1 Regression and the Normal Distribution 1
1.1 What Is Regression Analysis? 1
1.2 Fitting Data to a Normal Distribution 3
1.3 Power Transforms 7
1.4 Sampling and the Role of Normality 8
1.5 Regression and Sampling Designs 10
1.6 Actuarial Applications of Regression 12
1.7 Further Reading and References 13
1.8 Exercises 14
1.9 Technical Supplement – Central Limit Theorem 18
Part I Linear Regression
2 Basic Linear Regression 23
2.1 Correlations and Least Squares 23
2.2 Basic Linear Regression Model 29
2.3 Is the Model Useful? Some Basic Summary Measures 32
2.4 Properties of Regression Coef?cient Estimators 35
2.5 Statistical Inference 37
2.6 Building a Better Model: Residual Analysis 41
2.7 Application: Capital Asset Pricing Model 46
2.8 Illustrative Regression Computer Output 51
2.9 Further Reading and References 54
2.10 Exercises 54
2.11 Technical Supplement – Elements of Matrix Algebra 62
3 Multiple Linear Regression – I 70
3.1 Method of Least Squares 70
3.2 Linear Regression Model and Properties of Estimators 76
3.3 Estimation and Goodness of Fit 81
3.4 Statistical Inference for a Single Coef?cient 85
3.5 Some Special Explanatory Variables 92
3.6 Further Reading and References 100
3.7 Exercises 101
viiviii Contents
4 Multiple Linear Regression – II 107
4.1 The Role of Binary Variables 107
4.2 Statistical Inference for Several Coef?cients 113
4.3 One Factor ANOVA Model 120
4.4 Combining Categorical and Continuous Explanatory Variables 126
4.5 Further Reading and References 133
4.6 Exercises 133
4.7 Technical Supplement – Matrix Expressions 138
5 Variable Selection 148
5.1 An Iterative Approach to Data Analysis and Modeling 148
5.2 Automatic Variable Selection Procedures 149
5.3 Residual Analysis 153
5.4 In?uential Points 160
5.5 Collinearity 165
5.6 Selection Criteria 171
5.7 Heteroscedasticity 175
5.8 Further Reading and References 179
5.9 Exercises 180
5.10 Technical Supplements for Chapter 5 182
6 Interpreting Regression Results 189
6.1 What the Modeling Process Tells Us 190
6.2 The Importance of Variable Selection 196
6.3 The Importance of Data Collection 198
6.4 Missing Data Models 205
6.5 Application: Risk Managers’ Cost-Effectiveness 209
6.6 Further Reading and References 218
6.7 Exercises 219
6.8 Technical Supplements for Chapter 6 222
Part II Topics in Time Series
7 Modeling Trends 227
7.1 Introduction 227
7.2 Fitting Trends in Time 229
7.3 Stationarity and Random Walk Models 236
7.4 Inference Using Random Walk Models 238
7.5 Filtering to Achieve Stationarity 243
7.6 Forecast Evaluation 245
7.7 Further Reading and References 248
7.8 Exercises 249
8 Autocorrelations and Autoregressive Models 251
8.1 Autocorrelations 251
8.2 Autoregressive Models of Order One 254Contents ix
8.3 Estimation and Diagnostic Checking 256
8.4 Smoothing and Prediction 258
8.5 Box-Jenkins Modeling and Forecasting 260
8.6 Application: Hong Kong Exchange Rates 265
8.7 Further Reading and References 269
8.8 Exercises 270
9 Forecasting and Time Series Models 273
9.1 Smoothing with Moving Averages 273
9.2 Exponential Smoothing 275
9.3 Seasonal Time Series Models 278
9.4 Unit Root Tests 284
9.5 ARCH/GARCH Models 285
9.6 Further Reading and References 288
10 Longitudinal and Panel Data Models 289
10.1 What Are Longitudinal and Panel Data? 289
10.2 Visualizing Longitudinal and Panel Data 291
10.3 Basic Fixed Effects Models 293
10.4 Extended Fixed Effects Models 296
10.5 Random Effects Models 299
10.6 Further Reading and References 301
Part III Topics in Nonlinear Regression
11 Categorical Dependent Variables 305
11.1 Binary Dependent Variables 305
11.2 Logistic and Probit Regression Models 307
11.3 Inference for Logistic and Probit Regression Models 312
11.4 Application: Medical Expenditures 315
11.5 Nominal Dependent Variables 318
11.6 Ordinal Dependent Variables 325
11.7 Further Reading and References 328
11.8 Exercises 329
11.9 Technical Supplements – Likelihood-Based Inference 337
12 Count Dependent Variables 343
12.1 Poisson Regression 343
12.2 Application: Singapore Automobile Insurance 348
12.3 Overdispersion and Negative Binomial Models 352
12.4 Other Count Models 354
12.5 Further Reading and References 359
12.6 Exercises 360
13 Generalized Linear Models 362
13.1 Introduction 362
13.2 GLM Model 364x Contents
13.3 Estimation 367
13.4 Application: Medical Expenditures 371
13.5 Residuals 374
13.6 Tweedie Distribution 375
13.7 Further Reading and References 376
13.8 Exercises 377
13.9 Technical Supplements – Exponential Family 378
14 Survival Models 383
14.1 Introduction 383
14.2 Censoring and Truncation 385
14.3 Accelerated Failure Time Model 390
14.4 Proportional Hazards Model 392
14.5 Recurrent Events 395
14.6 Further Reading and References 397
15 Miscellaneous Regression Topics 399
15.1 Mixed Linear Models 399
15.2 Bayesian Regression 403
15.3 Density Estimation and Scatterplot Smoothing 406
15.4 Generalized Additive Models 409
15.5 Bootstrapping 410
15.6 Further Reading and References 412
Part IV Actuarial Applications
16 Frequency-Severity Models 417
16.1 Introduction 417
16.2 Tobit Model 418
16.3 Application: Medical Expenditures 421
16.4 Two-Part Model 424
16.5 Aggregate Loss Model 427
16.6 Further Reading and References 429
16.7 Exercises 432
17 Fat-Tailed Regression Models 433
17.1 Introduction 433
17.2 Transformations 434
17.3 Generalized Linear Models 437
17.4 Generalized Distributions 442
17.5 Quantile Regression 446
17.6 Extreme Value Models 448
17.7 Further Reading and References 449
17.8 Exercises 451Contents xi
18 Credibility and Bonus-Malus 452
18.1 Risk Classi?cation and Experience Rating 452
18.2 Credibility 453
18.3 Credibility and Regression 458
18.4 Bonus-Malus 464
18.5 Further Reading and References 465
19 Claims Triangles 467
19.1 Introduction 467
19.2 Regression Using Functions of Time as Explanatory Variables 471
19.3 Using Past Developments 475
19.4 Further Reading and References 477
19.5 Exercises 478
20 Report Writing: Communicating Data Analysis Results 481
20.1 Overview 481
20.2 Methods for Communicating Data 482
20.3 How to Organize 486
20.4 Further Suggestions for Report Writing 490
20.5 Case Study: Swedish Automobile Claims 491
20.6 Further Reading and References 503
20.7 Exercises 504
21 Designing Effective Graphs 505
21.1 Introduction 506
21.2 Graphic Design Choices Make a Difference 508
21.3 Design Guidelines 513
21.4 Empirical Foundations for Guidelines 520
21.5 Concluding Remarks 526
21.6 Further Reading and References 526

Thanks a lot

还是下不了 晕了

能下，非常感谢！

thanks a lot!