Cacoullos Discriminant Analysis and Applications

1. Auflage 2014
ISBN: 978-1-4832-6871-2
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 456 Seiten, Web PDF

Discriminant Analysis and Applications comprises the proceedings of the NATO Advanced Study Institute on Discriminant Analysis and Applications held in Kifissia, Athens, Greece in June 1972. The book presents the theory and applications of Discriminant analysis, one of the most important areas of multivariate statistical analysis. This volume contains chapters that cover the historical development of discriminant analysis methods; logistic and quasi-linear discrimination; and distance functions. Medical and biological applications, and computer graphical analysis and graphical techniques for multidimensional data are likewise discussed. Statisticians, mathematicians, and biomathematicians will find the book very interesting.

Autoren/Hrsg.

Cacoullos, T.

Inhaltsverzeichnis

1;Front Cover;1
2;Discriminant Analysis and Applications;4
3;Copyright Page;5
4;Table of Contents;8
5;CONTRIBUTORS;10
6;PREFACE;12
7;INTRODUCTORY ADDRESS;14
8;CHAPTER 1. LOGISTIC DISCRIMINATION
WITH MEDICAL APPLICATIONS;22
8.1;Summary;22
8.2;1. Introduction;23
8.3;2. Formulation of the
problem;23
8.4;3. Estimation when sampling the mixture;25
8.5;4. Estimation when each population is sampled separately;26
8.6;5. Unknown mixing proportions;29
8.7;6. Iterative estimation of the logistic parameters;29
8.8;7. Logistic discrimination in medical diagnosis;30
8.9;8. Logistic methods in epidemiology;32
8.10;9. Discussion;33
8.11;REFERENCES;34
9;CHAPTER 2. ASYMPTOTIC EVALUATION OF THE PROBABILITIES
OF MISCLASSIFICATION BY LINEAR DISCRIMINANT FUNCTIONS;38
9.1;1. Introduction;38
9.2;2. The asymptotio expansion of the distribution of the
classification statistic;40
9.3;3. The asymptotic expansion of the distribution of the
Studentized W;43
9.4;4. Numerical values of the correction term for the
Studentized W when N1 = N2;45
9.5;5. Comparison of the expansions of the distributions of
W and the Studentized W;46
9.6;6. Comparison of approximate densities and moments;48
9.7;7. Achieving a given probability of misolassifieation;50
9.8;REFERENCES;53
10;CHAPTER 3. GRAPHICAL TECHNIQUES FOR HIGH DIMENSIONAL DATA;58
10.1;1. Summary and Introduction;58
10.2;2. Function Plots of High-Dimensional Data;59
10.3;3. An Example Involving Clusters;61
10.4;4. Plotting Covariance Matrices;65
10.5;5. Concluding Remarks;67
10.6;ACKNOWLEDGEMENT;67
10.7;REFERENCES;67
11;CHAPTER 4. DISTANCE, DISCRIMINATION AND ERROR;82
11.1;Introduction;82
11.2;1. The problem for diffusion processes;83
11.3;2. Case of known M
and;85
11.4;3. The case of unknown means and known dispersion matrix;90
11.5;4. The ease of unknown parameters;92
11.6;REFERENCES;96
12;CHAPTER 5. THEORIES AND METHODS IN CLASSIFICATION: A REVIEW;98
12.1;1A. Introduction;98
12.2;2. Problems in classification; different situations;104
12.3;3. Classification into known distributions; general theory;106
12.4;4. General Theory of Classification When the Information
About the Distribution is Based on Samples;113
12.5;5. Classification Into Multivariate Normal
Populations–Nonsequential Methods;118
12.6;6. Discrete and Other Non-normal Distributions;135
12.7;7, Nonparametric or "Distribution-free" Methods;143
12.8;8. Miscellaneous References;156
13;CHAPTER 6. METHODS AND APPLICATIONS OF EQUAL-MEAN DISCRIMINATION;160
13.1;1. Introduction;160
13.2;2. Setup of the Problem and Some Remarks;161
13.3;3. Discrimination for Covariance Matrices of the Multivariate
Normal Populations from the Classical View point;165
13.4;4. Bayesian Discrimination Methods for Covarianoe Matrices
of Multivariate Normal Populations with Common Mean Vector;167
13.5;5. An Example;173
13.6;6. Multiple Birth Discrimination;176
13.7;REFERENCES;179
14;CHAPTER 7. COMPUTER GRAPHICAL ANALYSIS AND DISCRIMINATION;182
14.1;Summary;182
14.2;Introduction;182
14.3;A
pictorial introduction to the problem;183
14.4;The Program;185
14.5;Examples;188
14.6;REFERENCES;190
14.7;APPENDIX: Graphics Discriminant Analysis;191
15;CHAPTER 8. DISCRIMINANT PROBLEMS ABOUT GAUSSIAN PROCESSES;194
15.1;REFERENCE;198
16;CHAPTER 9. THE BASIC PROBLEMS OF CLUSTER ANALYSIS;200
16.1;Summary;200
16.2;Cluster and Shape;202
16.3;Scale;204
16.4;Distance;205
16.5;Delimitation of Clusters;207
16.6;The Role of Probability;209
16.7;The Discarding of Redundant Variables;211
16.8;REFERENCES;212
17;CHAPTER 10. SOME RESULTS ON THE MULTIPLE GROUP DISCRIMINANT PROBLEM;214
17.1;1. Introduction;214
17.2;2. Configuration of Population Means;216
17.3;3. Behavior of the Methods;221
17.4;4. Discussion;223
17.5;ACKNOWLEDGEMENTS;225
17.6;REFERENCES;225
18;CHAPTER 11. DISCRIMINATION AND THE AFFINITY OF DISTRIBUTIONS;234
18.1;1. Introduction;234
18.2;2. Affinity as a measure of information for discrimination;235
18.3;3. Projection for discrimination;238
18.4;4. Gaussian cases;241
18.5;REFERENCES;244
19;CHAPTER 12. SIMULATION EXPERIMENTS WITH MULTIPLE GROUP LINEAR
AND QUADRATIC DISCRIMINANT ANALYSIS;246
19.1;Summary;246
19.2;1. Introduction, notation;246
19.3;2. Description of the computer program;249
19.4;3. Results;250
19.5;4. Discussion;254
19.6;REFERENCES;255
20;CHAPTER 13. FINITE AND INFINITE MODELS FOR GENERALIZED GROUP-TESTING WITH UNEQUAL PROBABILITIES OF SUCCESS FOR EACH
ITEM;260
20.1;1. Introduction;260
20.2;2. Vertical vs. Horizontal Procedures;261
20.3;3. An Example of a Vertical Procedure Equivalent to a Horizontal
Procedure;263
20.4;4. Finding the Optimal Procedure: Trial and Error Method;267
20.5;5. Theoretical Results with Special Reference to;268
20.6;6. Using Recursive Equations to Find the Optimal Horizontal
Procedure;281
20.7;7. Comparison with Finite Models;286
20.8;8. The Asymptotic Equivalence of Horizontal and Vertical
Procedures;289
20.9;9. Lower Bounds;297
20.10;ACKNOWLEDGEMENTS;299
20.11;REFERENCES;300
21;CHAPTER 14. QUASI-LINEAR DISCRIMINATION;312
21.1;1. Introduction;312
21.2;2. The basic ideas for known populations;313
21.3;3. Quasi-linecoe discrimination with only accidental parameters;316
21.4;4.
Non-existence of quasi-linear discrimination with constant errors;320
21.5;5. A general set-up for discrimination;322
21.6;6. The quasi-linear discrimination
problem;324
21.7;7. The use of maximum likelihood estimation;325
21.8;8. Discrimination between two normal populations;327
21.9;9. Discrimination for Gumbel populations;328
21.10;REFERENCES;329
22;CHAPTER 15. THE DISCRIMINANT FUNCTION IN SYSTEMATIC BIOLOGY;332
22.1;1. Intvoduction;332
22.2;2. Studying changes of shape in relation to environment: Solution of a biological systematic problem by a linear
discriminant function;333
22.3;3. Distinctions between morphologically similar organisms:
The problem of homeomorphy;334
22.4;4. Systematic use of quadratic discriminant functions;335
22.5;5. Discriminant function and the analysis of shape flexibility;335
22.6;6. Discrimination Functions and Time Series of Fossils;336
22.7;7, Allotting a specimen to the nearest population;338
22.8;8. Old friends revisited;340
22.9;9. Burnaby rs Problem: The question of growth invariance;347
22.10;10. An example: Evolution in Upper Cretaceous echinoids;347
22.11;REFERENCES;351
23;CHAPTER 16. CLASSIFYING WHEN POPULATIONS ARE ESTIMATED;360
23.1;1. Introduction;360
23.2;2. Problem 1 reformulated;362
23.3;3. Construction and comparison of some level-a tests for
Problem 1;363
23.4;4. Problem 2 reformulated;367
23.5;5. Construction and oomparison of some level-a tests for
Problem 2;369
23.6;6. A very simple loss-function formulation for Problem;371
23.7;7. A very simple loss-function formulation for Problem;374
23.8;8. Extending Section 7 to the case
s2 unknown;376
23.9;9. Other problems;378
23.10;ACKNOWLEDGEMENTS;381
23.11;REFERENCES;381
24;CHAPTER 17. SOME OPERATING CHARACTERISTICS OF LINEAR
DISCRIMINANT FUNCTIONS;386
24.1;Introduction;386
24.2;1. An approooimation for the probability of mis classification when N1 = N2 = N and wo =
O;389
24.3;2. Comparison of the approximation with some exact values;394
24.4;REFERENCES;395
25;CHAPTER 18. A BIBLIOGRAPHY OF DISCRIMINANT ANALYSIS;396
25.1;1. INTRODUCTION;396
25.2;2. BOOKS;399
25.3;3. JOURNALS AND COLLECTIONS;402
25.4;4. RESEARCH PAPERS;406
25.5;5 . ADDENDA;453
26;BIBLIOGRAPHY;454