{"product_id":"mathematical-statistics-9781118771044","title":"Mathematical Statistics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003ePresents a unified approach to parametric estimation, confidence intervals, hypothesis testing, and statistical modeling, which are uniquely based on the likelihood function\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis book addresses mathematical statistics for upper-undergraduates and first year graduate students, tying chapters on estimation, confidence intervals, hypothesis testing, and statistical models together to present a unifying focus on the likelihood function. It also emphasizes the important ideas in statistical modeling, such as sufficiency, exponential family distributions, and large sample properties. \u003ci\u003eMathematical Statistics: An Introduction to Likelihood Based Inference\u003c\/i\u003e makes advanced topics accessible and understandable and covers many topics in more depth than typical mathematical statistics textbooks. It includes numerous examples, case studies, a large number of exercises ranging from drill and skill to extremely difficult problems, and many of the important theorems of mathematic\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003eAcknowledgments xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Probability 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Sample Spaces, Events, and ;;-Algebras 1\u003c\/p\u003e \u003cp\u003eProblems 7\u003c\/p\u003e \u003cp\u003e1.2 Probability Axioms and Rules 9\u003c\/p\u003e \u003cp\u003eProblems 14\u003c\/p\u003e \u003cp\u003e1.3 Probability with Equally Likely Outcomes 16\u003c\/p\u003e \u003cp\u003eProblems 18\u003c\/p\u003e \u003cp\u003e1.4 Conditional Probability 19\u003c\/p\u003e \u003cp\u003eProblems 25\u003c\/p\u003e \u003cp\u003e1.5 Independence 28\u003c\/p\u003e \u003cp\u003eProblems 31\u003c\/p\u003e \u003cp\u003e1.6 Counting Methods 33\u003c\/p\u003e \u003cp\u003eProblems 38\u003c\/p\u003e \u003cp\u003e1.7 Case Study –The Birthday Problem 41\u003c\/p\u003e \u003cp\u003eProblems 44\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Random Variables and Random Vectors 45\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Random Variables 45\u003c\/p\u003e \u003cp\u003e2.1.1 Properties of Random Variables 46\u003c\/p\u003e \u003cp\u003eProblems 50\u003c\/p\u003e \u003cp\u003e2.2 Random Vectors 53\u003c\/p\u003e \u003cp\u003e2.2.1 Properties of Random Vectors 53\u003c\/p\u003e \u003cp\u003eProblems 60\u003c\/p\u003e \u003cp\u003e2.3 Independent Random Variables 63\u003c\/p\u003e \u003cp\u003eProblems 66\u003c\/p\u003e \u003cp\u003e2.4 Transformations of Random Variables 68\u003c\/p\u003e \u003cp\u003e2.4.1 Transformations of Discrete Random Variables 68\u003c\/p\u003e \u003cp\u003e2.4.2 Transformations of Continuous Random Variables 69\u003c\/p\u003e \u003cp\u003e2.4.3 Transformations of Continuous Bivariate Random Vectors 73\u003c\/p\u003e \u003cp\u003eProblems 75\u003c\/p\u003e \u003cp\u003e2.5 Expected Values for Random Variables 77\u003c\/p\u003e \u003cp\u003e2.5.1 Expected Values and Moments of Random Variables 77\u003c\/p\u003e \u003cp\u003e2.5.2 The Variance of a Random Variable 81\u003c\/p\u003e \u003cp\u003e2.5.3 Moment Generating Functions 86\u003c\/p\u003e \u003cp\u003eProblems 89\u003c\/p\u003e \u003cp\u003e2.6 Expected Values for Random Vectors 94\u003c\/p\u003e \u003cp\u003e2.6.1 Properties of Expectation with Random Vectors 96\u003c\/p\u003e \u003cp\u003e2.6.2 Covariance and Correlation 99\u003c\/p\u003e \u003cp\u003e2.6.3 Conditional Expectation and Variance 106\u003c\/p\u003e \u003cp\u003eProblems 110\u003c\/p\u003e \u003cp\u003e2.7 Sums of Random Variables 114\u003c\/p\u003e \u003cp\u003eProblems 120\u003c\/p\u003e \u003cp\u003e2.8 Case Study – HowMany Times Was the Coin Tossed? 123\u003c\/p\u003e \u003cp\u003e2.8.1 The Probability Model 124\u003c\/p\u003e \u003cp\u003eProblems 126\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Probability Models 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Discrete Probability Models 129\u003c\/p\u003e \u003cp\u003e3.1.1 The Binomial Model 129\u003c\/p\u003e \u003cp\u003e3.1.1.1 Binomial Setting 130\u003c\/p\u003e \u003cp\u003e3.1.2 The HypergeometricModel 132\u003c\/p\u003e \u003cp\u003e3.1.2.1 Hypergeometric Setting 132\u003c\/p\u003e \u003cp\u003e3.1.3 The Poisson Model 134\u003c\/p\u003e \u003cp\u003e3.1.4 The Negative BinomialModel 135\u003c\/p\u003e \u003cp\u003e3.1.4.1 Negative Binomial Setting 135\u003c\/p\u003e \u003cp\u003e3.1.5 The MultinomialModel 138\u003c\/p\u003e \u003cp\u003e3.1.5.1 Multinomial Setting 139\u003c\/p\u003e \u003cp\u003eProblems 140\u003c\/p\u003e \u003cp\u003e3.2 Continuous Probability Models 147\u003c\/p\u003e \u003cp\u003e3.2.1 The Uniform Model 147\u003c\/p\u003e \u003cp\u003e3.2.2 The Gamma Model 149\u003c\/p\u003e \u003cp\u003e3.2.3 The Normal Model 152\u003c\/p\u003e \u003cp\u003e3.2.4 The Log-normal Model 155\u003c\/p\u003e \u003cp\u003e3.2.5 The Beta Model 156\u003c\/p\u003e \u003cp\u003eProblems 158\u003c\/p\u003e \u003cp\u003e3.3 Important Distributional Relationships 163\u003c\/p\u003e \u003cp\u003e3.3.1 Sums of Random Variables 163\u003c\/p\u003e \u003cp\u003e3.3.2 The T and F Distributions 166\u003c\/p\u003e \u003cp\u003eProblems 170\u003c\/p\u003e \u003cp\u003e3.4 Case Study –The Central LimitTheorem 172\u003c\/p\u003e \u003cp\u003e3.4.1 Convergence in Distribution 172\u003c\/p\u003e \u003cp\u003e3.4.2 The Central LimitTheorem 173\u003c\/p\u003e \u003cp\u003eProblems 176\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Parametric Point Estimation 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Statistics 177\u003c\/p\u003e \u003cp\u003e4.1.1 Sampling Distributions 178\u003c\/p\u003e \u003cp\u003e4.1.2 Unbiased Statistics and Estimators 179\u003c\/p\u003e \u003cp\u003e4.1.3 Standard Error and Mean Squared Error 181\u003c\/p\u003e \u003cp\u003e4.1.4 The Delta Method 186\u003c\/p\u003e \u003cp\u003eProblems 186\u003c\/p\u003e \u003cp\u003e4.2 Sufficient Statistics 190\u003c\/p\u003e \u003cp\u003e4.2.1 Exponential Family Distributions 195\u003c\/p\u003e \u003cp\u003eProblems 200\u003c\/p\u003e \u003cp\u003e4.3 Minimum Variance Unbiased Estimators 203\u003c\/p\u003e \u003cp\u003e4.3.1 Cramér–Rao Lower Bound 205\u003c\/p\u003e \u003cp\u003eProblems 212\u003c\/p\u003e \u003cp\u003e4.4 Case Study –The Order Statistics 214\u003c\/p\u003e \u003cp\u003eProblems 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Likelihood-based Estimation 223\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Maximum Likelihood Estimation 226\u003c\/p\u003e \u003cp\u003e5.1.1 Properties of MLEs 226\u003c\/p\u003e \u003cp\u003e5.1.2 One-parameter Probability Models 228\u003c\/p\u003e \u003cp\u003e5.1.3 Multiparameter Probability Models 235\u003c\/p\u003e \u003cp\u003eProblems 240\u003c\/p\u003e \u003cp\u003e5.2 Bayesian Estimation 247\u003c\/p\u003e \u003cp\u003e5.2.1 The Bayesian Setting 247\u003c\/p\u003e \u003cp\u003e5.2.2 Bayesian Estimators 250\u003c\/p\u003e \u003cp\u003eProblems 255\u003c\/p\u003e \u003cp\u003e5.3 Interval Estimation 258\u003c\/p\u003e \u003cp\u003e5.3.1 Exact Confidence Intervals 259\u003c\/p\u003e \u003cp\u003e5.3.2 Large Sample Confidence Intervals 264\u003c\/p\u003e \u003cp\u003e5.3.3 Bayesian Credible Intervals 267\u003c\/p\u003e \u003cp\u003eProblems 269\u003c\/p\u003e \u003cp\u003e5.4 Case Study – Modeling Obsidian Rind Thicknesses 273\u003c\/p\u003e \u003cp\u003e5.4.1 Finite Mixture Model 274\u003c\/p\u003e \u003cp\u003eProblems 278\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Hypothesis Testing 281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Components of a Hypothesis Test 282\u003c\/p\u003e \u003cp\u003eProblems 286\u003c\/p\u003e \u003cp\u003e6.2 Most Powerful Tests 288\u003c\/p\u003e \u003cp\u003eProblems 293\u003c\/p\u003e \u003cp\u003e6.3 Uniformly Most Powerful Tests 296\u003c\/p\u003e \u003cp\u003e6.3.1 Uniformly Most Powerful Unbiased Tests 299\u003c\/p\u003e \u003cp\u003eProblems 301\u003c\/p\u003e \u003cp\u003e6.4 Generalized Likelihood Ratio Tests 305\u003c\/p\u003e \u003cp\u003eProblems 311\u003c\/p\u003e \u003cp\u003e6.5 Large Sample Tests 314\u003c\/p\u003e \u003cp\u003e6.5.1 Large Sample Tests Based on the MLE 314\u003c\/p\u003e \u003cp\u003e6.5.2 Score Tests 316\u003c\/p\u003e \u003cp\u003eProblems 320\u003c\/p\u003e \u003cp\u003e6.6 Case Study – Modeling Survival of the Titanic Passengers 323\u003c\/p\u003e \u003cp\u003e6.6.1 Exploring the Data 324\u003c\/p\u003e \u003cp\u003e6.6.2 Modeling the Probability of Survival 325\u003c\/p\u003e \u003cp\u003e6.6.3 Analysis of the Fitted Survival Model 327\u003c\/p\u003e \u003cp\u003eProblems 328\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Generalized Linear Models 331\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Generalized LinearModels 332\u003c\/p\u003e \u003cp\u003eProblems 334\u003c\/p\u003e \u003cp\u003e7.2 Fitting a Generalized LinearModel 336\u003c\/p\u003e \u003cp\u003e7.2.1 Estimating ⃗ ;; 336\u003c\/p\u003e \u003cp\u003e7.2.2 Model Deviance 338\u003c\/p\u003e \u003cp\u003eProblems 340\u003c\/p\u003e \u003cp\u003e7.3 Hypothesis Testing in a Generalized Linear Model 341\u003c\/p\u003e \u003cp\u003e7.3.1 Asymptotic Properties 341\u003c\/p\u003e \u003cp\u003e7.3.2 Wald Tests and Confidence Intervals 342\u003c\/p\u003e \u003cp\u003e7.3.3 Likelihood Ratio Tests 343\u003c\/p\u003e \u003cp\u003eProblems 346\u003c\/p\u003e \u003cp\u003e7.4 Generalized LinearModels for a Normal Response Variable 348\u003c\/p\u003e \u003cp\u003e7.4.1 Estimation 349\u003c\/p\u003e \u003cp\u003e7.4.2 Properties of the MLEs 353\u003c\/p\u003e \u003cp\u003e7.4.3 Deviance 357\u003c\/p\u003e \u003cp\u003e7.4.4 Hypothesis Testing 359\u003c\/p\u003e \u003cp\u003eProblems 362\u003c\/p\u003e \u003cp\u003e7.5 Generalized LinearModels for a Binomial Response Variable 365\u003c\/p\u003e \u003cp\u003e7.5.1 Estimation 366\u003c\/p\u003e \u003cp\u003e7.5.2 Properties of the MLEs 368\u003c\/p\u003e \u003cp\u003e7.5.3 Deviance 370\u003c\/p\u003e \u003cp\u003e7.5.4 Hypothesis Testing 371\u003c\/p\u003e \u003cp\u003eProblems 373\u003c\/p\u003e \u003cp\u003e7.6 Case Study – IDNAP Experimentwith Poisson Count Data 375\u003c\/p\u003e \u003cp\u003e7.6.1 The Model 376\u003c\/p\u003e \u003cp\u003e7.6.2 StatisticalMethods 376\u003c\/p\u003e \u003cp\u003e7.6.3 Results of the First Experiment 379\u003c\/p\u003e \u003cp\u003eProblems 381\u003c\/p\u003e \u003cp\u003eReferences 383\u003c\/p\u003e \u003cp\u003eA Probability Models 385\u003c\/p\u003e \u003cp\u003eB DataSets 387\u003c\/p\u003e \u003cp\u003eProblem Solutions 389\u003c\/p\u003e \u003cp\u003eIndex 413\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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