Download Edward W. Frees - Regression Modeling With Actuarial and Financial Applications - 2009 PDF

TitleEdward W. Frees - Regression Modeling With Actuarial and Financial Applications - 2009
File Size4.3 MB
Total Pages585
Table of Contents
	Who Is This Book For?
	What Is This Book About?
	How Does This Book Deliver Its Message?
		Chapter Development
		Real Data
		Statistical Software and Data
		Technical Supplements
		Suggested Courses
1 Regression and the Normal Distribution
	1.1 What Is Regression Analysis?
	1.2 Fitting Data to a Normal Distribution
		Normal Curve Approximation
		Box Plot
		Quantile-Quantile Plots
	1.3 Power Transforms
	1.4 Sampling and the Role of Normality
	1.5 Regression and Sampling Designs
	1.6 Actuarial Applications of Regression
		Pricing and Adverse Selection
		Reserving and Solvency Testing
		Other Risk Management Applications
	1.7 Further Reading and References
	Chapter References
	1.8 Exercises
	1.9 Technical Supplement - Central Limit Theorem
Part I Linear Regression
	2 Basic Linear Regression
		2.1 Correlations and Least Squares
			Scatter Plot and Correlation Coefficients – Basic Summary Tools
			Method of Least Squares
		2.2 Basic Linear Regression Model
		2.3 Is the Model Useful? Some Basic Summary Measures
			2.3.1 Partitioning the Variability
			2.3.2 The Size of a Typical Deviation: s
		2.4 Properties of Regression Coefficient Estimators
		2.5 Statistical Inference
			2.5.1 Is the Explanatory Variable Important? The t-Test
			2.5.2 Confidence Intervals
			2.5.3 Prediction Intervals
		2.6 Building a Better Model: Residual Analysis
		2.7 Application: Capital Asset Pricing Model
			Unusual Points
			Sensitivity Analysis
		2.8 Illustrative Regression Computer Output
			Legend Annotation Definition, Symbol
		2.9 Further Reading and References
		Chapter References
		2.10 Exercises
		2.11 Technical Supplement - Elements of Matrix Algebra
			2.11.1 Basic Definitions
			2.11.2 Some Special Matrices
			2.11.3 Basic Operations
				Scalar Multiplication
				Addition and Subtraction of Matrices
				Matrix Multiplication
				Matrix Inverses
			2.11.4 Random Matrices
	3 Multiple Linear Regression - I
		3.1 Method of Least Squares
			Summarizing the Data
			Method of Least Squares
			Matrix Notation
		3.2 Linear Regression Model and Properties of Estimators
			3.2.1 Regression Function
			3.2.2 Regression Coefficient Interpretation
			3.2.3 Model Assumptions
			3.2.4 Properties of Regression Coefficient Estimators
		3.3 Estimation and Goodness of Fit
			Residual Standard Deviation
			The Coefficient of Determination: R2
		3.4 Statistical Inference for a Single Coefficient
			3.4.1 The t-Test
			3.4.2 Confidence Intervals
			3.4.3 Added Variable Plots
			3.4.4 Partial Correlation Coefficients
		3.5 Some Special Explanatory Variables
			3.5.1 Binary Variables
			3.5.2 Transforming Explanatory Variables
			3.5.3 Interaction Terms
		3.6 Further Reading and References
		Chapter References
		3.7 Exercises
	4 Multiple Linear Regression - II
		4.1 The Role of Binary Variables
		4.2 Statistical Inference for Several Coefficients
			4.2.1 Sets of Regression Coefficients
			4.2.2 The General Linear Hypothesis
				Some Special Cases
			4.2.3 Estimating and Predicting Several Coefficients
				Estimating Linear Combinations of Regression Coefficients
				Prediction Intervals
		4.3 One Factor ANOVA Model
			Model Assumptions and Analysis
			Link with Regression
		4.4 Combining Categorical and Continuous Explanatory Variables
			Combining a Factor and Covariate
			Combining Two Factors
			General Linear Model
		4.5 Further Reading and References
		Chapter References
		4.6 Exercises
		4.7 Technical Supplement - Matrix Expressions
			4.7.1 Expressing Models with Categorical Variables in Matrix Form
				One Categorical Variable Model
				One Categorical and One Continuous Variable Model
			4.7.2 Calculating Least Squares Recursively
				Partitioned Matrix Results
				Reparameterized Model
				Extra Sum of Squares
			4.7.3 General Linear Model
				Normal Equations
				Unique Fitted Values
				Generalized Inverses
				Estimable Functions
				Testable Hypotheses
				General Linear Hypothesis
				One Categorical Variable Model
	5 Variable Selection
		5.1 An Iterative Approach to Data Analysis and Modeling
		5.2 Automatic Variable Selection Procedures
		5.3 Residual Analysis
			5.3.1 Residuals
			5.3.2 Using Residuals to Identify Outliers
			5.3.3 Using Residuals to Select Explanatory Variables
		5.4 Influential Points
			5.4.1 Leverage
			5.4.2 Cook’s Distance
		5.5 Collinearity
			5.5.1 What Is Collinearity?
			5.5.2 Variance Inflation Factors
			5.5.3 Collinearity and Leverage
			5.5.4 Suppressor Variables
			5.5.5 Orthogonal Variables
		5.6 Selection Criteria
			5.6.1 Goodness of Fit
			5.6.2 Model Validation
			5.6.3 Cross-Validation
		5.7 Heteroscedasticity
			5.7.1 Detecting Heteroscedasticity
			5.7.2 Heteroscedasticity-Consistent Standard Errors
			5.7.3 Weighted Least Squares
			5.7.4 Transformations
		5.8 Further Reading and References
		Chapter References
		5.9 Exercises
		5.10 Technical Supplements for Chapter 5
			5.10.1 Projection Matrix
			5.10.2 Leave-One-Out Statistics
			5.10.3 Omitting Variables
	6 Interpreting Regression Results
		6.1 What the Modeling Process Tells Us
			6.1.1 Interpreting Individual Effects
				Substantive Significance
				Statistical Significance
				Causal Effects
		6.2 The Importance of Variable Selection
			6.2.1 Overfitting the Model
			6.2.2 Underfitting the Model
		6.3 The Importance of Data Collection
			6.3.1 Sampling Frame Error and Adverse Selection
			6.3.2 Limited Sampling Regions
			6.3.3 Limited Dependent Variables, Censoring, and Truncation
			6.3.4 Omitted and Endogenous Variables
			6.3.5 Missing Data
		6.4 Missing Data Models
			6.4.1 Missing at Random
			6.4.2 Nonignorable Missing Data
				Heckman Two-Stage Procedure
				EM Algorithm
		6.5 Application: Risk Managers' Cost-Effectiveness
				Preliminary Analysis
				Back to the Basics
				Some New Models
		6.6 Further Reading and References
		Chapter References
		6.7 Exercises
		6.8 Technical Supplements for Chapter 6
			6.8.1 Effects of Model Misspecification
Part II Topics in Time Series
	7 Modeling Trends
		7.1 Introduction
			Time Series and Stochastic Processes
			Time Series versus Causal Models
		7.2 Fitting Trends in Time
			Understanding Patterns over Time
			Fitting Trends in Time
			Fitting Seasonal Trends
			Reliability of Time Series Forecasts
		7.3 Stationarity and Random Walk Models
			White Noise
			Random Walk
		7.4 Inference Using Random Walk Models
			Model Properties
			Identifying Stationarity
			Identifying Random Walks
			Random Walk versus Linear Trend in Time Models
		7.5 Filtering to Achieve Stationarity
		7.6 Forecast Evaluation
		7.7 Further Reading and References
		Chapter References
		7.8 Exercises
	8 Autocorrelations and Autoregressive Models
		8.1 Autocorrelations
			Application: Inflation Bond Returns
		8.2 Autoregressive Models of Order One
			Model Definition and Properties
			Model Selection
			Meandering Process
		8.3 Estimation and Diagnostic Checking
		8.4 Smoothing and Prediction
		8.5 Box-Jenkins Modeling and Forecasting
			8.5.1 Models
				AR(p) Models
				MA(q) Models
				ARMA and ARIMA Models
			8.5.2 Forecasting
				Optimal Point Forecasts
				Forecast Interval
		8.6 Application: Hong Kong Exchange Rates
			Model Selection and Partial Autocorrelations
			Residual Checking
			Residual Autocorrelation
			Testing Several Lags
		8.7 Further Reading and References
		Chapter References
		8.8 Exercises
	9 Forecasting and Time Series Models
		9.1 Smoothing with Moving Averages
			Application: Medical Component of the CPI
			Weighted Least Squares
		9.2 Exponential Smoothing
			Weighted Least Squares
		9.3 Seasonal Time Series Models
			Fixed Seasonal Effects
			Seasonal Autoregressive Models
			Seasonal Exponential Smoothing
		9.4 Unit Root Tests
		9.5 ARCH/GARCH Models
			ARCH Model
			GARCH Model
		9.6 Further Reading and References
		Chapter References
	10 Longitudinal and Panel Data Models
		10.1 What Are Longitudinal and Panel Data?
		10.2 Visualizing Longitudinal and Panel Data
			Trellis Plot
		10.3 Basic Fixed Effects Models
		10.4 Extended Fixed Effects Models
			Analysis of Covariance Models
			Variable Coefficients Models
			Models with Serial Correlation
		10.5 Random Effects Models
			Basic Random Effects Model
			Extended Random Effects Models
		10.6 Further Reading and References
		Chapter References
Part III Topics in Nonlinear Regression
	11 Categorical Dependent Variables
		11.1 Binary Dependent Variables
			Linear Probability Models
		11.2 Logistic and Probit Regression Models
			11.2.1 Using Nonlinear Functions of Explanatory Variables
			11.2.2 Threshold Interpretation
			11.2.3 Random Utility Interpretation
			11.2.4 Logistic Regression
				Odds Interpretation
		11.3 Inference for Logistic and Probit Regression Models
			11.3.1 Parameter Estimation
			11.3.2 Additional Inference
		11.4 Application: Medical Expenditures
			Dependent Variable
			Explanatory Variables
			Summary Statistics
		11.5 Nominal Dependent Variables
			11.5.1 Generalized Logit
				Parameter Interpretations
			11.5.2 Multinomial Logit
			11.5.3 Nested Logit
		11.6 Ordinal Dependent Variables
			11.6.1 Cumulative Logit
			11.6.2 Cumulative Probit
		11.7 Further Reading and References
		Chapter References
		11.8 Exercises
		11.9 Technical Supplements - Likelihood-Based Inference
			11.9.1 Properties of Likelihood Functions
			11.9.2 Maximum Likelihood Estimators
			11.9.3 Hypothesis Tests
			11.9.4 Information Criteria
	12 Count Dependent Variables
		12.1 Poisson Regression
			12.1.1 Poisson Distribution
			12.1.2 Regression Model
			12.1.3 Estimation
			12.1.4 Additional Inference
		12.2 Application: Singapore Automobile Insurance
		12.3 Overdispersion and Negative Binomial Models
			Adjusting Standard Errors for Data Not Equidispersed
			Negative Binomial
		12.4 Other Count Models
			12.4.1 Zero-Inflated Models
			12.4.2 Hurdle Models
			12.4.3 Heterogeneity Models
			12.4.4 Latent Class Models
		12.5 Further Reading and References
		Chapter References
		12.6 Exercises
	13 Generalized Linear Models
		13.1 Introduction
		13.2 GLM Model
			13.2.1 Linear Exponential Family of Distributions
			13.2.2 Link Functions
		13.3 Estimation
			13.3.1 Maximum Likelihood Estimation for Canonical Links
			13.3.2 Overdispersion
			13.3.3 Goodness-of-Fit Statistics
		13.4 Application: Medical Expenditures
		13.5 Residuals
		13.6 Tweedie Distribution
		13.7 Further Reading and References
		Chapter References
		13.8 Exercises
		13.9 Technical Supplements - Exponential Family
			13.9.1 Linear Exponential Family of Distributions
			13.9.2 Moments
			13.9.3 Maximum Likelihood Estimation for General Links
			13.9.4 Iterated Reweighted Least Squares
	14 Survival Models
		14.1 Introduction
		14.2 Censoring and Truncation
			14.2.1 Definitions and Examples
			14.2.2 Likelihood Inference
			14.2.3 Product-Limit Estimator
		14.3 Accelerated Failure Time Model
			Location-Scale Distributions
			Inference for AFT Models
		14.4 Proportional Hazards Model
			14.4.1 Proportional Hazards
			14.4.2 Inference
		14.5 Recurrent Events
		14.6 Further Reading and References
		Chapter References
	15 Miscellaneous Regression Topics
		15.1 Mixed Linear Models
			15.1.1 Weighted Least Squares
			15.1.2 Variance Components Estimation
			15.1.3 Best Linear Unbiased Prediction
		15.2 Bayesian Regression
		15.3 Density Estimation and Scatter plot Smoothing
		15.4 Generalized Additive Models
		15.5 Bootstrapping
		15.6 Further Reading and References
		Chapter References
Part IV Actuarial Applications
	16 Frequency-Severity Models
		16.1 Introduction
		16.2 Tobit Model
		16.3 Application: Medical Expenditures
			Summary Statistics
		16.4 Two-Part Model
			Tobit Type II Model
		16.5 Aggregate Loss Model
			Frequency of Claims
		16.6 Further Reading and References
			Property and Casualty
			Health Care
		Chapter References
		16.7 Exercises
	17 Fat-Tailed Regression Models
		17.1 Introduction
		17.2 Transformations
		17.3 Generalized Linear Models
			17.3.1 What Is Fat Tailed?
			17.3.2 Application: Wisconsin Nursing Homes
				Summarizing the Data
				Fitting Generalized Linear Models
		17.4 Generalized Distributions
			Application: Wisconsin Nursing Homes
		17.5 Quantile Regression
		17.6 Extreme Value Models
		17.7 Further Reading and References
		Chapter References
		17.8 Exercises
	18 Credibility and Bonus-Malus
		18.1 Risk Classification and Experience Rating
		18.2 Credibility
			18.2.1 Limited Fluctuation Credibility
			18.2.2 Greatest Accuracy Credibility
		18.3 Credibility and Regression
			18.3.1 One-Way Random Effects Model
			18.3.2 Longitudinal Models
		18.4 Bonus-Malus
		18.5 Further Reading and References
		Chapter References
	19 Claims Triangles
		19.1 Introduction
			19.1.1 Claims Evolution
			19.1.2 Claims Triangles
			19.1.3 Chain-Ladder Method
		19.2 Regression Using Functions of Time as Explanatory Variables
			19.2.1 Lognormal Model
			19.2.2 Hoerl Curve
			19.2.3 Poisson Models
		19.3 Using Past Developments
			19.3.1 Mack Model
			19.3.2 Distributional Models
		19.4 Further Reading and References
		Chapter References
		19.5 Exercises
	20 Report Writing: Communicating Data Analysis Results
		20.1 Overview
		20.2 Methods for Communicating Data
			Within-Text Data
		20.3 How to Organize
			Title and Abstract
			Data Characteristics
			Model Selection and Interpretation
			Summary and Concluding Remarks
			References and Appendix
		20.4 Further Suggestions for Report Writing
		20.5 Case Study: Swedish Automobile Claims
			Determinants of Swedish Automobile Claims
			Section 1. Introduction
			Section 2. Data Characteristics
			Section 3. Model Selection and Interpretation
				Discussion of the Frequency Model
				Discussion of the Severity Model
			Section 4. Summary and Concluding Remarks
			Appendix Table of Contents
				A1. References
				A2. Variable Definitions
				A3. Basic Summary Statistics for Frequency
				A4. Final Fitted Frequency Regression Model: R Output
				A5. Checking Significance of Factors in the Final Fitted Frequency Regression Model: R Output
				A6. Final Fitted Severity Regression Model: R Output
				A7. Checking Significance of Factors in the Final Fitted Severity Regression Model: R Output
		20.6 Further Reading and References
		Chapter References
		20.7 Exercises
	21 Designing Effective Graphs
		21.1 Introduction
		21.2 Graphic Design Choices Make a Difference
		21.3 Design Guidelines
			Guideline 1: Avoid Chartjunk
			Guideline 2: Use Small Multiples to Promote Comparisons and Assess Change
			Guideline 3: Use Complex Graphs to Portray Complex Patterns
			Guideline 4: Relate Graph Size to Information Content
			Guideline 5: Use Graphical Forms That Promote Comparisons
			Guideline 6: Integrate Graphs and Text
			Guideline 7: Demonstrate an Important Message
			Guideline 8: Know Your Audience
		21.4 Empirical Foundations for Guidelines
			21.4.1 Viewers as Units of Study
			21.4.2 Graphs as Units of Study
		21.5 Concluding Remarks
		21.6 Further Reading and References
		Chapter References
Brief Answers to Selected Exercises
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 8
	Chapter 11
	Chapter 12
Appendix 1: Basic Statistical Inference
	A1.1 Distributions of Functions of Random Variables
	A1.2 Estimation and Prediction
	A1.3 Testing Hypotheses
Appendix 2: Matrix Algebra
	A2.1 Basic Definitions
	A2.2 Review of Basic Operations
	A2.3 Further Definitions
Appendix 3: Probability Tables
	A3.1 Normal Distribution
	A3.2 Chi-Square Distribution
	A3.3 t-Distribution
	A3.4 F-Distribution

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