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Optimization Heuristics in Econometrics and Statistics: Applications Using Threshold Accepting

Peter Winker
Format
Book
Published
New York ; Chichester : Wiley, 2000.
Language
English
Series
Wiley Series in Probability and Statistics
ISBN
0471856312
Contents
  • 1.1 Optimization is all around 2
  • 1.2 A Flavour of Optimization Heuristics 4
  • 1.3 Outline of the Book 15
  • I Optimization in Statistics and Econometrics 19
  • 2 Optimization in Economics 21
  • 2.2 Optimization in Economic Theory and Practice 22
  • 2.2.1 Household behaviour 22
  • 2.2.2 Firm behaviour 25
  • 2.2.3 Fiscal and monetary policy instances 26
  • 2.3 Complexity and Heuristics 27
  • 2.3.1 Complexity 28
  • 2.3.2 Heuristics 30
  • 2.3.3 Economics of computation 32
  • 3 Optimization in Statistics and Econometrics 35
  • 3.1 Statistics is Optimization 35
  • 3.1.1 Data description 36
  • 3.1.2 Modelling 40
  • 3.1.3 Statistical inference 42
  • 3.1.4 Optimization methods in statistics 43
  • 3.2 Econometrics through an Optimizer's Eye 44
  • 3.2.1 Money demand model selection 45
  • 3.2.2 Estimation of money demand 46
  • 3.2.3 Implications of optimization 49
  • 3.3 Complexity Issues 50
  • 3.3.1 Low complexity problems 54
  • 3.3.2 More complex problems 54
  • 3.3.3 Highly complex problems 55
  • 4 Heuristic Optimization Paradigm 57
  • 4.1 Classical Optimization Paradigm 57
  • 4.2 Limits of the Classical Paradigm 59
  • 4.3 Heuristics 61
  • II Heuristic Optimization: Threshold Accepting 67
  • 5 Optimization Methods 69
  • 5.1 Classical Optimization Methods 70
  • 5.1.1 Least squares 70
  • 5.1.2 Gradient methods 71
  • 5.1.3 Enumeration 73
  • 5.1.4 Grid search 74
  • 5.1.5 Local search 75
  • 5.2 Optimization Heuristics 79
  • 5.2.1 Simulated annealing 80
  • 5.2.2 Genetic algorithms 82
  • 5.2.3 Tabu search 83
  • 5.2.4 Great-Deluge algorithm 83
  • 5.2.5 Noising method 84
  • 5.2.6 Ruin and recreate 84
  • 5.2.7 Hybrid methods 85
  • 5.2.8 Neural networks 86
  • 6 Global Optimization Heuristic Threshold Accepting 89
  • 6.1 Algorithm 89
  • 6.2 Proceeding of Threshold Accepting: An Example 95
  • 6.3 Some Applications 98
  • 7 Relative Performance of Threshold Accepting 101
  • 7.2 Asymptotic Behaviour 102
  • 7.3 Convergence of Simulated Annealing 106
  • 7.4 Convergence of Threshold Accepting 108
  • 7.5 Results of Comparative Implementations 109
  • 8 Tuning of Threshold Accepting 113
  • 8.1 Travelling Salesman Problem 114
  • 8.2 An Example with 442 Points 115
  • 8.3 Choice of Neighbourhoods 117
  • 8.4 Choice of Parameters for Threshold Accepting 122
  • 8.5 Restart Threshold Accepting 129
  • 9 A Practical Guide to the Implementation of Threshold Accepting 137
  • 9.1 Three Steps for a Successful Implementation 137
  • 9.2 Make it an Optimization Problem 138
  • 9.3 Give it Local Structure 142
  • 9.4 Cross the Thresholds 145
  • III Applications in Statistics and Econometrics 149
  • 11 Experimental Design 155
  • 11.1.1 What is 'experimental design'? 155
  • 11.1.2 Where is experimental design used? 156
  • 11.1.3 Experimental design in economics and statistics 158
  • 11.1.4 Experimental design as an optimization problem 159
  • 11.2 Problem and Complexity of Optimal Experimental Design 160
  • 11.2.1 Objective 160
  • 11.2.2 Solution approaches 164
  • 11.3 Threshold Accepting Implementation 168
  • 11.3.1 Optimization problem 168
  • 11.3.2 Local structure 170
  • 11.4 Results for Uniform and Mixture Level Designs 174
  • 11.4.1 Uniform designs for the star-discrepancy 175
  • 11.4.2 Uniform designs for alternative discrepancy measures 178
  • 11.4.3 Mixture level designs 179
  • 11.4.4 Uniformity and orthogonality 181
  • 11.5 Ruin and Recreate 183
  • 11.6 Applications 185
  • 11.6.1 Experimental economics 185
  • 11.6.2 Response surface analysis 186
  • 11.6.3 Quasi-Monte Carlo methods 191
  • 12 Identification of Multivariate Lag Structures 193
  • 12.2 Lag Structure Identification Problem 198
  • 12.3 Model Selection Criteria 201
  • 12.4 Implementation of Threshold Accepting 204
  • 12.5- Results of Monte Carlo Simulations 209
  • 12.5.1 A bivariate VAR process 209
  • 12.5.2 Further bivariate VAR processes 218
  • 12.5.3 Randomly generated bivariate structures 222
  • 12.5.4 A real trivariate process 225
  • 12.5.5 Money demand example 227
  • 12.6 Second-Step Statistics 229
  • 13 Optimal Aggregation 233
  • 13.2 Measuring Aggregation Bias 236
  • 13.3 An Application to Price Indices 242
  • 13.4 Threshold Accepting Implementation 244
  • 13.5 Results from Optimal Aggregation 248
  • 13.5.1 German industrial classification system 249
  • 13.5.2 Swedish industrial classification system 253
  • 13.6 Robustness 255
  • 13.7 A Dynamic Model 258
  • 13.9 Appendix: The Computational Complexity of Optimal Aggregation 261
  • 13.9.2 NP-completeness 262
  • 13.9.3 Computational complexity of Optimal Aggregation 265
  • 13.10 Appendix: Commodity Groups and Weights 270
  • 14 Censored Quantile Regression 273
  • 14.2 Interpolation Property 275
  • 14.3 Algorithms for the CQR Estimation Problem 277
  • 14.3.1 Enumeration 278
  • 14.3.2 Threshold accepting implementation 279
  • 14.4 Simulation Set-Up and Results 280
  • 14.4.1 Absolute performance 283
  • 14.4.2 Relative performance 284
  • 14.4.3 Properties of coefficient estimates 285
  • 14.4.4 Timing 287
  • 15 Continuous Global Optimization 289
  • 15.2 Implementation of Threshold Accepting 293
  • 15.3 Performance of Optimization Heuristics for Continuous Global Optimization 294
  • 16.1 Optimization Paradigms 301
  • 16.2 Art of Implementing Threshold Accepting 302
  • 16.3 Using Threshold Accepting in Statistics and Econometrics 304
  • 17 Outlook for Further Research 307
  • 17.1 Change in the Optimization Paradigm 308
  • 17.2 Asymptotic Considerations 308
  • 17.3 Improvements of Performance 309
  • 17.4 Further Applications 310.
Description
xii, 333 p. : ill. ; 24 cm.
Notes
Includes bibliographical references and index.
Technical Details
  • Access in Virgo Classic
  • Staff View

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    g| 1.1 t| Optimization is all around g| 2 -- g| 1.2 t| A Flavour of Optimization Heuristics g| 4 -- g| 1.3 t| Outline of the Book g| 15 -- g| I t| Optimization in Statistics and Econometrics g| 19 -- g| 2 t| Optimization in Economics g| 21 -- g| 2.2 t| Optimization in Economic Theory and Practice g| 22 -- g| 2.2.1 t| Household behaviour g| 22 -- g| 2.2.2 t| Firm behaviour g| 25 -- g| 2.2.3 t| Fiscal and monetary policy instances g| 26 -- g| 2.3 t| Complexity and Heuristics g| 27 -- g| 2.3.1 t| Complexity g| 28 -- g| 2.3.2 t| Heuristics g| 30 -- g| 2.3.3 t| Economics of computation g| 32 -- g| 3 t| Optimization in Statistics and Econometrics g| 35 -- g| 3.1 t| Statistics is Optimization g| 35 -- g| 3.1.1 t| Data description g| 36 -- g| 3.1.2 t| Modelling g| 40 -- g| 3.1.3 t| Statistical inference g| 42 -- g| 3.1.4 t| Optimization methods in statistics g| 43 -- g| 3.2 t| Econometrics through an Optimizer's Eye g| 44 -- g| 3.2.1 t| Money demand model selection g| 45 -- g| 3.2.2 t| Estimation of money demand g| 46 -- g| 3.2.3 t| Implications of optimization g| 49 -- g| 3.3 t| Complexity Issues g| 50 -- g| 3.3.1 t| Low complexity problems g| 54 -- g| 3.3.2 t| More complex problems g| 54 -- g| 3.3.3 t| Highly complex problems g| 55 -- g| 4 t| Heuristic Optimization Paradigm g| 57 -- g| 4.1 t| Classical Optimization Paradigm g| 57 -- g| 4.2 t| Limits of the Classical Paradigm g| 59 -- g| 4.3 t| Heuristics g| 61 -- g| II t| Heuristic Optimization: Threshold Accepting g| 67 -- g| 5 t| Optimization Methods g| 69 -- g| 5.1 t| Classical Optimization Methods g| 70 -- g| 5.1.1 t| Least squares g| 70 -- g| 5.1.2 t| Gradient methods g| 71 -- g| 5.1.3 t| Enumeration g| 73 -- g| 5.1.4 t| Grid search g| 74 -- g| 5.1.5 t| Local search g| 75 -- g| 5.2 t| Optimization Heuristics g| 79 -- g| 5.2.1 t| Simulated annealing g| 80 -- g| 5.2.2 t| Genetic algorithms g| 82 -- g| 5.2.3 t| Tabu search g| 83 -- g| 5.2.4 t| Great-Deluge algorithm g| 83 -- g| 5.2.5 t| Noising method g| 84 -- g| 5.2.6 t| Ruin and recreate g| 84 -- g| 5.2.7 t| Hybrid methods g| 85 -- g| 5.2.8 t| Neural networks g| 86 -- g| 6 t| Global Optimization Heuristic Threshold Accepting g| 89 -- g| 6.1 t| Algorithm g| 89 -- g| 6.2 t| Proceeding of Threshold Accepting: An Example g| 95 -- g| 6.3 t| Some Applications g| 98 -- g| 7 t| Relative Performance of Threshold Accepting g| 101 -- g| 7.2 t| Asymptotic Behaviour g| 102 -- g| 7.3 t| Convergence of Simulated Annealing g| 106 -- g| 7.4 t| Convergence of Threshold Accepting g| 108 -- g| 7.5 t| Results of Comparative Implementations g| 109 -- g| 8 t| Tuning of Threshold Accepting g| 113 -- g| 8.1 t| Travelling Salesman Problem g| 114 -- g| 8.2 t| An Example with 442 Points g| 115 -- g| 8.3 t| Choice of Neighbourhoods g| 117 -- g| 8.4 t| Choice of Parameters for Threshold Accepting g| 122 -- g| 8.5 t| Restart Threshold Accepting g| 129 -- g| 9 t| A Practical Guide to the Implementation of Threshold Accepting g| 137 -- g| 9.1 t| Three Steps for a Successful Implementation g| 137 -- g| 9.2 t| Make it an Optimization Problem g| 138 -- g| 9.3 t| Give it Local Structure g| 142 -- g| 9.4 t| Cross the Thresholds g| 145 -- g| III t| Applications in Statistics and Econometrics g| 149 -- g| 11 t| Experimental Design g| 155 -- g| 11.1.1 t| What is 'experimental design'? g| 155 -- g| 11.1.2 t| Where is experimental design used? g| 156 -- g| 11.1.3 t| Experimental design in economics and statistics g| 158 -- g| 11.1.4 t| Experimental design as an optimization problem g| 159 -- g| 11.2 t| Problem and Complexity of Optimal Experimental Design g| 160 -- g| 11.2.1 t| Objective g| 160 -- g| 11.2.2 t| Solution approaches g| 164 -- g| 11.3 t| Threshold Accepting Implementation g| 168 -- g| 11.3.1 t| Optimization problem g| 168 -- g| 11.3.2 t| Local structure g| 170 -- g| 11.4 t| Results for Uniform and Mixture Level Designs g| 174 -- g| 11.4.1 t| Uniform designs for the star-discrepancy g| 175 -- g| 11.4.2 t| Uniform designs for alternative discrepancy measures g| 178 -- g| 11.4.3 t| Mixture level designs g| 179 -- g| 11.4.4 t| Uniformity and orthogonality g| 181 -- g| 11.5 t| Ruin and Recreate g| 183 -- g| 11.6 t| Applications g| 185 -- g| 11.6.1 t| Experimental economics g| 185 -- g| 11.6.2 t| Response surface analysis g| 186 -- g| 11.6.3 t| Quasi-Monte Carlo methods g| 191 -- g| 12 t| Identification of Multivariate Lag Structures g| 193 -- g| 12.2 t| Lag Structure Identification Problem g| 198 -- g| 12.3 t| Model Selection Criteria g| 201 -- g| 12.4 t| Implementation of Threshold Accepting g| 204 -- g| 12.5- t| Results of Monte Carlo Simulations g| 209 -- g| 12.5.1 t| A bivariate VAR process g| 209 -- g| 12.5.2 t| Further bivariate VAR processes g| 218 -- g| 12.5.3 t| Randomly generated bivariate structures g| 222 -- g| 12.5.4 t| A real trivariate process g| 225 -- g| 12.5.5 t| Money demand example g| 227 -- g| 12.6 t| Second-Step Statistics g| 229 -- g| 13 t| Optimal Aggregation g| 233 -- g| 13.2 t| Measuring Aggregation Bias g| 236 -- g| 13.3 t| An Application to Price Indices g| 242 -- g| 13.4 t| Threshold Accepting Implementation g| 244 -- g| 13.5 t| Results from Optimal Aggregation g| 248 -- g| 13.5.1 t| German industrial classification system g| 249 -- g| 13.5.2 t| Swedish industrial classification system g| 253 -- g| 13.6 t| Robustness g| 255 -- g| 13.7 t| A Dynamic Model g| 258 -- g| 13.9 t| Appendix: The Computational Complexity of Optimal Aggregation g| 261 -- g| 13.9.2 t| NP-completeness g| 262 -- g| 13.9.3 t| Computational complexity of Optimal Aggregation g| 265 -- g| 13.10 t| Appendix: Commodity Groups and Weights g| 270 -- g| 14 t| Censored Quantile Regression g| 273 -- g| 14.2 t| Interpolation Property g| 275 -- g| 14.3 t| Algorithms for the CQR Estimation Problem g| 277 -- g| 14.3.1 t| Enumeration g| 278 -- g| 14.3.2 t| Threshold accepting implementation g| 279 -- g| 14.4 t| Simulation Set-Up and Results g| 280 -- g| 14.4.1 t| Absolute performance g| 283 -- g| 14.4.2 t| Relative performance g| 284 -- g| 14.4.3 t| Properties of coefficient estimates g| 285 -- g| 14.4.4 t| Timing g| 287 -- g| 15 t| Continuous Global Optimization g| 289 -- g| 15.2 t| Implementation of Threshold Accepting g| 293 -- g| 15.3 t| Performance of Optimization Heuristics for Continuous Global Optimization g| 294 -- g| 16.1 t| Optimization Paradigms g| 301 -- g| 16.2 t| Art of Implementing Threshold Accepting g| 302 -- g| 16.3 t| Using Threshold Accepting in Statistics and Econometrics g| 304 -- g| 17 t| Outlook for Further Research g| 307 -- g| 17.1 t| Change in the Optimization Paradigm g| 308 -- g| 17.2 t| Asymptotic Considerations g| 308 -- g| 17.3 t| Improvements of Performance g| 309 -- g| 17.4 t| Further Applications g| 310.
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    a| QA402.5 .W56 2000 w| LC i| X004476388 l| STACKS m| SCI-ENG t| BOOK
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