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Corso dottorato di Statistical Inference docente Daniela ICHIM (ISTAT) libro di testo: Probability and Statistics Jeffrey Rosenthal and Michael Evans vedi http://www.amazon.com/Probability-Statistics-The-ScienceUncertainty/dp/1429224622 Programma del corso basato sul testo "Probability and Statistics" di J. Rosenthal e M. Evans, Palgrave - Mc Millan LEZIONE 1 4 Sampling Distributions and Limits 4.1 Sampling Distributions 4.5 Monte Carlo Approximations LEZIONE 2 4.6 Normal Distribution Theory 4.6.1 The Chi-Squared Distribution 4.6.2 The t Distribution 4.6.3 The F Distribution 199 200 224 234 236 239 240 LEZIONE 3 5 Statistical Inference 5.1 Why Do We Need Statistics? 5.2 Inference Using a Probability Model 5.3 Statistical Models 5.4 Data Collection 5.4.1 Finite Populations 5.4.2 Simple Random Sampling 5.4.3 Histograms 5.4.4 Survey Sampling 253 254 258 262 269 270 271 274 276 LEZIONE 4 5.5 Some Basic Inferences 5.5.1 Descriptive Statistics 5.5.2 Plotting Data 5.5.3 Types of Inferences 282 282 287 289 LEZIONE 5 6 Likelihood Inference 6.1 The Likelihood Function 6.1.1 Sufficient Statistics 6.2 Maximum Likelihood Estimation 297 297 302 LEZIONE 6 6.2.1 Computation of the MLE 310 6.2.2 The Multidimensional Case (Advanced) 316 6.3 Inferences Based on the MLE 320 6.3.1 Standard Errors, Bias, and Consistency 308 321 LEZIONE 7 6.3.2 Confidence Intervals 6.3.3 Testing Hypotheses and P-Values 6.3.4 Inferences for the Variance 326 332 338 LEZIONE 8 6.3.5 Sample-Size Calculations: Confidence Intervals 6.3.6 Sample-Size Calculations: Power 6.4 Distribution-Free Methods 6.4.1 Method of Moments 6.4.2 Bootstrapping 6.4.3 The Sign Statistic and Inferences about Quantiles 6.5 Asymptotics for the MLE (Advanced) LEZIONE 9 8 Optimal Inferences 8.1 Optimal Unbiased Estimation 8.1.1 The Rao-Blackwell Theorem and Rao-Blackwellization 8.1.2 Completeness and the Lehmann-Scheff Theorem 438 8.1.3 The Crame-Rao Inequality (Advanced) LEZIONE 10 8.2 Optimal Hypothesis Testing 8.2.1 The Power Function of a Test 8.2.2 Type I and Type II Errors 8.2.3 Rejection Regions and Test Functions 8.2.4 The Neyman-Pearson Theorem 8.2.5 Likelihood Ratio Tests (Advanced) 446 446 447 448 449 455 LEZIONE 11 9 Model Checking 479 9.1 Checking the Sampling Model 9.1.1 Residual and Probability Plots 9.1.2 The Chi-Squared Goodness of Fit Test 9.1.3 Prediction and Cross-Validation 9.1.4 What Do We Do When a Model Fails? 9.2 Checking for Prior-Data Conflict 9.3 The Problem with Multiple Checks 479 486 490 495 496 502 509 340 341 349 349 351 357 364 433 434 435 440