Statistical Modelling and Regression Structures (eBook)

Foreword 5
Acknowledgements 7
Contents 8
List of Contributors 17
The Smooth Complex Logarithm and Quasi- Periodic Models 23
1 Foreword 23
2 Introduction 23
3 Data and Models 24
4 More to Explore 34
5 Discussion 37
References 39
P-spline Varying Coefficient Models for Complex Data 40
1 Introduction 40
2 ÏLarge Scale" VCM, without Backfitting 43
3 Notation and Snapshot of a Smoothing Tool: B-splines 45
4 Using B-splines for Varying Coefficient Models 47
5 P-spline Snapshot: Equally-Spaced Knots & Penalization
6 Optimally Tuning P-splines 52
7 MoreKTBResults 54
8 Extending P-VCM into the Generalized Linear Model 54
9 Two-dimensional Varying Coefficient Models 57
10 Discussion Toward More Complex VCMs 62
References 63
Penalized Splines, Mixed Models and Bayesian Ideas 65
1 Introduction 65
2 Notation and Penalized Splines as Linear Mixed Models 66
3 Classification with Mixed Models 68
4 Variable Selection with Simple Priors 70
5 Discussion and Extensions 76
References 77
Bayesian Linear RegressionÛ Different Conjugate Models and Their ( In) Sensitivity to Prior- Data Conflict 79
1 Introduction 79
2 Prior-data Conflict in the i.i.d. Case 82
3 The Standard Approach for Bayesian Linear Regression (SCP) 84
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4 An Alternative Approach for Conjugate Priors in Bayesian Linear Regression ( CCCP) 88
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5 Discussion and Outlook 96
References 97
An Efficient Model Averaging Procedure for Logistic Regression Models Using a Bayesian Estimator with Laplace Prior 99
1 Introduction 99
2 Model Averaging 100
3 Simulation Study 106
4 Conclusion and Outlook 108
References 109
Posterior and Cross-validatory Predictive Checks: A Comparison of MCMC and INLA 111
1 Introduction 111
2 The INLA Approach 112
3 Predictive Model Checks with MCMC 116
4 Application 119
5 Discussion 127
References 129
Data Augmentation and MCMC for Binary and Multinomial Logit Models 131
1 Introduction 131
2 MCMC Estimation Based on Data Augmentation for Binary Logit Regression Models 133
3 MCMC Estimation Based on Data Augmentation for the Multinomial Logit Regression Model 140
4 MCMC Sampling without Data Augmentation 143
5 Comparison of the Various MCMC Algorithms 145
6 Concluding Remarks 150
References 151
Generalized Semiparametric Regression with Covariates Measured with Error 153
1 Introduction 153
2 Semiparametric Regression Models with Measurement Error 155
3 Bayesian Inference 159
4 Simulations 163
5 Incident Heart Failure in the ARIC Study 170
6 Summary 173
References 173
Determinants of the Socioeconomic and Spatial Pattern of Undernutrition by Sex in India: A Geoadditive Semi- parametric Regression Approach 175
1 Introduction 175
2 TheData 178
3 Measurement and Determinants of Undernutrition 180
4 Variables Included in the Regression Model 182
5 Statistical Methodology - Semiparametric Regression Analysis 187
6 Results 190
7 Conclusion 197
References 198
Boosting for Estimating Spatially Structured Additive Models 200
1 Introduction 200
2 Methods 202
3 Results 208
4 Discussion 213
References 214
Generalized Linear Mixed Models Based on Boosting 216
1 Introduction 216
2 Generalized Linear Mixed Models - GLMM 217
3 Boosted Generalized Linear Mixed Models - bGLMM 219
4 Application to CD4 Data 231
5 Concluding Remarks 233
References 233
Measurement and Predictors of a Negative Attitude towards Statistics among LMU Students 235
1 Introduction 235
2 Method 237
3 Results 239
4 Discussion and Conclusion 245
References 247
Graphical Chain Models and their Application 249
1 Introduction 249
2 Graphical Chain Models 251
3 Model Selection 253
4 Data Set 254
5 Results 258
6 Discussion 261
References 262
Appendix 264
Indirect Comparison of Interaction Graphs 266
1 Introduction 267
2 Methods 268
3 Example 272
4 Discussion 274
References 276
Appendix 277
. 278
Modelling, Estimation and Visualization of Multivariate Dependence for High- frequency Data 283
1 Multivariate Risk Assessment for Extreme Risk 283
2 Measuring Extreme Dependence 286
3 Extreme Dependence Estimation 296
4 High-frequency Financial Data 301
5 Conclusion 314
References 315
Ordinal- and Continuous-Response Stochastic Volatility Models for Price Changes: An Empirical Comparison 317
1 Introduction 317
2 Ordinal- and Continuous-Response Stochastic Volatility Models 319
3 Application 324
4 Summary and Discussion 335
References 336
Copula Choice with Factor Credit Portfolio Models 337
1 Introduction 337
2 Factor Models 339
3 The Berkowitz Test 341
4 Simulation Study and Analyses 344
5 Conclusion 351
References 351
Penalized Estimation for Integer Autoregressive Models 353
1 Introduction 353
2 Integer Autoregressive Processes and Inference 355
3 Penalized Conditional Least Squares Inference 357
4 Examples 359
5 Discussion 365
References 366
Appendix 367
Bayesian Inference for a Periodic Stochastic Volatility Model of Intraday Electricity Prices 369
1 Introduction 369
2 Periodic Autoregressions 371
3 Periodic Stochastic VolatilityModel 372
4 Bayesian Posterior Inference 375
5 Intraday Electricity Prices 377
6 Discussion 384
References 386
Appendix 388
S 391
Online Change-Point Detection in Categorical Time Series 393
1 Introduction 393
2 Modeling Categorical Time Series 394
3 Prospective CUSUM Changepoint Detection 398
4 Applications 404
5 Discussion 410
References 411
Multiple Linear Panel Regression with Multiplicative Random Noise 414
1 Introduction 414
2 The Model 416
3 The Naive Estimator and its Bias 417
4 Corrected Estimator 420
5 Residual Variance and Intercept 422
6 Asymptotic Covariance Matrix 423
7 Simulation 424
8 Conclusion 427
References 428
A Note on Using Multiple Singular Value Decompositions to Cluster Complex Intracellular Calcium Ion Signals 433
1 Introduction 433
2 Experiment 435
3 Methods 436
Ca2+ 437
Ca2+ 438
4 Clustering 441
5 Conclusion 441
References 442
On the self-regularization property of the EM algorithm for Poisson inverse problems 445
1 Introduction 445
2 Scaling properties of the EM algorithm 453
3 The effect of the initial guess 457
References 460
Sequential Design of Computer Experiments for Constrained Optimization 463
1 Introduction 464
2 Modeling 465
3 A Minimization Algorithm 467
4 An Autoregressive Model and Example 472
5 Discussion 480
References 485