Mahalanobis / Rao Contributions to Statistics

1. Auflage 2014
ISBN: 978-1-4832-8280-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 534 Seiten, Web PDF

Contributions to Statistics focuses on the processes, methodologies, and approaches involved in statistics. The book is presented to Professor P. C. Mahalanobis on the occasion of his 70th birthday. The selection first offers information on the recovery of ancillary information and combinatorial properties of partially balanced designs and association schemes. Discussions focus on combinatorial applications of the algebra of association matrices, sample size analogy, association matrices and the algebra of association schemes, and conceptual statistical experiments. The book then examines lattice sampling by means of Lahiri's sampling scheme; contributions of interpenetrating networks of samples; and apparently unconnected problems encountered in sampling work. The publication takes a look at screening processes, place of the design of experiments in the logic of scientific inference, and rarefaction. Topics include mathematical probability, scientific experience, combinatorial progress, gains and losses, criterion and scores, simple drug screening process, and screening of crop varieties. The manuscript then reviews the estimation and interpretation of gross differences and the simple response variance; partially balanced asymmetrical factorial designs; and approximation of distributions of sums of independent summands by infinitely divisible distributions. The selection is a dependable reference for statisticians and researchers interested in the processes, methodologies, and approaches employed in statistics.

Autoren/Hrsg.

Mahalanobis, P. C.

Rao, C. R.

Inhaltsverzeichnis

1;Front Cover;1
2;Contributions to Statistics;2
3;Copyright Page;3
4;Table of Contents;4
5;FOREWORD;6
6;CHAPTER 1. RECOVERY OF ANCILLARY INFORMATION;12
6.1;1. INTRODUCTION;12
6.2;2. THE SAMPLE SIZE ANALOGY;17
6.3;3. A LOGICAL DIFFICULTY;20
6.4;4. CONCEPTUAL STATISTICAL EXPERIMENTS;22
6.5;REFERENCES;25
7;CHAPTER 2. COMBINATORIAL PROPERTIES OF PARTIALLY BALANCED DESIGNS AND ASSOCIATION SCHEMES;26
7.1;1. DEFINITION OF ASSOCIATION SCHEMES AND PARTIALLY BALANCED INCOMPLETE BLOCK (PBIB) DESIGNS;26
7.2;2. RELATIONS AMONG THE PARAMETERS OF ASSOCIATION SCHEMES;27
7.3;3. A LESS DEMANDING DEFINITION
OF TWO CLASS ASSOCLlTION SCHEMES;28
7.4;4. SOME EXAMPLES OF TWO CLASS ASSOCIATION SCHEMES AND PBIB
DESIGNS BASED ON THEM;29
7.5;5. ASSOCIATION MATRICES AND THE ALGEBRA OF ASSOCIATION SCHEMES;35
7.6;6. COMBINATOBIAL APPLICATIONS OF THE ALGBBBA OF ASSOCIATION MATRICES;38
7.7;7. PARTIAL GEOMETRIES AND THE CORRESPONDING PBIB DESIGNS;43
7.8;8. PSEUDO-GEOMETRIC ASSOCIATION SCHEMES AND UNIQUENESS AND
EMBEDDING THEOREMS;47
7.9;References;52
8;CHAPTER 3. LATTICE SAMPLING BY MEANS OF LAHIRI'S SAMPLING SCHEME;54
8.1;1. INTRODUCTION;54
8.2;2. A GENERAL EXPOSITION OF LAHIRI'S SAMPLING SCHEME;54
8.3;3. APPLYING LAHIRI'S SAMPLING SCHEME TO LATTICE SAMPLING;57
8.4;REFERENCES;60
9;CHAPTER 4. ON SOME OF THE CONTRIBUTIONS OF INTERPENETRATING NETWORKS OF SAMPLES;62
9.1;BREADTH OF APPLICATION;62
9.2;ADVANTAGES OF IPNS;62
9.3;DETECTION OF PEBSISTENT ERRORS AND OF GROSS BLUNDEKS;63
9.4;BRIEF DESCRIPTION OF THE METHOD;65
9.5;EXAMPLE OF FORMAT FOR CALCULATION;66
9.6;ESTIMATES OF VARIANCE AND OF BIAS;68
10;CHAPTER 5. SOME APPARENTLY UNCONNECTED PROBLEMS ENCOUNTERED IN SAMPLING WORK;72
10.1;1. INTRODUCTION;72
10.2;2. THE PROBLEM OF MEDIAN-BIAS IN PPS SAMPLING;72
10.3;3. STABILITY OF THE VARIANCE ESTIMATE IN PPS SAMPLING;73
10.4;4. ESTIMATING VARIANCES BY FORMING RANDOM GROUPS;75
10.5;REFERENCES;77
11;CHAPTER 6. SCREENING PROCESSES: PROBLEMS AND ILLUSTRATIONS;78
11.1;SUMMARY;78
11.2;1. INTRODUCTION;78
11.3;2. TYPES OF ENTITY;79
11.4;3. POLYTOMOUS SCREENING;81
11.5;4. REGRADED SCREENING;81
11.6;5. COHORTS;82
11.7;6. CRITERION AND SCORES;83
11.8;7. GAINS AND LOSSES;85
11.9;8. COSTS;87
11.10;9. A SIMPLE DRUG SCREENING PROCESS;88
11.11;10. MORE GENERAL ASPECTS OF DRUG SCREENING;90
11.12;11. SCREENING OF CROP VARIETIES;92
11.13;12. OPERATING CHARAOTERISTIOS FOR VARIETAL SELECTION;94
11.14;13. EDUCATIONAL SCREENING;98
11.15;14. FURTHER MATHEMATICAL THEORY;100
11.16;15. MULTIVARIATE CRITERIA;102
11.17;REFERENCES;104
12;CHAPTER 7.
THE PLACE OF THE DESIGN OF EXPERIMENTS IN THE LOGIC OF SCIENTIFIC INFERENCE;106
12.1;1. EARLY AIMS;106
12.2;2. COMBINATORIAL PROGRESS;106
12.3;3. SCIENTIFIC EXPERIENCE;107
12.4;4. MATHEMATICAL PROBABILITY;108
12.5;5. MEASUREMENT IN NATURE;109
12.6;6. LOGICAL AND OPERATIVE CONDITIONS;110
13;CHAPTER 8. ON RAREFACTION;112
13.1;SUMMARY;112
13.2;INTRODUCTION;112
13.3;DEFINITIONS;113
13.4;PROOF;113
13.5;REFERENCES;115
14;CHAPTER 9. THE ESTIMATION AND INTERPRETATION OF GROSS DIFFERENCES AND THE SIMPLE RESPONSE VARIANCE;116
14.1;1. INTRODUCTION;116
14.2;2. CRITERIA FOR DESIGN OF STATISTICAL SURVEYS;117
14.3;3. THE MODEL;118
14.4;4. SIMPLE RESPONSE VARIANOE: SOME USEFUL RELATIONSHIPS AND APPROXIMATE
ESTTIMATORS;122
14.5;5. EXPEEIMENTAL MEASUREMENTS OF SIMPLE RESPONSE VARIANCE;131
14.6;6. DISCUSSION OF STATISTICAL ENGINEERING IMPLICATIONS OF SIMPLE RESPONSE VARIANCE;139
14.7;ACKNOWLEDGEMENTS;141
14.8;REFERENCES;141
15;CHAPTER 10.
VON MISES FUNCTIONALS AND MAXIMUM LIKELIHOOD ESTIMATION;142
15.1;1. INTRODUCTION;142
15.2;2. VON MISES FUNCTION ALS OF THE SECOND ORDER;143
15.3;3. THE MAXIMUM LIKELIHOOD FUNCTIONAL AND ITS PROPERTIES;145
15.4;4. EFFICIENCY OF . RELATIVE TO THE CLASS
M;150
15.5;REFERENCES;151
16;CHAPTER 11. PARTIALLY BALANCED ASYMMETRICAL FACTORIAL DESIGNS;152
16.1;SUMMARY;152
16.2;1. INTRODUCTION;152
16.3;2. BALANCED AND PARTIALLY BALANCED ASYMMETRICAL FACTORIAL DESIGNS;153
16.4;3. CONSTRUCTION OF PBAF DESIGNS OF THE CLASS q X 22;154
16.5;4. LIST OF IJSEFUL PBAF DESIGNS OF THE CLASS qx2^,q EVEN;158
16.6;5. CONSTRUCTION OF PBAF DESIGNS OF THE CLASS qx32;158
16.7;6. LIST OF USEFUL P B A F DESIGNS OF THE CLASS qx3^(q=2t or 3t);162
16.8;7. PBAF DESIGNS DERIVABLE BY USE OF PSEUDO-FACTORS;163
16.9;REFERENCES;163
17;CHAPTER 12. ON THE APPROXIMATION OF DISTRIBUTIONS OF SUMS OF INDEPENDENT SUMMANDS BY INFINITELY DIVISIBLE DISTRIBUTIONS;164
17.1;1. EIGHT LEMMAS;167
17.2;2. PROOF OF THEOREM 1;169
17.3;3. PROOF OF THEOREM 2;172
17.4;REFERENCES;178
18;CHAPTER 13. MULTI-SUBJECT SAMPLE SURVEY SYSTEM: SOME THOUGHTS BASED ON INDIAN EXPERIENCE;180
18.1;INTRODUCTION;180
18.2;CHABAOTEBISTIOS OF SELECTED SURVEY SYSTEM;180
18.3;CENSUS versus SAMPLE SURVEY;181
18.4;SAVINGS THROUGH USE OF SAMPLING;183
18.5;INTERDEPENDENCE OF NEEDS AND TECHNIQUES;187
18.6;NON-SAMPLING ERRORS AND RATIONAL BEHAVIOUR;188
18.7;NON-SAMPLING ERRORS AND SAMPLING;188
18.8;FACTORS PECULIAR TO UNDER-DEVELOPED COUNTRIES;190
18.9;QUESTIONNAIRE versus SCHEDULE OF ENQUIRY;192
18.10;TYPE OF INVESTIGATORS;193
18.11;PERMANENT ORGANISATION AND PROMOTION OF SAMPLE SURVEYS;201
18.12;PERMANENT ORGANISATION AND PROBLEM OF SAMPLING FRAMES;202
18.13;PERMANENT ORGANISATION AND ASSESSMENT AND CONTROL OF NON-SAMPLING ERRORS;205
18.14;INTERPENETRATING NETWORK OF SAMPLES;206
18.15;SURVEY PLAN AND COMMUNICATION DIFFICULTIES;208
18.16;STAGGERED SURVEY;210
18.17;SAMPLING FOR SPECIAL GROUPS AND MULTI-SUBJECT ENQUIRIES;212
18.18;COSTS AND INTEGRATED DESIGN;214
18.19;FIXED FIELD-STRENGTH AND SAMPLE DESIGN;219
18.20;OPTIMALITY OF A OONTINUING SURVEY ORGANISATION;220
18.21;CONCLUDING REMARKS;225
19;CHAPTER 14. FITTING ASYMPTOTIC REGRESSION CURVES WITH DIFFERENT ASYMPTOTES;226
19.1;I. INTRODUCTION;226
19.2;2. ESTIMATION;227
19.3;3. ANALYSIS OF DATA OF A PHYSIOLOGICAL EXPERIMENT;229
19.4;ACKNOWLEDGEMENT;233
19.5;REFERENCES;233
20;CHAPTER 15. SOME ASYMPTOTIC EXPANSIONS FOR THE DISTRIBUTION OF THE MAXIMUM LIKELIHOOD ESTIMATE;234
20.1;REFERENCES;243
21;CHAPTER 16. A GEOMETRICAL PROBLEM RELATED TO CYCLIC DESIGNS;244
21.1;REFERENCES;249
22;CHAPTER 17. INCREASE OF HUMAN STATURE IN INDIA AND ELSEWHERE;250
22.1;SUMMARY;250
22.2;INTRODUCTION;250
22.3;ANTHROPOMETRIC STUDIES;250
22.4;ACCEPTED AND REJECTED CANDIDATES;251
22.5;AGE OF REORUITS;252
22.6;COMMUNITIES;254
22.7;GEOGRAPHICAL VARIATION;255
22.8;YEARS OF RECRUITMENT;257
22.9;DATA FROM OTHER COUNTRIES;260
22.10;REFERENCES;263
23;CHAPTER 18. SOCIAL RESEARCH AND MAHALANOBIS'S D2;264
23.1;REFERENCES;286
24;CHAPTER 19. ON MAHALANOBIS' CONTRIBUTIONS TO THE DEVELOPMENT OF SAMPLE SURVEY THEORY AND METHODS;288
24.1;1. INTRODUCTION;288
24.2;2. HISTORICAL NOTE;288
24.3;3. DEVELOPMEKT OF SAMPLING THEORY;293
24.4;4. ASSESSMENT AND CONTROL OF ERRORS;306
24.5;5. ORGANIZATION OF LABGE-SOALE SAMPLE SURVEYS;314
24.6;6. BIBLIOGRAPHICAL NOTE;318
24.7;7. CONCLUSIONS;319
24.8;8. ACKNOWLEDGEMENTS;319
24.9;REFERENCES;319
25;CHAPTER 20. SOME NOTES ON SQC;322
25.1;I. INTRODUCTION;322
25.2;II. PEOSPEOTING;324
25.3;III. PROSPECTING CRITERIA;327
25.4;CONCLUSION;329
25.5;REFERENCES;329
26;CHAPTER 21. INTERNATIONAL ASPECTS OF QUALITY CONTROL ACTIVITY;330
26.1;1. INTRODUCTION;330
26.2;2. QUALITY OONTROL: A WAY OF HELPING OTHERS HELP THEMSELVES;330
26.3;3. Two ASPECTS OF QUALITY CONTROL ACTIVITIES;331
26.4;4. QUALITY CONTROL IN OTHER OOUNTBIBS;332
26.5;5. QUALITY CONTROL IN LESS DEVELOPED COUNTRIES;337
26.6;6. CONCLUSION;338
26.7;REFERENCES;339
27;CHAPTER 22. ESTIMATION FOR THE GENERALIZED POWER SERIES DISTRIBUTION WITH TWO PARAMETERS AND ITS APPLICATION TO BINOMIAL DISTRIBUTION;340
27.1;1. INTRODUCTION;340
27.2;2. ESTIMATION OF THE TWO PARAMETERS FOB THE
GPSD;340
27.3;3. ESTIMATION OF THE TWO PARAMETERS FOR THE BINOMIAL DISTRIBUTION;342
27.4;4. ESTIMATION FOR THE TRUNCATED BINOMIAL AND INCOMPLETE DIBETA AND TRIBETA FUNCTIONS;343
27.5;5. ILLUSTRATIVE EXAMPLES;345
27.6;REFERENCES;349
28;CHAPTER 23. CRITERIA OF ESTIMATION IN LARGE SAMPLES;350
28.1;SUMMARY;350
28.2;1. INTRODUCTION;350
28.3;2. CONSISTENCY;352
28.4;3. EFFICIENCY;352
28.5;4. SOME LEMMAS;355
28.6;5. SECOND ORDEB
EFFICIENCY;360
28.7;REFERENCES;367
29;CHAPTER 24. DISCRIMINATION OF GAUSSIAN PROCESSES;368
29.1;SUMMARY;368
29.2;1. CONTRIBUTIONS OF MAHALANOBIS;368
29.3;2. INTRODUCTION;368
29.4;3. MATHEMATICAL PRELIMINARIES;369
29.5;4. GAUSSIAN PROCESSES;371
29.6;5. GAUSSIAN MEASURES IN HILBERT SPACE;377
29.7;6. LIKELIHOOD RATIOS;380
29.8;REFERENCES;395
30;CHAPTER 25. CLIMATES ANCIENT AND MODERN;396
30.1;REFERENCES;414
31;CHAPTER 26. PUNCHED CARD PROCESSING OF SAMPLE SURVEY DATA FOR FRACTILE GRAPHICAL ANALYSIS;416
31.1;1. INTRODUCTION;416
31.2;2. PROCESSING OF NATIONAL SAMPLE SURVEY: CONSUMER'S EXPENDITURE DATA;417
31.3;3. A MECHANISED PROCEDURE FOR DETERMINATION OF FRACTILE POINTS;418
31.4;4. THE SUMMARY PUNCH METHOD;421
31.5;5. THE UNRELATED PROGRAMME METHOD;422
31.6;6. COST COMPARISON;422
31.7;REFERENCES;423
32;CHAPTER 27. HIERARCHICAL AND
p-BLOCK MULTIRESPONSE DESIGNS AND THEIR ANALYSIS;424
32.1;1. INTRODUCTORY REMARKS ON MULTIRESPONSE DESIGNS IN GENERAL;424
32.2;2. GENERAL DESCRIPTION OF HIERARCHICAL DESIGNS AND THE PROBLEMS UNDER THAT CLASS;425
32.3;3. A SKETCH OF THE MATHEMATICAL JUSTIFICATION OF THE PROCEDURE PROPOSED (ASSUMING TESTABILITY OF
H;427
32.4;4. MULTIRESPONSE DESIGNS WITH
p-BLOOK SYSTEMS;429
32.5;5. TESTABILITY CONDITIONS OF HIERARCHICAL DESIGNS WITH p-BLOCK SYSTEMS;430
32.6;6. NATURE OF THE MULTIVARIATE DESIGNS FOR AN IMPORTANT SPECIAL CASE;433
33;CHAPTER 28. A STUDY OF THE FIELD COST FOR THE COLLECTION OF HOUSEHOLD CONSUMPTION DATA BY AN INTERVIEW METHOD;434
33.1;1. INTRODUCTION;434
33.2;2. RESULTS OF THE EXPERIMENT;436
33.3;3. MODEL SCHEMES FOR A FOOD CONSUMPTION SURVEY;443
33.4;CONOLUSION;448
33.5;ACKNOWLEDGEMENT;449
33.6;REFERENCES;449
33.7;Appendix;450
34;CHAPTER 29. FIXED INTERVAL ANALYSIS AND FRACTILE ANALYSIS;454
34.1;SUMMARY;454
34.2;1. THE METHODS OF FIXED INTERVAL ANALYSIS AND FRACTILE ANALYSIS;454
34.3;2. NOTATIONS, DEFINITIONS ETC;459
34.4;3. LIMIT DISTRIBUTIONS;462
34.5;4. THEORETICAL APPLICATIONS;464
34.6;5. METHODS OF TESTING WITH JUST ONE SAMPLE;468
34.7;6. SOME HISTORICAL NOTES AND COMMENTS;471
34.8;REFERENCES;474
35;CHAPTER 30. AFFINE a-RESOLVABLE INCOMPLETE BLOCK DESIGNS;476
35.1;SUMMARY;476
35.2;1. INTRODUCTION AND PRELIMINARY RESULTS;476
35.3;2. BLOCK STRUCTURE OF CERTAIN Li
(s) DESIGNS;479
35.4;3. a-RESOLVABLE BIB DESIGNS;479
35.5;4. NONEXISTENCE OF AFFINE a-RESOLVABLE
BIB DESIGNS;480
35.6;5. a-RESOLVABLE PBIB DESIGNS WITH TWO ASSOCIATE CLASSES;481
35.7;6. NONEXISTENCE OF AFFINE a-RESOLVABLE PBIB DESIGNS WITH TWO ASSOCIATE CLASSES;482
35.8;REFERENCES;485
36;CHAPTER 31. A NOTE ON THE RELATION BETWEEN MAHALANOBIS DISTANCE AND WEIGHTED REGRESSION;486
36.1;REFERENCES;488
37;CHAPTER 32.
WHAT IS WRONG WITH THE TEACHING OF STATISTICS ?;490
37.1;REFERENCES;499
38;CHAPTER 33. SCIENTIFIC
CONTRIBUTIONS OF PROFESSOR P. C. MAHALANOBIS;500
38.1;1. LEADER OF STATISTICAL MOVEMENT IN INDIA;500
38.2;2. MAHALANOBIS DISTANCE;502
38.3;3. METEOROLOGIOAL RESEARCH;502
38.4;4. RECONSTRUCTION OF INFORMATION THROUGH SCRUTINY;503
38.5;5. EARLY EXAMPLES OF OPERATIONS RESEARCH;503
38.6;6. EDUCATIONAL TESTS;504
38.7;7. ERRORS IN FIELD EXPERIMENTATION;504
38.8;8, SAMPLE SURVEYS, SEQUENTLAL SAMPLING AND INTERPENETRATING NETWORK
OF SAMPLES (IPNS);505
38.9;9. NATIONAL PLANNING;506
38.10;10. FRACTILE GRAPHICAL ANALYSIS;506
38.11;BIBLIOGRAPHY;508
39;MESSAGES;522