Page 22 - Probability and Statistical Inference

Contents xvii

9.2.2 The Pivotal Approach 446
9.2.3 The Interpretation of a Confidence Coefficient 451
9.2.4 Ideas of Accuracy Measures 452
9.2.5 Using Confidence Intervals in the Tests
of Hypothesis 455
9.3 Two-Sample Problems 456
9.3.1 Comparing the Location Parameters 456
9.3.2 Comparing the Scale Parameters 460
9.4 Multiple Comparisons 463
9.4.1 Estimating a Multivariate Normal Mean Vector 463
9.4.2 Comparing the Means 465
9.4.3 Comparing the Variances 467
9.5 Exercises and Complements 469
10 Bayesian Methods 477
10.1 Introduction 477
10.2 Prior and Posterior Distributions 479
10.3 The Conjugate Priors 481
10.4 Point Estimation 485
10.5 Credible Intervals 488
10.5.1 Highest Posterior Density 489
10.5.2 Contrasting with the Confidence Intervals 492
10.6 Tests of Hypotheses 493
10.7 Examples with Non-Conjugate Priors 494
10.8 Exercises and Complements 497

11 Likelihood Ratio and Other Tests 507
11.1 Introduction 507
11.2 One-Sample Problems 508
11.2.1 LR Test for the Mean 509
11.2.2 LR Test for the Variance 512
11.3 Two-Sample Problems 515
11.3.1 Comparing the Means 515
11.3.2 Comparing the Variances 519
11.4 Bivariate Normal Observations 522
11.4.1 Comparing the Means: The Paired Difference
t Method 522
11.4.2 LR Test for the Correlation Coefficient 525
11.4.3 Tests for the Variances 528
11.5 Exercises and Complements 529
12 Large-Sample Inference 539
12.1 Introduction 539
12.2 The Maximum Likelihood Estimation 539
12.3 Confidence Intervals and Tests of Hypothesis 542