Data gathering, analysis and protection of privacy through randomized response techniques: qualitative and quantitative human traits
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| Format: | Book |
| Language: | English |
| Published: |
Amsterdam
Elsevier, North Holland
[2016]
|
| Series: | Handbook of statistics
volume 34 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xviii, 525 Seiten Diagramme 24 cm |
| ISBN: | 9780444635709 |
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| 245 | 1 | 0 | |a Data gathering, analysis and protection of privacy through randomized response techniques |b qualitative and quantitative human traits |c edited by Arijit Chaudhuri, Tasos C. Christofides, C.R. Rao |
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| adam_text | Contents
Contributors xv
Preface xvij
1. Review of Certain Recent Advances in Randomized
Response Techniques 1
T.J. Rao and C.R. Rao
1 Introduction 1
2 Warner s and Related Techniques 2
3 Cryptographic RRT 3
4 Reverse RRT 4
5 Certain Recent Theoretical and Practical Results 5
5.1 Unified Theory 5
5.2 Stratification and RRT 6
5.3 Cramer—Rao Lower Bound 7
5.4 Game Theory and RRT 7
5.5 Smart Phones and RRT 7
5.6 Alternatives to RRT 8
5.7 Meta Analysis 8
6 Epilogue 8
Acknowledgment 9
References 9
2. The Background and Genesis of Randomized
Response Techniques 1 3
A. Chaudhuri
3. How Randomized Response Techniques Need not Be Confined to Simple Random Sampling
but Liberally Applicable to General Sampling Schemes 1 7
A. Chaudhuri
1 Introduction 1 7
2 Two Prominent RR Devices Revised for General Applications 19
2.1 Warner Stanley s (1965) Device 19
2.2 Simmon s RR Device Revised 20
3 Quantitative RRs 22
v
VI
Contents
4 Protection of Privacy
4.1 When a Characteristic Is Qualitative and SRSWR Is Allowed
4.2 When a General Sampling Design Is Allowed to Cover a Qualitative Characteristic
4.3 Protection of Privacy Covering Quantitative Variables
5 Optional RR Techniques References
4. The Classical Randomized Response Techniques: Reading Warner (1965) and Greenberg et al. (1969) 50 Years Later
T.C. Christofides
1 Introduction
2 Warner s Randomized Response Technique
3 The Unrelated Question Model
4 Reading Warner (1965) and Greenberg et al. (1969)
50 Years Later
5 Epilogue References
29
29 U) 1 }
7
40
40
5. On the Estimation of Correlation Coefficient Using Scrambled Responses
S. Singh
1 Introduction
2 Two Scrambling Variable Randomized Response Technique
3 Scrambling Variables Are Dependent
4 Estimation of the Correlation Coefficient pxy
5 Bias and Mean Squared Error of r^
6 Scrambling Variables Are Independent
7 Bias and Mean Square Error of r-
8 Single Scrambling Variable Randomized Response Technique
9 Bias and Mean Squared Error of r2
10 Correlation Between Sensitive and Nonsensitive Variable
11 Bias and Mean Square Error of r3
12 Simulation Study Acknowledgments Appendix References
6. Admissible and Optimal Estimation in Finite Population Sampling Under Randomized Response Models
S. Sengupta
1 Introduction
2 Notations and Preliminaries
43
4 3
45
46 48 54
58
59 61 63 67 69 69 82 83 89
91
91
92
Contents
* • VII
3 Estimation Based on Single RR 96
3.1 Nonexistence of a Best Estimator 96
3.2 Admissibility Results 96
3.3 Optimality Results 98
4 Estimation Based on Independent Multiple Responses 99
4.1 Nonexistence of a Best Estimator 100
4.2 Admissibility Results 100
4.3 Optimality Results 101
5 Concluding Remarks 101
References 102
7. A Mixture of True and Randomized Responses in the Estimation of the Number of People
Having a Certain Attribute 1 05
A. Quatember
1 Introduction 105
2 A General RR Technique for the Estimation of
Group Size 108
3 Combining True and Randomized Responses 109
4 A Vivid Illustration of This Strategy Including True
and Masked Responses 11 4
References 11 7
8. Estimation of Complex Population Parameters
Under the Randomized Response Theory 119
L. Barabesi, G. Diana, and P.F. Perri
1 Introduction 119
2 Foundations of Functional Linearization 121
3 Functional Linearization with the RR Technique 123
4 Some Simple Examples 125
5 Further Examples with Some Inequality Indices 126
6 Final Remarks 1 29
Acknowledgments 129
References 130
9. An Efficient Randomized Response Model Using Two Decks of Cards Under Simple and
Stratified Random Sampling 133
S. Abdelfatah and /?. Mazloum
1 Introduction 133
2 Efficient Randomized Response Model Under Simple
Random Sampling 1 36
2.1 The Proposed Model 136
2.2 Efficiency Comparison 139
viii
3 Simulation Study .
4 Efficient Randomized Response Model Under Strati
tied
Random Sampling
4.1 The Proposed Stratified Model
4.2 Efficiency Comparison
5 Double Sampling for the Proposed Stratified Model
6 Conclusion References
10. Software for Randomized Response Techniques
M. Rueda, B. Cobo, A Arcos, and R. Amah
1 Introduction
2 Software for Helping to Conduct a Survey with RR
3 Software for the Estimation with Data Obtained Using KK Techniques
4 Summary Acknowledgments References
11. Poststratification Based on the Choice of Use of a Quantitative Randomization Device
O. Odumade, R. Arnab, and S. Singh
1 Introduction
2 Poststratification Based on the Choice of a Quantitative Randomization Device
3 Relative Efficiency Appendix References
12. Variance Estimation in Randomized Response Surveys
A.K. Adhikary
1 Introduction
2 Variance of Horvitz-Thompson (1952) Estimator
3 Variance of Hansen-Hurwitz (1943) Estimator
4 Variance of Raj s (1956) Ordered Estimator
5 Variance of Murthy s (1957) Unordered Estimator
6 Variance of Ratio Estimator Based on Lahiri (1951), Midzuno (1952), and Sen s (1953) Sampling Scheme
7 Variance of Hartley-Ross (1954) Unbiased Ratio-Type Estimator
References
( t intents
1 41
142
142
147
148 1 ~ i 1 1
lr r)
1 V)
I r 6
1 r H 1 2 M 164
169
1 69
170
171 174 189
191
191
194
197
200
202
204
206
207
Contents ¡x
13. Behavior of Some Scrambled Randomized Response Models Under Simple Random Sampling,
Ranked Set Sampling and Rao-Hartley-Cochran Designs 209
C.N. Bouza-Herrera
1 Introduction 209
2 Scrambling Procedures 210
3 Behavior Under RHC Unequal Probability Model 212
4 Behavior Under RSS 214
5 Conclusions 219
Acknowledgments 220
References 220
14. Estimation of a Finite Population Variance Under
Linear Models for Randomized Response Designs 221
P. Mukhopadhyay
1 Introduction 221
2 Optimal Estimation of V 224
3 UMVU Estimation 228
References 230
15. Randomized Response and New Thoughts
on Politz-Simmons Technique 233
T.J. Rao, J.Sarkar, and B.K. Sinha
1 Introduction 233
2 Not-at-Home s 234
2.1 Randomized Response Hartley—Politz-Simmons [RR-HPS]
Technique 234
2.2 A New RR-HPS Technique 236
Acknowledgments 246
Appendix 246
References 251
16. Optional Randomized Response: A Critical Review 253
R. Arnab and M. Rueda
1 Introduction 253
1.1 Warner s Technique: The Pioneering Method 254
1.2 Ericksson s Technique 255
1.3 A More General Model 256
2 General Method of Estimation 256
3 Optional Randomized Response Techniques 258
3.1 Full ORT 258
3.2 Partial ORT 264
X
4 Efficiency of the ORT
5 Conclusion References
C ontenis
267
268 269
17. A Concise Theory of Randomized Response Techniques for Privacy and Confidentiality Protection
T.K. Nayak, S.A. Adeshiyan, and C. Zhang
1 Introduction
2 Vital Attributes of Randomization Experiments
3 Statistical Estimation for Fixed P
4 Estimation Under Invariant Post-randomization
5 Assessing Privacy and Confidentiality Protection
6 Discussion Acknowledgments References
273
17 J 27r 278 2 HO 282 284 284 28r
18. A Review of Regression Procedures for Randomized Response Data, Including Univariate and Multivariate Logistic Regression, the Proportional Odds Model and Item Response Model, and Self-Protective Responses
CruyffU. Bdckenholt, RG.M. van der Heijden, and LE. Frank
1 Introduction
2 Univariate and Multivariate RR Data, No Explanatory Variables
2.1 Theory
2.2 Estimation
3 Logistic Regression of Univariate RR Data
3.1 Theory
3.2 Estimation
3.3 Extensions
4 Extensions of Regression Approaches to Multivariate RR Data
4.1 The Multivariate Logistic Regression Model Proposed by Glonek and McCullagh
4.2 Proportional Odds Model
5 Models Including Self-Protective Responses
5.1 Item Response Models
5.2 Self-Protective Responses
5.3 Example
5.4 Remaining Issues References
287
288
289 289 29 292
292
293
294
297
297
301
304
304
305
306 31 1 313
Contents xi
19. Eliciting Information on Sensitive Features: Block
Total Response Technique and Related Inference 317
K. Nandy, M. Marcovitz, and B.K. Sinha
1 Randomized Response Technique 317
2 Block Total Response Technique 318
3 SBTRM : Use of BIBD and Complimentary BIBD 320
4 Relative Comparison of BIBD-Based SBTRMs 320
5 Deriving the EB Estimators 321
6 Illustrative Example 324
7 Concluding Remarks 326
Acknowledgment 326
Appendix 326
A.1 Illustrative Examples 327
References 328
20. Optional Randomized Response Revisited 331
/?. Mukerjee
1 Introduction 331
2 Early Work 332
3 Scrambled Response 334
4 General Sampling Designs 337
5 Concluding Remarks 338
Acknowledgments 339
References 339
21. Measures of Respondent Privacy in Randomized
Response Surveys 341
M. Bose
1 Introduction 341
2 Qualitative Stigmatizing Variable 343
3 Quantitative Stigmatizing Variable 346
3.1 Continuous Stigmatizing Variable 346
3.2 Discrete Stigmatizing Variable 347
4 Concluding Remarks 349
References 350
22. Cramer-Rao Lower Bounds of Variance for Estimating
Two Proportions and Their Overlap by Using
Two Decks of Cards 353
C.-S. Lee, S.A. Sedory, and S. Singh
1 Introduction 353
1.1 Simple Model 354
1.2 Crossed Model 356
xii
2 Cramer—Rao Lower Bounds of Variances for the Simple Model
3 Cramer—Rao Lower Bounds of Variances for the Crossed Model
4 Comparison of the Variances and Lower Bounds
5 Unique Estimates
6 Range Restricted Maximum Likelihood Estimates Acknowledgment
Appendix A
Appendix B Codes Used in Simulation Studies References
23. Estimating a Finite Population Proportion Beari a Sensitive Attribute from a Single Probability Sample by Item Count Technique
R Shaw
Introduction
Item Count Technique Using a Single Sample
An Alternative Estimator of VP Numerical Presentation Conclusion Acknowledgments References
24. Surveying a Varying Probability Adaptive Sampl to Estimate Cost of Hospital Treatments of Sensitive Diseases by RR Data Gathering
S. Pal and S. Roy
1 Introduction
2 Formulation of Problem
3 RR Surveys
4 Adaptive Cluster Sampling
4.1 Network
5 Revised Adaptive Randomized Response Surveys
6 Simulation Study
7 Concluding Remarks References
25. Estimation of Means of Two Rare Sensitive Characteristics: Cramer-Rao Lower Bound of Variances
S.-C. Su, C.-S. Lee, S.A. Sedory and S. Singh
1 Introduction
2 Estimation of Two Rare Sensitive Attributes
Contents
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407
408 408 410 41 41
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Contents Xt
3 Proposed Randomized Response Model for Two Rare
Sensitive Attributes 419
4 Relative Efficiency 422
Acknowledgments 424
Appendix 424
References 425
26. Estimating Sensitive Population Proportion
by Generating Randomized Response Following Direct and Inverse Hypergeometric Distribution 427
K. Dihidar
1 Introduction 427
2 Generating RR by Hypergeometric Distribution 429
3 Generating RR by Negative Hypergeometric Distribution 430
4 Comparative Efficiencies of Inverse Hypergeometric vs Direct Hypergeometric RR Generation for Different
Sampling Schemes 432
4.1 SRSWR in n Draws 433
4.2 SRSWOR in n Draws 433
4.3 PPSWR in n Draws 434
4.4 Rao, Hartley, and Cochran s Sampling of Size n 434
4.5 Midzuno s (1952) Sampling of n Persons 435
4.6 Comparison of the Efficiencies 436
5 Numerical Illustration Showing Relative Performances
by Simulation 437
6 Concluding Remarks 440
Acknowledgment 440
References 440
27. Incredibly Efficient Use of a Negative Hypergeometric Distribution in Randomized
Response Techniques 443
M.L Johnson, S.A. Sedory, and S. Singh
1 Introduction 443
2 Singh and Sedory Randomization Device 447
3 Proposed Incredibly Efficient Randomization Device 452
4 Efficiency Comparison 457
5 Limiting Case with Four Decks of Cards 459
6 Relative Efficiency of the Limiting Case 463
Acknowledgments 466
Appendix 466
References 469
xiv Contents
28. Comparison of Different Imputing Methods
for Scrambled Responses 471
C. Mohamed, S.A Sedory, and S. Singh
1 Introduction 471
2 Ratio Method of Imputing Scrambled Responses 474
3 Regression Method of Imputing Scrambled Responses 475
4 Imputing Scrambled Responses Using Higher Order
Moments of An Auxiliary Variable 476
5 Some Useful Results 477
6 Properties of Different Estimators 478
7 Application to a Real Data Set 482
Acknowledgments 493
References 493
29. On an Indirect Response Model 497
V.R. Padmawar
1 Preliminaries 497
2 Introducing the Model 499
2.1 Method of Moments 500
2.2 Maximum Likelihood or Pseudolikelihood Method 504
2.3 Bayesian Framework 509
Acknowledgments 512
References 513
Index 515
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| spelling | Data gathering, analysis and protection of privacy through randomized response techniques qualitative and quantitative human traits edited by Arijit Chaudhuri, Tasos C. Christofides, C.R. Rao Amsterdam Elsevier, North Holland [2016] © 2016 xviii, 525 Seiten Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Handbook of statistics volume 34 Datenschutz (DE-588)4011134-9 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Datenerfassung (DE-588)4011123-4 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Datensammlung gnd rswk-swf Datenerfassung (DE-588)4011123-4 s Datensammlung f Datenanalyse (DE-588)4123037-1 s Datenschutz (DE-588)4011134-9 s b DE-604 Chaudhuri, Arijit 1940- (DE-588)170310973 edt Handbook of statistics volume 34 (DE-604)BV000002510 34 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028948362&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Data gathering, analysis and protection of privacy through randomized response techniques qualitative and quantitative human traits Handbook of statistics Datenschutz (DE-588)4011134-9 gnd Datenanalyse (DE-588)4123037-1 gnd Datenerfassung (DE-588)4011123-4 gnd |
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| title | Data gathering, analysis and protection of privacy through randomized response techniques qualitative and quantitative human traits |
| title_auth | Data gathering, analysis and protection of privacy through randomized response techniques qualitative and quantitative human traits |
| title_exact_search | Data gathering, analysis and protection of privacy through randomized response techniques qualitative and quantitative human traits |
| title_full | Data gathering, analysis and protection of privacy through randomized response techniques qualitative and quantitative human traits edited by Arijit Chaudhuri, Tasos C. Christofides, C.R. Rao |
| title_fullStr | Data gathering, analysis and protection of privacy through randomized response techniques qualitative and quantitative human traits edited by Arijit Chaudhuri, Tasos C. Christofides, C.R. Rao |
| title_full_unstemmed | Data gathering, analysis and protection of privacy through randomized response techniques qualitative and quantitative human traits edited by Arijit Chaudhuri, Tasos C. Christofides, C.R. Rao |
| title_short | Data gathering, analysis and protection of privacy through randomized response techniques |
| title_sort | data gathering analysis and protection of privacy through randomized response techniques qualitative and quantitative human traits |
| title_sub | qualitative and quantitative human traits |
| topic | Datenschutz (DE-588)4011134-9 gnd Datenanalyse (DE-588)4123037-1 gnd Datenerfassung (DE-588)4011123-4 gnd |
| topic_facet | Datenschutz Datenanalyse Datenerfassung Aufsatzsammlung Datensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028948362&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002510 |
| work_keys_str_mv | AT chaudhuriarijit datagatheringanalysisandprotectionofprivacythroughrandomizedresponsetechniquesqualitativeandquantitativehumantraits |