah, ea.) 337-344. Academic Press, New York.
CEIERNOFF, H. (1973b). The use of faces to represent points in
k-dimensional space graphically. c7. Anger. Statist. Assoc. CS
361-368.
-CLUNIES-ROSS, C. W. and RIFFENBURGH, R. H. (1960).
Geometry and linear discrimination. Biometrika 47 185-189.
CORMACK, R. M. (19711. A review of classification (with discus-
sion). e7. Roy. Statist. Soc. A 134 321-367.
CORNFIELD, J. (19621. Joint dependence of rish of coronary
heart disease on serum cholesterol and systolic blood pressure:
a discriminant function analysis. Federal Proceedings 21 58-
61.
COVER, T. M. (1968~. Estimation by the nearest neighbor rule.
IEEE Transactions Information Theory 1~-14 50-55.
COVER, T. M. and HART, P. E. (19671. Nearest neighbor pattern
classification. IEEE Transactions, Information Theory IT-13
21-27.
DALLAL, G. E. (1975) A user's guide to J. A. Hartigan's clustering
algorithms. (unpublished manuscnpt) Yale University.
DAY, N. E. (19691. Estimating the components of a mixture of nor-
mal distributions. Biometrika 66 463-474.
DAY, N. E., and KERRIDGE, D. F., (1967~. A general maximum
likelihood discriminant. Biometrics 23 313-323.
94
OCR for page 95
DEFAYS, D (1977) An efficient algorithm for a complete link
method Computer Journal 20 364-366.
DICK, N P and BOWDEN, D C (1973) Maximum likelihood
estimation for mixtures of two normal distributions
Biometrzcs 29 781-790
DIXON, W ~ led ~ (1981) BMDP Statistical Software. University
of California Press, Berkeley
DONOHO, A W. DONOHO, D L and GASKO, M (1985) MacS-
pin graphical data analysis software D2 Software, Austin
DUDA, R O and HART, P E. (1973~. Pattern Classification and
Scene Analysis. Wiley, New York
EDMONSTON, B (1985) MICRO-CLUSTER Cluster analysis
software for microcomputers Journal of Classification 2 127-
130
EFRON, B (1975) The efficiency of logistic regression compared
to normal discnminant analysis J Amer. Statist. Assoc. 70
892-898
EFRON, B (1979) Bootstrap methods Another look at the jack-
knife Ann. Statist. 71-26.
EFRON, B (1982) The Jackknife, lithe Bootstrap, and Other
Resampling Plans, SIAM NSF-CBMS, Monograph #38
EF RON, B (1983) Estimating the error rate of a prediction rule
Improvements on cross-validation ~ Amer. Statist. Assoc. 7f;
316-331
EVERI1Y?, B (1980) Cluster Analysis. 2nd ed Halsted, New
York
EVERITT, B S and HAND, D J (1981) Finite Mixture Distribu-
tions. Chapman and Hall, London
FARVER, T B and DUNN, O ~ (1979) Stepwise variable selec-
tioninciassificationproblems Biom. J. 21 145-153
95
OCR for page 96
FISHER, R. A. (19361. The He of multiple measurements in tame
noetic problems. Ann. Eugenics 7 (part 2) 179-~.
FISHERKELLER, M. A., FRIEDMAN, J. H., and TUKEY, J. W.
(19741. Prim-9: An interactive multidimensional data display
and analysis system. SLAG-Pub. 140S, Stanford Linear
Accelerator Center, Stanford, California.
PITCH, W. M. and MARGOLIASH, E. (1967~. Construction of
phylogenetic trees. Science 155 279-2~34.
FIX, E. and HODGES, J. (1951~. Discriminatory analysis, non-
parametric discrimination: consistency properties. Technical
Report. Randolph Field, Texas: USAF School of Aviation
Medicine.
FOWLKES, E. B. (19871. Some diagnostics for binary logistic
regression Ma smoothing. Biometrika to appear.
FOWLKES, E. B., GNANADESIKAN, R. and KETTENRING, J. R.
(1987~. Variable selection in clustering and other contexts. In
Design, Data, and Analysis, by Some Friends of Cuth~rt
Daniel (C. L. Mallows, em.. Wiley, New York, to appear.
FOWLKES, E. B. and MALLOWS, C. L. (19831. A method for com-
paring two hierarchical clusterings (with discussion). J. Amer.
Statist. Assoc. 78 553-583.
FRIEDMAN, H. P. and RUBIN, J. (1967~. On some invariant cri-
tena for grouping data. Journal of American Statistical Asso-
ciation 62 1159-1178.
FRIEDMAN, J. H. and TUKEY, J. W. (19741. A projection pursuit
aIgonthm for exploratory data analysis. IEEE Trans. Comput.
C-23 881-889.
GNANADESIKAN, R. (19771. Methocls for Statistical Data
Analysis of Multivariate Observations. Wiley, New York.
GNANADESIKAN, R. and KE1~ENRING, J. R. (1984~. A prag-
matic review of multivariate methods in applications. In
Statistics: An Appraisal. (H. A. David and H. T. David, eds.~.
96
OCR for page 97
309-337. Iowa State University Press.
GNANADESIKAN, R., KE1~ENRING, J. R., and LANDWEHR, J.
M. (19771. Interpreting and assessing the results of cluster
analyses. Bull. Int. Statist. Inst. 47 451-463.
GNANADESIKAN, R., KE1~ENRING, J. R. and LANDW~;HR, J.
M. (1982~. Projection plots for displaying clusters. In Statis-
tics and Probability: Essays in Honor of C. R. Rao. (G. Kalli-
anpur, P. R. K~ishnaiah and J. K Ghosh, eds.) 281-294.
North-Holiand, Amsterdam.
GOLDMAN, L., WEINBERG, M., WEISBERG, M., OLSHEN, R.,
COOK; F., SARGENT, R. K, LAMAS, G. A., DENNIS, C.,
DECKELBAM, L., FINEBERG, H., STIRATELLI, R. and the
MEDICAL HOUSESTAFES AT YALE-NEW HAVEN HOSPI-
TAL AND BRIGHAM AND WOMEN'S HOSPITAL (1982). A
computer-derived protocol to aid in the diagnosis of emergency
room patients with acute chest pain. We New England Jour-
nal of Medicine 307 588-596.
GONG, G. (1982~. Cross-validation, the jackknife, and the
bootstrap: excess error estimation in forward logistic regres-
sion. Ph.D. dissertation. Stanford University Technical
Report No. 80. Department of Statistics.
GORDON, L. and OLSHEN, R. A. (1978~. Asymptotically efficient
solutions to the classification problem. Ann. Statist. 6 515-
533.
GORDON, L. and OLSHE:N, R. A. (1980~. Consistent non-
parametric regression from recursive partitioning schemes. J.
Mull. Anal. 10 611-627.
GORDON, L. and OLSHEN, R. A. (1984~. Almost surely consistent
nonparametric regression from recursive partitioning
schemes. J. Mult. Anal. 15147-163.
GOWER, J. C. and ROSS, G. J. S. (19691. Minimum spanning
trees and single linkage cluster analysis. Appl. Statist. 18
54-65.
97
OCR for page 98
GRAY, J. B. and LING, R. F. (1984~. K-clustering as a detection
tool for influential subsets regression (with discussion). Tech-
nometrics 26 305-330.
HAFF, L. R. (19861. On linear log-odds and estimation of discrim-
inant coefficients. Commun. Statist.-Th~or. Meth. 15 2131-
2144.
EIALL, D. J. and KHANNA, D. (19771. The ISODATA method of
computation for relative perception of singularities and di~er-
ences in complex and real data. In Statistical Methods for
Digital Computers Olol. 3~. (K Enslein, A. ELalston, and H. W.
Wilf,eds.) New York: John Wiley.
HAND, D. J. (1981~. Discrimination and Classification. Wiley,
New York.
EIARTIGAN, J. A. (1967~. Representation of similarity matrices by
trees. A. Amer. Statist. Assoc. 62 1140-1158.
HARTIGAN, J. A. (1975~. Clustering Algorithms. Wiley, New
York.
HARTIGAN, J. A. (19771. Distribution problems in clustering. In
Classification and Clustering (J. Van Ryz:in, ea.) 45-71.
Academic Press, New York.
HARTIGAN, J. A. (1978~. Asymptotic distributions for clustering
criteria. Ann. Statist. 6 117-131.
HARTIGAN, J. A. (1981~. Consistency of single linkage for high
density clusters. J. Amer. Statist. Assoc. 76 388-394.
HARTIGAN, J. A. and HARTIGAN, P. M. (19851. The dip test of
multimodality. Ann. of Statist. 13 70-84.
HERMANS, J., HABBEMA, J., and SCHAEFER, R. (1982~. The
ALLOC80 package for discriminant analysis, Stat. Software
Newsletter, 8 15-20.
HODSON, F. R., SHEATH, P. H. A. and DORAN, J. E. (1966).
Some experiments in the numerical analysis of archaeological
data. Biometrika 53 311-324.
98
OCR for page 99
HOSMER, D. W. (1973~. A comparison of iterative maximum likel-
ihood estimates of the parameters of a mixture of two normal
distributions under three different types of sample.
Biometrics 29 761-770.
HUBER, P. J. (19851. Projection pursuit (with discussion). Ann.
Statist.. 6 701-726.
International Mathematical and Statistical Library (1977~. Refer-
ence manual library 1, ed. 6. Vol. 1. Houston.
JAMES, W. and STEIN, C. (19611. Estimation with quadratic loss.
Proc. Fourth Berkeley Symp. Math. Statist. Proh. 1 311-319.
JAMBU, M. and kEBEAUX, M. O. (19831. Cluster Analysis ant!
Data Analysis. North-HolIand Publishing Company, Amster-
dam.
JARDINE, C. J., JARDINE, N. and SIBSON, R. (19671. The
structure and construction of taxonomic hierarchies. Math.
Biosci. 1 173-179.
JENNRICH, R. I< (19621. Linear Discrimination in the Case of
Unequal Covariance Matrices. Unpublished manuscript.
JENNRICH, R. and MOORE, R. H. (1975~. Maximum likelihood
estimation by means of nonlinear least squares. Proceedings
of the Statistical Computing Section, American Statistical
Association, 57-65.
JOHNSON, S. C. (19671. Hierarchical clustering schemes.
Psychometrika 32 241-254.
KETTENRING, J. R., ROGERS, W. H., SMITH, M. E., and
WAEUlER, J. L. (1976~. Cluster analysis applied to the valida-
tion of course objectives. J. Ecluc. Statist. 1 39-57.
KLEINER, B. AND HARTIGAN, J. A. (1981~. Representing points
in many dimensions by trees and castles (with discussion). J.
Amer. Statist. Assoc. 76 260-276.
99
OCR for page 100
LACHENBRUCH, P. A. (19751. Discriminant Analysis. lIalner
Press, New York.
LACHENBRUCH, P. A. (19821. Robustness of dis~minant func-
tions. SUGI-SAS Group Proceedings 7 62~632.
LANDWEEIR, J. M., PREGIBON, D., and SHOEMAE[E:R, ~ C.
(1984~. Graphical methods for assessing logistic regression
models (with discussion). A. Amour. Statist. Assoc. 7g 61-83.
LENNINGTON, R. K. and ROSSBACH, M. E. (19781. CLASSY:
An adaptive maximum likelihood clustering algorithm. Paper
presented at 1978 meeting of the Classification Society.
LEVISOE~, J. R. and FUNK, S. G. (19741. CLUSTER: A
hierarchical clustering program for large data sets (n2100~.
Research Memo #40, Thurstone Psychometric Laboratory,
University of North Carolina.
LING, R. F. (1973~. A probability theory of cluster analysis. IT.
Amer. Statist. Assoc. 68 159-169.
MACQUEEN, d. (19671. Some methods for classification and
analysis of multivariate observations. Proc. Fifth Berkeley
Symp. Math. Statist. Prob. 1281-297.
MARKS, S. and DUNN, O. J. (19741. Discriminant functions when
covanance matrices are unequal. J. Amer. Statist. Assoc. 69
555-559.
MCCULLAGH, P. and WELDER, J. A. (1983~. Generalized! Linear
Models. Chapman anal Hall, London.
MCKAY, EL. J. (1978~. A graphical aid to selection of variables in
two-group disc~minant analysis. Appl. Statist. 27 259-263.
MCKAY, R. J. and CAMPBELL, N. A. (1982a). Variable selection
techniques in discuminant analysis. I. Description. Br. A.
Math. Stat. Psychol. 351-29.
MCKAY, R. J. and CAMPBELL, N. A. (1982b). Variable selection
techniques in discriminant analysis. II. Allocation. Br. J.
Math. Stat. Psychol. 35 30~1.
100
OCR for page 101
MICHENER, C. D. and SOKAL R. R. (1957~. A quantitative
approach to a problem in classification. Evolution 11 130-162.
MOJENA, R. (19771. Hierarchical grouping methods and stopping
~ es -- An evaluation. Computer Journal 20 359-363.
MOJENA, R. and WISHART, D. (1980~. Stopping rules for Ward's
clustering method. Proceedings of COMPSTAT. Physica-
VerIag 426-432.
MORGAN, J. N. and SONQUIST, d. A. (19631. Problems in the
analysis of survey data, and a proposal. A. Amer. Statist.
Assoc. U' 415-435.
WELDER, J. A. and WEDDERBURN, R. W. M. (19721. General-
ized linear models. A. Roy. Statist. Soc. A 135 370-384.
MORGAN, J. N. and MESSENGER, R. C. (19731. THAID: a
sequential search program for the analysis of nominal scale
dependent variables. Institute for Social Research, U. of
Michigan, Ann Arbor.
OLSHEN, R. A., GILPIN, E., HENNING, H. LEWINTER, M.,
COLLINS, D., and ROSS., J., JR. (1985~. Twelve month prog-
nosis following myocardial infarction: classification trees,
logistic regression, and stepwise linear discrimination.
Proceedings of the Berkeley Conference in Honor of Jerzy Ney-
man and Jack Kiefer. (L. LeCam and R. O1shen, eds.) 1 245-
267. Wadsworth Advanced Books and Software, Monterey,
California and the Institute of Mathematical Statistics, Hay-
ward, Califorrna.
POLLARD, D. (1982~. A central limit theorem for k-means cluster-
ing. Ann. Prob. 10 919-926.
PREGIBON, D. (19811. Logistic regression diagnostics. Ann. Sta-
tist. 9 705-724.
RABINER, L. R., LEVINSON, S. E., ROSENBERG, A. E. and and
WILPON, J. G. (19791. Speaker independent recognition of
isolated words using clustering techniques. IEEE Trans.
Accoust. Speech Signal Process. 27 336-349.
101
OCR for page 102
RAO, C. R. (19481. The utilization of multiple measurements in
problems of biological classification. J. Roy. Statist. Soc. Ser.
B 10 159-203.
RAO, C. R. (19521. Advanced Statistical Methods in Biometric
Research. Wiley, New York.
RAO, C. R. (19601. Multivariate analysis: an indispensable #tatist-
ical aid in applied research. SanAhya 22 317-338.
MAO, C. R. (1962~. Use of discriminant and allied functions in
m~tivariate analysis. Sanibya A24 149-154.
RAO, C. R. (1965~. Linear Statistical Inference and Its AppZica-
tions. Wiley, New York.
RIFFENBURGH, R. H. and CLUNIES-ROSS, C.W. (19601. Linear
discriminant analysis. Pacific Science 14 251-256.
ROHLF, F. J. (1977~. Computational efficacy of agglomerative
clustering algorithms. Technical Report RC-6831. IBM Wat-
son Research Center
ROHLF, F. J. (19821. Single-link clustering algorithms. In Hand-
book of Statistics: Vol. 2, (P. R. Krishnaiah and L. N. Kanal,
eds.) 267-284. North-Holiand Publishing Company, Amster-
dam.
ROTMAN, S. R., FISHER, A. D., and STAELIN, D. H. (19~31~.
Analysis of multiple-angle microwave observations of snow
and ice using cluster analysis techniques. A. Glaciology 27
89-97.
RYAN, T., JOINER, B., and RYAN, B. (1982). Minitab Reference
Manual. Dumbly Press, Boston.
SAS Institute, Inc. (1985~. SAS User's Guide: Statistics, Version 5
Edition. Sas Institute, Inc., Cary, NC.
SEBER, G. A. F. (1984~. Multivariate Observations. Wiley, New
York.
102
OCR for page 103
SHE:PARD9 R. N. and ARABIE, P. (1979). Additive clustering:
representation of similarities as combinations of discrete over-
lapping properties. Psychological Review 86 87-123.
SHIBATA, R. (1981~. Art optimal selection of regression variables.
Biometrika 68 45-54.
SIBSON, R. (19731. SLINK: An optimally efficient algorithm for
single-link cluster methods. Computer Journal 16 30-34.
SIEGEL, J. H., GOLDWYN, R. M., and FRIEDMAN, H. P. (1971~.
Pattern and process in the evolution of human septic shock.
Surgery 70 232-245.
SILVERMAN, B. W. (1986~. Density Estimation for Statistics and
Data Analysis. Chapman and Hall, London.
SMYTHE, R. T. and VVIERMAN, J. C. (1978~. First passage perco-
lation on the square lattice. Lecture Notes in Mathematics
671. Springer-Veriag, Berlin.
SNEATH, P. H. A. and SOKAL, R. R. (1973~. Numerical Taxon-
omy. Freeman, San Francisco.
SOKAL, R. R. (1974~. Classification: purposes, principles, pro-
gress, prospects. Science 185 1115-1123.
SPSS, INC. (19861. SPSSX (a computer program). McGraw-Hill,
New York.
STEIN, C. (19561. Inadmissibility of the usual estimator for the
mean of a multivanate normal ~stnbution. 17iird Berkeley
Symp. Math. Statist. Prob. 1 197-206.
STONE, C. J. (1977~. Consistent nonparametric regression (with
discussion). Ann. Statist. 5 595-645.
STONE, M. (1977~. Cross-validation: a review. Math. Operation-
forsch. Statist. Ser. Statist. 9127-139.
TARTER, M. and KRONMAL, R. (1970~. On multivariate density
estimates based on orthogonal expansions. Ann. Math. Sta-
tist. 4 718-722.
103
OCR for page 104
TOUSSAINT, G. T. (1974). Bibliography on estimation of
miscIassification. IEEE Transactions on Information Theory
1~-20 472-479.
TRUEST, J., CORNFIELD, J. and KANNEL, W. (1967). A mul-
tivariate analysis of the risk of coronary heart disease in
Fra~ngham. J. of Chronic Diseases 20 511-524.
TRYON, R. C. (1939). Cluster Analysis. edwards Brothers, Ann
Arbor, MI.
VAPNIK, V. N. and CHERVONEN~S, A. YA. (1971). On the uni-
form convergence of relative frequencies of events to their pro
babilities. Theor. Prob. Appl. 16 264-2~30.
VAF,NIK, V. N. and CHERVONENKIS, A. YA. (1974). Theory of
Pattern Recognition (in Russian). Nauka, Moscow.
VELOMAN, D. J. (1967). FOR17LAN Programming for the
Behavioral Sciences. Holt, Rinehart and Winston, New York.
VRIdENHOEK, R. C., DOUGLAS, M. E., and MEFFE, G. K
(1985). Conservation genetics of endangered fish populations
in Arizona. Science 229 100-402.
WALD, A. (1944). On a statistical problem arising in the
classification of an individual into one of two groups. Ann.
Math. Statist. 16145-162.
WALKER, S. B. and DUNCAN, D. B. (1967). Estimation of the
probability of an event as a function of several independent
variables. Biometrika 54 167-179.
VVISHART, D. (19691. Mode Analysis: A generalization of nearest
neighbor which reduces chaining effects in Numerical Taxon-
omy, (A. J. Cole, ed.), Academic Press, London.
WOLFE, J. H. (1970~. Pattern clustering by muitivariate mature
analysis. Mq24Itivariate Behavioral Research 5 329-350.
q
104
OCR for page 105
WOLFE, J. H. (1971~. ~ Monte-CarIo study of the sampling distn-
bution of the likelihood ratio for mixtures of multinormal ~s-
tributions. Research Memorandum 72-2, Naval Personnel and
Research Training Laboratory, San Diego.
105
OCR for page 106
Representative terms from entire chapter:
discriminant analysis
