During the last two decades, many areas of statistical inference have experienced phenomenal growth. This book presents a timely analysis and overview of some of these new developments and a contemporary outlook on the various frontiers of statistics. Eminent leaders in the field have contributed 16 review articles and 6 research articles covering areas including semi-parametric models, data analytical nonparametric methods, statistical learning, network tomography, longitudinal data analysis, financial econometrics, time series, bootstrap and other re-sampling methodologies, statistical computing, generalized nonlinear regression and mixed effects models, martingale transform tests for model diagnostics, robust multivariate analysis, single index models and wavelets. This volume is dedicated to Prof. Peter J Bickel in honor of his 65th birthday. The first article of this volume summarizes some of Prof. Bickel's distinguished contributions.
Author(s): Hira L Koul, Jianqing Fan
Publisher: Imperial College Press
Year: 2006
Language: English
Pages: 552
City: London
Tags: Математика;Теория вероятностей и математическая статистика;Математическая статистика;
Contents ......Page 12
1.1 Introduction ......Page 29
1.2 Doing Well at a Point and Beyond ......Page 30
1.4 Distribution Free Tests Higher Order Expansions and Challenging Projects ......Page 32
1.5 From Adaptive Estimation to Semiparametric Models ......Page 33
1.6 Hidden Markov Models ......Page 34
1.7 Non- and Semi-parametric Testing ......Page 35
References ......Page 36
Bickel's Publication ......Page 39
Part I. Semiparametric Modeling ......Page 51
2.1 Introduction ......Page 53
2.3 Testing and Profile Likelihood Theory ......Page 56
2.4 Semiparametric Mixture Model Theory ......Page 57
2.6 Bayes Methods and Theory ......Page 58
2.7 Model Selection Methods ......Page 59
2.9 Transformation and Frailty Models ......Page 60
2.10 Semiparametric Regression Models ......Page 61
2.11 Extensions to Non-i.i.d. Data ......Page 62
2.12 Critiques and Possible Alternative Theories ......Page 63
References ......Page 64
3.1 Introduction ......Page 73
3.2 Characterization of Efficient Estimators ......Page 75
3.3 Autoregression Parameter ......Page 78
3.4 Innovation Distribution ......Page 80
3.5 Innovation Density ......Page 82
3.6 Conditional Expectation ......Page 83
3.7 Stationary Distribution ......Page 85
3.8 Stationary Density ......Page 86
3.9 Transition Density ......Page 87
References ......Page 88
4.1 Introduction ......Page 91
4.2 Estimation via Outer Product of Gradients ......Page 94
4.3 Global Minimization Estimation Methods ......Page 96
4.4 Sliced Inverse Regression Method ......Page 98
4.5 Asymptotic Distributions ......Page 99
4.6 Comparisons in Some Special Cases ......Page 101
4.7 Proofs of the Theorems ......Page 102
References ......Page 112
5.1 Introduction ......Page 115
5.2 Estimating Function Based Cross-Validation ......Page 118
5.3 Some Examples ......Page 123
5.4 General Finite Sample Result ......Page 129
5.5 Appendix ......Page 133
References ......Page 136
Part II. Nonparametric Methods ......Page 139
6. Powerful Choices: Tuning Parameter Selection Based on Power ......Page 141
6.1 Introduction: Local Testing and Asymptotic Power ......Page 142
6.2 Maximizing Asymptotic Power ......Page 144
6.3 Examples ......Page 157
6.4 Appendix ......Page 162
References ......Page 167
7. Nonparametric Assessment of Atypicality ......Page 171
7.1 Introduction ......Page 172
7.2 Estimating Atypicality ......Page 173
7.3 Theoretical Properties ......Page 176
7.4 Numerical Properties ......Page 179
7.5 Outline of Proof of Theorem 7.1 ......Page 185
References ......Page 188
8.1 Introduction ......Page 191
8.2 Wavelets ......Page 192
8.3 Nonparametric Regression ......Page 194
8.4 Inverse Problems ......Page 200
8.5 Change-points ......Page 202
8.6 Local Self-similarity and Non-stationary Stochastic Process ......Page 204
References ......Page 207
9.1 Introduction ......Page 211
9.2 Lack-of-fit Tests ......Page 225
9.3 Censoring ......Page 229
9.4 Khamaladze Transform or Bootstrap ......Page 230
References ......Page 231
Part III. Statistical Learning and Bootstrap ......Page 235
10.1 Introduction ......Page 237
10.2 Boosting and Functional Gradient Descent ......Page 239
10.3 L2-Boosting for High-dimensional Multivariate Regression ......Page 245
10.4 L2-Boosting for Multivariate Linear Time Series ......Page 250
References ......Page 257
11.1 Introduction ......Page 259
11.2 Bootstrap for i.i.d Data ......Page 261
11.3 Model Based Bootstrap ......Page 266
11.4 Block Bootstrap ......Page 268
11.5 Sieve Bootstrap ......Page 271
11.6 Transformation Based Bootstrap ......Page 272
11.7 Bootstrap for Markov Processes ......Page 273
11.8 Bootstrap under Long Range Dependence ......Page 274
11.9 Bootstrap for Spatial Data ......Page 276
References ......Page 278
12.1 Introduction ......Page 285
12.2 Proof of Theorem 12.1 ......Page 290
12.3 Evaluation of the Oscillatory Term ......Page 299
References ......Page 301
Part IV. Longitudinal Data Analysis ......Page 303
13.1 Introduction ......Page 305
13.2 Nonparametric Model with a Single Covariate ......Page 307
13.3 Partially Linear Models ......Page 311
13.4 Varying-Coefficient Models ......Page 319
13.5 An Illustration ......Page 321
13.6 Generalizations ......Page 322
13.7 Estimation of Covariance Matrix ......Page 324
References ......Page 327
14.1 Introduction and Review ......Page 333
14.2 The Functional Approach to Longitudinal Responses ......Page 339
14.3 Predicting Longitudinal Trajectories from a Covariate ......Page 341
14.4 Illustrations ......Page 344
References ......Page 349
Part V. Statistics in Science and Technology ......Page 353
15. Statistical Physics and Statistical Computing: A Critical Link ......Page 355
15.2 The Ising Model ......Page 356
15.3 The Swendsen-Wang Algorithm and Criticality ......Page 357
15.4 Instantaneous Hellinger Distance and Heat Capacity ......Page 359
15.5 A Brief Overview of Perfect Sampling ......Page 362
15.6 Huber's Bounding Chain Algorithm ......Page 364
15.7 Approximating Criticality via Coupling Time ......Page 368
15.8 A Speculation ......Page 370
References ......Page 371
16. Network Tomography: A Review and Recent Developments ......Page 373
16.1 Introduction ......Page 374
16.2 Passive Tomography ......Page 376
16.3 Active Tomography ......Page 380
16.4 An Application ......Page 387
16.5 Concluding Remarks ......Page 391
References ......Page 392
Part VI. Financial Econometrics ......Page 395
17.1 Introduction ......Page 397
17.2 The Univariate Case ......Page 399
17.3 Multivariate Likelihood Expansions ......Page 406
17.4 Connection to Saddlepoint Approximations ......Page 411
17.5 An Example with Nonlinear Drift and Diffusion Specifications ......Page 414
17.6 An Example with Stochastic Volatility ......Page 417
17.7 Inference When the State is Partially Observed ......Page 419
17.8 Application to Specification Testing ......Page 427
17.9 Derivative Pricing Applications ......Page 428
17.10 Likelihood Inference for Diffusions under Nonstationarity ......Page 429
References ......Page 430
18.1 The Frontier Model ......Page 435
18.2 Envelope Estimators ......Page 437
18.3 Order-m Estimators ......Page 445
18.4 Conditional Frontier Models ......Page 449
18.5 Outlook ......Page 451
References ......Page 452
Part VII. Parametric Techniques and Inferences ......Page 455
19.1 Introduction ......Page 457
19.2 Newton's Estimate of Mixing Distributions ......Page 459
19.3 Review of Newton's Result on Convergence ......Page 460
19.4 Convergence Results ......Page 461
19.5 Other Results ......Page 466
19.6 Simulation ......Page 468
References ......Page 470
20.1 Introduction ......Page 473
20.2 Linear Mixed Models ......Page 474
20.3 Generalized Linear Mixed Models ......Page 478
20.4 Nonlinear Mixed Effects Models ......Page 483
References ......Page 488
21.1 Introduction ......Page 495
21.2 Robustness Criteria ......Page 497
21.3 Robust Multivariate Location and Scatter Estimators ......Page 501
21.4 Applications ......Page 509
21.5 Conclusions and Future Works ......Page 512
References ......Page 513
22.1 Introduction ......Page 519
22.2 Kullback-Leibler Loss and Exponential Families ......Page 521
22.3 Mean Square Error Loss ......Page 523
22.4 Location Families ......Page 524
22.5 Approximate Solutions ......Page 526
22.6 Convergence of the Loss Estimate ......Page 530
References ......Page 534
Subject Index ......Page 535
Author Index ......Page 539
