Acknowledgments |
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ix | |
1 Introduction |
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1 | (18) |
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1.1 Can You Repeat That Please? |
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2 | (2) |
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1.2 Simulation and Resampling Methods |
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4 | (4) |
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1.2.1 Simulations as Experiments |
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4 | (1) |
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1.2.2 Simulations Help Develop Intuition |
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5 | (1) |
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1.2.3 An Overview of Simulation |
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6 | (1) |
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1.2.4 Resampling Methods as Simulation |
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7 | (1) |
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1.3 OLS as a Motivating Example |
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8 | (4) |
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12 | (3) |
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1.4.1 Example 1: A Statistical Simulation |
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13 | (2) |
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1.4.2 Example 2: A Substantive Theory Simulation |
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15 | (1) |
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15 | (2) |
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16 | (1) |
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1.5.2 A Preview of the Book |
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16 | (1) |
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17 | (2) |
2 Probability |
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19 | (26) |
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19 | (1) |
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2.2 Some Basic Rules of Probability |
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20 | (4) |
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2.2.1 Introduction to Set Theory |
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20 | (2) |
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2.2.2 Properties of Probability |
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22 | (1) |
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2.2.3 Conditional Probability |
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22 | (1) |
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2.2.4 Simple Math With Probabilities |
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23 | (1) |
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2.3 Random Variables and Probability Distributions |
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24 | (5) |
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2.4 Discrete Random Variables |
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29 | (4) |
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2.4.1 Some Common Discrete Distributions |
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30 | (3) |
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2.5 Continuous Random Variables |
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33 | (10) |
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2.5.1 Two Common Continuous Distributions |
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36 | (3) |
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2.5.2 Other Continuous Distributions |
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39 | (4) |
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43 | (2) |
3 Introduction to R |
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45 | (18) |
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45 | (1) |
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45 | (1) |
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46 | (1) |
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3.3 Using R With a Text Editor |
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46 | (1) |
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47 | (1) |
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47 | (1) |
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3.5 Basic Manipulation of Objects |
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48 | (2) |
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3.5.1 Vectors and Sequences |
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48 | (1) |
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49 | (1) |
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50 | (2) |
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3.6.1 Matrix Algebra Functions |
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51 | (1) |
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3.6.2 Creating New Functions |
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51 | (1) |
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52 | (7) |
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52 | (1) |
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53 | (1) |
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54 | (3) |
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3.7.4 Generalized Linear Models |
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57 | (2) |
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59 | (2) |
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61 | (2) |
4 Random Number Generation |
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63 | (20) |
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63 | (1) |
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4.2 Probability Distributions |
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63 | (5) |
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4.2.1 Drawing Random Numbers |
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65 | (2) |
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4.2.2 Creating Your Own Distribution Functions |
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67 | (1) |
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4.3 Systematic and Stochastic |
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68 | (4) |
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4.3.1 The Systematic Component |
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69 | (1) |
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4.3.2 The Stochastic Component |
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70 | (1) |
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4.3.3 Repeating the Process |
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71 | (1) |
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72 | (5) |
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73 | (1) |
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4.4.2 Efficient Programming |
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74 | (2) |
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76 | (1) |
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4.5 Completing the OLS Simulation |
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77 | (6) |
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4.5.1 Anatomy of a Script File |
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80 | (3) |
5 Statistical Simulation of the Linear Model |
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83 | (44) |
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83 | (1) |
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5.2 Evaluating Statistical Estimators |
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84 | (12) |
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5.2.1 Bias, Efficiency, and Consistency |
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84 | (3) |
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5.2.2 Measuring Estimator Performance in R |
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87 | (9) |
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5.3 Simulations as Experiments |
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96 | (29) |
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96 | (7) |
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103 | (2) |
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105 | (4) |
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109 | (3) |
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112 | (2) |
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114 | (4) |
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5.3.7 Heavy-Tailed Errors |
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118 | (7) |
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125 | (2) |
6 Simulating Generalized Linear Models |
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127 | (42) |
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127 | (1) |
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6.2 Simulating OLS as a Probability Model |
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128 | (2) |
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130 | (15) |
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130 | (5) |
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135 | (6) |
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141 | (4) |
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145 | (17) |
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6.4.1 Ordered or Multinomial? |
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145 | (5) |
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150 | (7) |
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157 | (5) |
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6.5 Computational Issues for Simulations |
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162 | (5) |
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162 | (1) |
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6.5.2 Parallel Processing |
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163 | (4) |
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167 | (2) |
7 Testing Theory Using Simulation |
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169 | (32) |
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169 | (1) |
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169 | (2) |
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171 | (10) |
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7.3.1 Testing Zipf's Law With Frankenstein |
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171 | (3) |
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7.3.2 From Patterns to Explanations |
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174 | (7) |
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7.4 Punctuated Equilibrium and Policy Responsiveness |
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181 | (9) |
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7.4.1 Testing Punctuated Equilibrium Theory |
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183 | (2) |
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7.4.2 From Patterns to Explanations |
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185 | (5) |
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190 | (10) |
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7.5.1 Reward and Punishment |
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193 | (2) |
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7.5.2 Damned If You Do, Damned If You Don't |
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195 | (2) |
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197 | (3) |
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200 | (1) |
8 Resampling Methods |
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201 | (30) |
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201 | (1) |
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8.2 Permutation and Randomization Tests |
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202 | (7) |
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8.2.1 A Basic Permutation Test |
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203 | (2) |
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8.2.2 Randomization Tests |
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205 | (3) |
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8.2.3 Permutation/Randomization and Multiple Regression Models |
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208 | (1) |
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209 | (6) |
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210 | (3) |
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8.3.2 An Application: Simulating Heteroskedasticity |
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213 | (1) |
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8.3.3 Pros and Cons of Jackknifing |
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214 | (1) |
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215 | (13) |
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8.4.1 Bootstrapping Basics |
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217 | (3) |
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8.4.2 Bootstrapping With Multiple Regression Models |
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220 | (5) |
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8.4.3 Adding Complexity: Clustered Bootstrapping |
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225 | (3) |
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228 | (3) |
9 Other Simulation-Based Methods |
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231 | (38) |
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231 | (1) |
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232 | (23) |
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9.2.1 Statistical Overview |
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232 | (3) |
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235 | (10) |
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9.2.3 Simulating QI With zelig |
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245 | (4) |
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9.2.4 Average Case Versus Observed Values |
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249 | (5) |
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9.2.5 The Benefits of QI Simulation |
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254 | (1) |
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255 | (12) |
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257 | (1) |
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258 | (8) |
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9.3.3 Using R Functions for CV |
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266 | (1) |
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267 | (2) |
10 Final Thoughts |
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269 | (6) |
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10.1 A Summary of the Book |
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270 | (1) |
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271 | (1) |
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272 | (3) |
References |
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275 | (8) |
Index |
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283 | |