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| Acknowledgments | |
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| Introduction | |
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| Introduction | |
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| What Is a Monte Carlo Study? | |
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| Simulating the Rolling of a Die Twice | |
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| Why Is Monte Carlo Simulation Often Necessary? | |
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| What Are Some Typical Situations Where a Monte Carlo Study Is Needed? | |
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| Assessing the Consequences of Assumption Violations | |
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| Determining the Sampling Distribution of a Statistic That Has No Theoretical Distribution | |
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| Why Use the SAS System for Conducting Monte Carlo Studies? | |
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| About the Organization of This Book | |
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| References | |
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| Basic Procedures for Monte Carlo Simulation | |
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| Introduction | |
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| Asking Questions Suitable for a Monte Carlo Study | |
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| Designing a Monte Carlo Study | |
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| Simulating Pearson Correlation Coefficient Distributions | |
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| Generating Sample Data | |
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| Generating Data from a Distribution with Known Characteristics | |
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| Transforming Data to Desired Shapes | |
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| Transforming Data to Simulate a Specified Population Inter-variable Relationship Pattern | |
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| Implementing the Statistical Technique in Question | |
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| Obtaining and Accumulating the Statistic of Interest | |
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| Analyzing the Accumulated Statistic of Interest | |
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| Drawing Conclusions Based on the MC Study Results | |
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| Summary | |
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| Generating Univariate Random Numbers in SAS | |
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| Introduction | |
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| RANUNI, the Uniform Random Number Generator | |
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| Uniformity (the EQUIDST Macro) | |
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| Randomness (the CORRTEST Macro) | |
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| Generating Random Numbers with Functions versus CALL Routines | |
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| Generating Seed Values (the SEEDGEN Macro) | |
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| List of All Random Number Generators Available in SAS | |
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| Examples for Normal and Lognormal Distributions | |
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| Random Sample of Population Height (Normal Distribution) | |
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| Random Sample of Stock Prices (Lognormal Distribution) | |
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| The RANTBL Function | |
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| Examples Using the RANTBL Function | |
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| Random Sample of Bonds with Bond Ratings | |
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| Generating Random Stock Prices Using the RANTBL Function | |
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| Summary | |
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| References | |
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| Generating Data in Monte Carlo Studies | |
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| Introduction | |
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| Generating Sample Data for One Variable | |
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| Generating Sample Data from a Normal Distribution with the Desired Mean and Standard Deviation | |
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| Generating Data from Non-Normal Distributions | |
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| Using the Generalized Lambda Distribution (GLD) System | |
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| Using Fleishman's Power Transformation Method | |
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| Generating Sample Data from a Multivariate Normal Distribution | |
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| Generating Sample Data from a Multivariate Non-Normal Distribution | |
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| Examining the Effect of Data Non-normality on Inter-variable Correlations | |
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| Deriving Intermediate Correlations | |
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| Converting between Correlation and Covariance Matrices | |
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| Generating Data That Mirror Your Sample Characteristics | |
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| Summary | |
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| References | |
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| Automating Monte Carlo Simulations | |
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| Introduction | |
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| Steps in a Monte Carlo Simulation | |
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| The Problem of Matching Birthdays | |
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| The Seed Value | |
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| Monitoring the Execution of a Simulation | |
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| Portability | |
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| Automating the Simulation | |
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| A Macro Solution to the Problem of Matching Birthdays | |
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| Full-Time Monitoring with Macros | |
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| Simulation of the Parking Problem (Renyi's Constant) | |
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| Summary | |
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| References | |
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| Conducting Monte Carlo Studies That Involve Univariate Statistical Techniques | |
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| Introduction | |
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| Example 1: Assessing the Effect of Unequal Population Variances in a T-Test | |
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| Computational Aspects of T-Tests | |
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| Design Considerations | |
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| Different SAS Programming Approaches | |
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| T-Test Example: First Approach | |
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| T-Test Example: Second Approach | |
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| Example 2: Assessing the Effect of Data Non-Normality on the Type I Error Rate in ANOVA | |
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| Design Considerations | |
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| ANOVA Example Program | |
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| Example 3: Comparing Different R[superscript 2] Shrinkage Formulas in Regression Analysis | |
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| Different Formulas for Correcting Sample R[superscript 2] Bias | |
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| Design Considerations | |
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| Regression Analysis Sample Program | |
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| Summary | |
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| References | |
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| Conducting Monte Carlo Studies for Multivariate Techniques | |
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| Introduction | |
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| Example 1: A Structural Equation Modeling Example | |
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| Descriptive Indices for Assessing Model Fit | |
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| Design Considerations | |
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| SEM Fit Indices Studied | |
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| Design of Monte Carlo Simulation | |
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| Deriving the Population Covariance Matrix | |
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| Dealing with Model Misspecification | |
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| SEM Example Program | |
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| Some Explanations of Program 7.2 | |
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| Selected Results from Program 7.2 | |
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| Example 2: Linear Discriminant Analysis and Logistic Regression for Classification | |
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| Major Issues Involved | |
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| Design | |
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| Data Source and Model Fitting | |
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| Example Program Simulating Classification Error Rates of PDA and LR | |
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| Some Explanations of Program 7.3 | |
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| Selected Results from Program 7.3 | |
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| Summary | |
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| References | |
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| Examples for Monte Carlo Simulation in Finance: Estimating Default Risk and Value-at-Risk | |
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| Introduction | |
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| Example 1: Estimation of Default Risk | |
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| Example 2: VaR Estimation for Credit Risk | |
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| Example 3: VaR Estimation for Portfolio Market Risk | |
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| Summary | |
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| References | |
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| Modeling Time Series Processes with SAS/ETS Software | |
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| Introduction to Time Series Methodology | |
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| Box and Jenkins ARIMA Models | |
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| Akaike's State Space Models for Multivariate Times Series | |
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| Modeling Multiple Regression Data with Serially Correlated Disturbances | |
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| Introduction to SAS/ETS Software | |
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| Example 1: Generating Univariate Time Series Processes | |
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| Example 2: Generating Multivariate Time Series Processes | |
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| Example 3: Generating Correlated Variables with Autocorrelated Errors | |
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| Example 4: Monte Carlo Study of How Autocorrelation Affects Regression Results | |
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| Summary | |
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| References | |
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| Index | |