vi Contents 3.5. Kernel Density Estimation 145 3.6. Quantile-Quantile Plots 150 3.7. Joint Distributions 155 3.8. Summary 163 Exercises 166 Chapter 4. Parameter Estimation and Testing 175 4.1. Statistical Models 175 4.2. Fitting Models by the Method of Moments 177 4.3. Estimators and Sampling Distributions 183 4.4. Limit Theorems 191 4.5. Inference for the Mean (Variance Known) 200 4.6. Estimating Variance 208 4.7. Inference for the Mean (Variance Unknown) 212 4.8. Confidence Intervals for a Proportion 223 4.9. Paired Tests 225 4.10. Developing New Tests 227 4.11. Summary 234 Exercises 238 Chapter 5. Likelihood-Based Statistics 251 5.1. Maximum Likelihood Estimators 251 5.2. Likelihood Ratio Tests 266 5.3. Confidence Intervals 274 5.4. Goodness of Fit Testing 277 5.5. Inference for Two-Way Tables 288 5.6. Rating and Ranking Based on Pairwise Comparisons 297 5.7. Bayesian Inference 304 5.8. Summary 312 Exercises 315 Chapter 6. Introduction to Linear Models 323 6.1. The Linear Model Framework 324 6.2. Simple Linear Regression 333 6.3. Inference for Simple Linear Regression 341 6.4. Regression Diagnostics 353 6.5. Transformations in Linear Regression 362 6.6. Categorical Predictors 369 6.7. Categorical Response (Logistic Regression) 377 6.8. Simulating Linear Models to Check Robustness 384
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