{"product_id":"mathematical-statistics-isbn-9781118771044","title":"Mathematical Statistics","description":"\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 mathematical statistics along with their proofs.\u003c\/p\u003e \u003cp\u003eIn addition to the connected chapters mentioned above, \u003ci\u003eMathematical Statistics\u003c\/i\u003e covers likelihood-based estimation, with emphasis on multidimensional parameter spaces and range dependent support. It also includes a chapter on confidence intervals, which contains examples of exact confidence intervals along with the standard large sample confidence intervals based on the MLE's and bootstrap confidence intervals. There’s also a chapter on parametric statistical models featuring sections on non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. \u003c\/p\u003e \u003cul\u003e \u003cli\u003ePrepares students with the tools needed to be successful in their future work in statistics data science\u003c\/li\u003e \u003cli\u003eIncludes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage\u003c\/li\u003e \u003cli\u003eEmphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties\u003c\/li\u003e \u003cli\u003eIncludes sections on Bayesian estimation and credible intervals\u003c\/li\u003e \u003cli\u003eFeatures examples, problems, and solutions\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eMathematical Statistics: An Introduction to Likelihood Based\u003c\/i\u003e \u003ci\u003eInference\u003c\/i\u003e is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and\/or statistical inference.\u003c\/p\u003ePräsentiert eine einheitliche Herangehensweise an die parametrische Schätzung, Konfidenzintervalle, Hypothesentests und statistische Modelle, die in einzigartiger Weise auf der Likelihood-Funktion basieren.\u003cbr\u003e \u003cbr\u003e Dieses Fachbuch beschäftigt sich mit der mathematischen Statistik für Studenten im höheren Grundstudium und zu Beginn des Hauptstudiums. Die Kapitel zu Schätzung, Konfidenzintervallen, Hypothesentests und statistischen Modellen zusammengenommen legen den Schwerpunkt auf die Likelihood-Funktion. Wichtige Aspekte statistischer Modelle, wie Suffizienz, Verteilungen in der Exponentialfamilie und Eigenschaften großer Stichproben, stehen ebenfalls im Vordergrund. Mathematical Statistics: An Introduction to Likelihood Based Inference macht komplexe Themen zugänglich und verständlich, deckt viele Themen ausführlicher ab als herkömmliche Lehrbücher zur mathematischen Statistik. Das Buch enthält unzählige Beispiele, Fallstudien, Übungen (von einfach bis schwierig) sowie viele wichtige Theoreme der mathematischen Statistik, inklusive deren Nachweise.\u003cbr\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  \t \u003cp\u003e\u003cb\u003eRichard J. Rossi, PhD,\u003c\/b\u003e is Director of the Statistics Program and Co-Director of the Data Science Program at Montana Tech of The University of Montana, in Butte, MT. He acted as President of the Montana Chapter of the American Statistical Association in 2001 and as Associate Editor for Biometrics from 1997-2000. Dr. Rossi is a member of the American Mathematical Society, the Institute of Mathematical Statistics, and the American Statistical Association. \t  \t \u003c\/p\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 mathematical statistics along with their proofs. \u003c\/p\u003e\u003cp\u003eIn addition to the connected chapters mentioned above, \u003ci\u003eMathematical Statistics\u003c\/i\u003e covers likelihood based estimation, with emphasis on multidimensional parameter spaces and range dependent support. It also includes a chapter on confidence intervals, which contains examples of exact confidence intervals along with the standard large sample confidence intervals based on the MLE's and bootstrap confidence intervals. There is also a chapter on parametric statistical models featuring sections on non-iid observations, linear regression, logistic regression, Poisson regression, and linear models. This book: \u003c\/p\u003e\u003cul\u003e \u003cli\u003ePrepares students with the tools needed to be successful in their future work in statistics data science\u003c\/li\u003e \u003cli\u003eIncludes practical case studies including real-life data collected from Yellowstone National Park, the Donner party, and the Titanic voyage\u003c\/li\u003e \u003cli\u003eEmphasizes the important ideas to statistical modeling, such as sufficiency, exponential family distributions, and large sample properties\u003c\/li\u003e \u003cli\u003eIncludes sections on Bayesian estimation and credible intervals\u003c\/li\u003e \u003cli\u003eFeatures examples, problems, and solutions\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eMathematical Statistics: An Introduction to Likelihood Based Inference\u003c\/i\u003e is an ideal textbook for upper-undergraduate and graduate courses in probability, mathematical statistics, and statistical inference.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989587640549,"sku":"NP9781118771044","price":108.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118771044.jpg?v=1761784708","url":"https:\/\/k12savings.com\/products\/mathematical-statistics-isbn-9781118771044","provider":"K12savings","version":"1.0","type":"link"}