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Regression Modeling with Actuarial and Financial Applications

Book Description

This text gives budding actuaries and financial analysts a foundation in multiple regression and time series. They will learn about these statistical techniques using data on the demand for insurance, lottery sales, foreign exchange rates, and other applications. Although no specific knowledge of risk management or finance is presumed, the approach introduces applications in which statistical techniques can be used to analyze real data of interest. In addition to the fundamentals, this book describes several advanced statistical topics that are particularly relevant to actuarial and financial practice, including the analysis of longitudinal, two-part (frequency/severity), and fat-tailed data. Datasets with detailed descriptions, sample statistical software scripts in 'R' and 'SAS', and tips on writing a statistical report, including sample projects, can be found on the book's Web site: http://research.bus.wisc.edu/RegActuaries.

Table of Contents

  1. Cover
  2. Half Title
  3. Dedication
  4. Title Page
  5. Copyright
  6. Contents
  7. Preface
  8. 1. Regression and the Normal Distribution
    1. 1.1 What Is Regression Analysis?
    2. 1.2 Fitting Data to a Normal Distribution
    3. 1.3 Power Transforms
    4. 1.4 Sampling and the Role of Normality
    5. 1.5 Regression and Sampling Designs
    6. 1.6 Actuarial Applications of Regression
    7. 1.7 Further Reading and References
    8. 1.8 Exercises
    9. 1.9 Technical Supplement – Central Limit Theorem
  9. Part I: Linear Regression
    1. 2. Basic Linear Regression
      1. 2.1 Correlations and Least Squares
      2. 2.2 Basic Linear Regression Model
      3. 2.3 Is the Model Useful? Some Basic Summary Measures
      4. 2.4 Properties of Regression Coefficient Estimators
      5. 2.5 Statistical Inference
      6. 2.6 Building a Better Model: Residual Analysis
      7. 2.7 Application: Capital Asset Pricing Model
      8. 2.8 Illustrative Regression Computer Output
      9. 2.9 Further Reading and References
      10. 2.10 Exercises
      11. 2.11 Technical Supplement – Elements of Matrix Algebra
    2. 3. Multiple Linear Regression – I
      1. 3.1 Method of Least Squares
      2. 3.2 Linear Regression Model and Properties of Estimators
      3. 3.3 Estimation and Goodness of Fit
      4. 3.4 Statistical Inference for a Single Coefficient
      5. 3.5 Some Special Explanatory Variables
      6. 3.6 Further Reading and References
      7. 3.7 Exercises
    3. 4. Multiple Linear Regression – II
      1. 4.1 The Role of Binary Variables
      2. 4.2 Statistical Inference for Several Coefficients
      3. 4.3 One Factor ANOVA Model
      4. 4.4 Combining Categorical and Continuous Explanatory Variables
      5. 4.5 Further Reading and References
      6. 4.6 Exercises
      7. 4.7 Technical Supplement – Matrix Expressions
    4. 5. Variable Selection
      1. 5.1 An Iterative Approach to Data Analysis and Modeling
      2. 5.2 Automatic Variable Selection Procedures
      3. 5.3 Residual Analysis
      4. 5.4 Influential Points
      5. 5.5 Collinearity
      6. 5.6 Selection Criteria
      7. 5.7 Heteroscedasticity
      8. 5.8 Further Reading and References
      9. 5.9 Exercises
      10. 5.10 Technical Supplements for Chapter 5
    5. 6. Interpreting Regression Results
      1. 6.1 What the Modeling Process Tells Us
      2. 6.2 The Importance of Variable Selection
      3. 6.3 The Importance of Data Collection
      4. 6.4 Missing Data Models
      5. 6.5 Application: Risk Managers’ Cost-Effectiveness
      6. 6.6 Further Reading and References
      7. 6.7 Exercises
      8. 6.8 Technical Supplements for Chapter 6
  10. Part II: Topics in Time Series
    1. 7. Modeling Trends
      1. 7.1 Introduction
      2. 7.2 Fitting Trends in Time
      3. 7.3 Stationarity and Random Walk Models
      4. 7.4 Inference Using Random Walk Models
      5. 7.5 Filtering to Achieve Stationarity
      6. 7.6 Forecast Evaluation
      7. 7.7 Further Reading and References
      8. 7.8 Exercises
    2. 8. Autocorrelations and Autoregressive Models
      1. 8.1 Autocorrelations
      2. 8.2 Autoregressive Models of Order One
      3. 8.3 Estimation and Diagnostic Checking
      4. 8.4 Smoothing and Prediction
      5. 8.5 Box-Jenkins Modeling and Forecasting
      6. 8.6 Application: Hong Kong Exchange Rates
      7. 8.7 Further Reading and References
      8. 8.8 Exercises
    3. 9. Forecasting and Time Series Models
      1. 9.1 Smoothing with Moving Averages
      2. 9.2 Exponential Smoothing
      3. 9.3 Seasonal Time Series Models
      4. 9.4 Unit Root Tests
      5. 9.5 ARCH/GARCH Models
      6. 9.6 Further Reading and References
    4. 10. Longitudinal and Panel Data Models
      1. 10.1 What Are Longitudinal and Panel Data?
      2. 10.2 Visualizing Longitudinal and Panel Data
      3. 10.3 Basic Fixed Effects Models
      4. 10.4 Extended Fixed Effects Models
      5. 10.5 Random Effects Models
      6. 10.6 Further Reading and References
  11. Part III: Topics in Nonlinear Regression
    1. 11. Categorical Dependent Variables
      1. 11.1 Binary Dependent Variables
      2. 11.2 Logistic and Probit Regression Models
      3. 11.3 Inference for Logistic and Probit Regression Models
      4. 11.4 Application: Medical Expenditures
      5. 11.5 Nominal Dependent Variables
      6. 11.6 Ordinal Dependent Variables
      7. 11.7 Further Reading and References
      8. 11.8 Exercises
      9. 11.9 Technical Supplements – Likelihood-Based Inference
    2. 12. Count Dependent Variables
      1. 12.1 Poisson Regression
      2. 12.2 Application: Singapore Automobile Insurance
      3. 12.3 Overdispersion and Negative Binomial Models
      4. 12.4 Other Count Models
      5. 12.5 Further Reading and References
      6. 12.6 Exercises
    3. 13. Generalized Linear Models
      1. 13.1 Introduction
      2. 13.2 GLM Model
      3. 13.3 Estimation
      4. 13.4 Application: Medical Expenditures
      5. 13.5 Residuals
      6. 13.6 Tweedie Distribution
      7. 13.7 Further Reading and References
      8. 13.8 Exercises
      9. 13.9 Technical Supplements – Exponential Family
    4. 14. Survival Models
      1. 14.1 Introduction
      2. 14.2 Censoring and Truncation
      3. 14.3 Accelerated Failure Time Model
      4. 14.4 Proportional Hazards Model
      5. 14.5 Recurrent Events
      6. 14.6 Further Reading and References
    5. 15. Miscellaneous Regression Topics
      1. 15.1 Mixed Linear Models
      2. 15.2 Bayesian Regression
      3. 15.3 Density Estimation and Scatterplot Smoothing
      4. 15.4 Generalized Additive Models
      5. 15.5 Bootstrapping
      6. 15.6 Further Reading and References
  12. Part IV: Actuarial Applications
    1. 16. Frequency-Severity Models
      1. 16.1 Introduction
      2. 16.2 Tobit Model
      3. 16.3 Application: Medical Expenditures
      4. 16.4 Two-Part Model
      5. 16.5 Aggregate Loss Model
      6. 16.6 Further Reading and References
      7. 16.7 Exercises
    2. 17. Fat-Tailed Regression Models
      1. 17.1 Introduction
      2. 17.2 Transformations
      3. 17.3 Generalized Linear Models
      4. 17.4 Generalized Distributions
      5. 17.5 Quantile Regression
      6. 17.6 Extreme Value Models
      7. 17.7 Further Reading and References
      8. 17.8 Exercises
    3. 18. Credibility and Bonus-Malus
      1. 18.1 Risk Classification and Experience Rating
      2. 18.2 Credibility
      3. 18.3 Credibility and Regression
      4. 18.4 Bonus-Malus
      5. 18.5 Further Reading and References
    4. 19. Claims Triangles
      1. 19.1 Introduction
      2. 19.2 Regression Using Functions of Time as Explanatory Variables
      3. 19.3 Using Past Developments
      4. 19.4 Further Reading and References
      5. 19.5 Exercises
    5. 20. Report Writing: Communicating Data Analysis Results
      1. 20.1 Overview
      2. 20.2 Methods for Communicating Data
      3. 20.3 How to Organize
      4. 20.4 Further Suggestions for Report Writing
      5. 20.5 Case Study: Swedish Automobile Claims
      6. 20.6 Further Reading and References
      7. 20.7 Exercises
    6. 21. Designing Effective Graphs
      1. 21.1 Introduction
      2. 21.2 Graphic Design Choices Make a Difference
      3. 21.3 Design Guidelines
      4. 21.4 Empirical Foundations for Guidelines
      5. 21.5 Concluding Remarks
      6. 21.6 Further Reading and References
  13. Brief Answers to Selected Exercises
  14. Appendix 1: Basic Statistical Inference
  15. Appendix 2: Matrix Algebra
  16. Appendix 3: Probability Tables
  17. Index