{"product_id":"fundamental-statistical-inference-9781119417866","title":"Fundamental Statistical Inference","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eA hands-on approach to statistical inference that addresses the latest developments in this ever-growing field\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThis clear and accessible book for beginning graduate students offers a practical and detailed approach to the field of statistical inference, providing complete derivations of results, discussions, and MATLAB programs for computation. It emphasizes details of the relevance of the material, intuition, and discussions with a view towards very modern statistical inference. In addition to classic subjects associated with mathematical statistics, topics include an intuitive presentation of the (single and double) bootstrap for confidence interval calculations, shrinkage estimation, tail (maximal moment) estimation, and a variety of methods of point estimation besides maximum likelihood, including use of characteristic functions, and indirect inference. Practical examples of all methods are given. Estimation issues associated with the discrete mixtures of normal di\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART I ESSENTIAL CONCEPTS IN STATISTICS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introducing Point and Interval Estimation 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Point Estimation \/ 4\u003c\/p\u003e \u003cp\u003e1.1.1 Bernoulli Model \/ 4\u003c\/p\u003e \u003cp\u003e1.1.2 Geometric Model \/ 6\u003c\/p\u003e \u003cp\u003e1.1.3 Some Remarks on Bias and Consistency \/ 11\u003c\/p\u003e \u003cp\u003e1.2 Interval Estimation via Simulation \/ 12\u003c\/p\u003e \u003cp\u003e1.3 Interval Estimation via the Bootstrap \/ 18\u003c\/p\u003e \u003cp\u003e1.3.1 Computation and Comparison with Parametric Bootstrap \/ 18\u003c\/p\u003e \u003cp\u003e1.3.2 Application to Bernoulli Model and Modification \/ 20\u003c\/p\u003e \u003cp\u003e1.3.3 Double Bootstrap \/ 24\u003c\/p\u003e \u003cp\u003e1.3.4 Double Bootstrap with Analytic Inner Loop \/ 26\u003c\/p\u003e \u003cp\u003e1.4 Bootstrap Confidence Intervals in the Geometric Model \/ 31\u003c\/p\u003e \u003cp\u003e1.5 Problems \/ 35\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Goodness of Fit and Hypothesis Testing 37\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Empirical Cumulative Distribution Function \/ 38\u003c\/p\u003e \u003cp\u003e2.1.1 The Glivenko–Cantelli Theorem \/ 38\u003c\/p\u003e \u003cp\u003e2.1.2 Proofs of the Glivenko–Cantelli Theorem \/ 41\u003c\/p\u003e \u003cp\u003e2.1.3 Example with Continuous Data and Approximate Confidence Intervals \/ 45\u003c\/p\u003e \u003cp\u003e2.1.4 Example with Discrete Data and Approximate Confidence Intervals \/ 49\u003c\/p\u003e \u003cp\u003e2.2 Comparing Parametric and Nonparametric Methods \/ 52\u003c\/p\u003e \u003cp\u003e2.3 Kolmogorov–Smirnov Distance and Hypothesis Testing \/ 57\u003c\/p\u003e \u003cp\u003e2.3.1 The Kolmogorov–Smirnov and Anderson–Darling Statistics \/ 57\u003c\/p\u003e \u003cp\u003e2.3.2 Significance and Hypothesis Testing \/ 59\u003c\/p\u003e \u003cp\u003e2.3.3 Small-Sample Correction \/ 63\u003c\/p\u003e \u003cp\u003e2.4 Testing Normality with KD and AD \/ 65\u003c\/p\u003e \u003cp\u003e2.5 Testing Normality with \u003ci\u003eW\u003csup\u003e2\u003c\/sup\u003e\u003c\/i\u003e and \u003ci\u003eU\u003csup\u003e2\u003c\/sup\u003e\u003c\/i\u003e \/ 68\u003c\/p\u003e \u003cp\u003e2.6 Testing the Stable Paretian Distributional Assumption: First Attempt \/ 69\u003c\/p\u003e \u003cp\u003e2.7 Two-Sample Kolmogorov Test \/ 73\u003c\/p\u003e \u003cp\u003e2.8 More on (Moron?) Hypothesis Testing \/ 74\u003c\/p\u003e \u003cp\u003e2.8.1 Explanation \/ 75\u003c\/p\u003e \u003cp\u003e2.8.2 Misuse of Hypothesis Testing \/ 77\u003c\/p\u003e \u003cp\u003e2.8.3 Use and Misuse of \u003ci\u003ep\u003c\/i\u003e-Values \/ 79\u003c\/p\u003e \u003cp\u003e2.9 Problems \/ 82\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Likelihood 85\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction \/ 85\u003c\/p\u003e \u003cp\u003e3.1.1 Scalar Parameter Case \/ 87\u003c\/p\u003e \u003cp\u003e3.1.2 Vector Parameter Case \/ 92\u003c\/p\u003e \u003cp\u003e3.1.3 Robustness and the MCD Estimator \/ 100\u003c\/p\u003e \u003cp\u003e3.1.4 Asymptotic Properties of the Maximum Likelihood Estimator \/ 102\u003c\/p\u003e \u003cp\u003e3.2 Cramér–Rao Lower Bound \/ 107\u003c\/p\u003e \u003cp\u003e3.2.1 Univariate Case \/ 108\u003c\/p\u003e \u003cp\u003e3.2.2 Multivariate Case \/ 111\u003c\/p\u003e \u003cp\u003e3.3 Model Selection \/ 114\u003c\/p\u003e \u003cp\u003e3.3.1 Model Misspecification \/ 114\u003c\/p\u003e \u003cp\u003e3.3.2 The Likelihood Ratio Statistic \/ 117\u003c\/p\u003e \u003cp\u003e3.3.3 Use of Information Criteria \/ 119\u003c\/p\u003e \u003cp\u003e3.4 Problems \/ 120\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Numerical Optimization 123\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Root Finding \/ 123\u003c\/p\u003e \u003cp\u003e4.1.1 One Parameter \/ 124\u003c\/p\u003e \u003cp\u003e4.1.2 Several Parameters \/ 131\u003c\/p\u003e \u003cp\u003e4.2 Approximating the Distribution of the Maximum Likelihood Estimator \/ 135\u003c\/p\u003e \u003cp\u003e4.3 General Numerical Likelihood Maximization \/ 136\u003c\/p\u003e \u003cp\u003e4.3.1 Newton–Raphson and Quasi-Newton Methods \/ 137\u003c\/p\u003e \u003cp\u003e4.3.2 Imposing Parameter Restrictions \/ 140\u003c\/p\u003e \u003cp\u003e4.4 Evolutionary Algorithms \/ 145\u003c\/p\u003e \u003cp\u003e4.4.1 Differential Evolution \/ 146\u003c\/p\u003e \u003cp\u003e4.4.2 Covariance Matrix Adaption Evolutionary Strategy \/ 149\u003c\/p\u003e \u003cp\u003e4.5 Problems \/ 155\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Methods of Point Estimation 157\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Univariate Mixed Normal Distribution \/ 157\u003c\/p\u003e \u003cp\u003e5.1.1 Introduction \/ 157\u003c\/p\u003e \u003cp\u003e5.1.2 Simulation of Univariate Mixtures \/ 160\u003c\/p\u003e \u003cp\u003e5.1.3 Direct Likelihood Maximization \/ 161\u003c\/p\u003e \u003cp\u003e5.1.4 Use of the EM Algorithm \/ 169\u003c\/p\u003e \u003cp\u003e5.1.5 Shrinkage-Type Estimation \/ 174\u003c\/p\u003e \u003cp\u003e5.1.6 Quasi-Bayesian Estimation \/ 176\u003c\/p\u003e \u003cp\u003e5.1.7 Confidence Intervals \/ 178\u003c\/p\u003e \u003cp\u003e5.2 Alternative Point Estimation Methodologies \/ 184\u003c\/p\u003e \u003cp\u003e5.2.1 Method of Moments Estimator \/ 185\u003c\/p\u003e \u003cp\u003e5.2.2 Use of Goodness-of-Fit Measures \/ 190\u003c\/p\u003e \u003cp\u003e5.2.3 Quantile Least Squares \/ 191\u003c\/p\u003e \u003cp\u003e5.2.4 Pearson Minimum Chi-Square \/ 193\u003c\/p\u003e \u003cp\u003e5.2.5 Empirical Moment Generating Function Estimator \/ 195\u003c\/p\u003e \u003cp\u003e5.2.6 Empirical Characteristic Function Estimator \/ 198\u003c\/p\u003e \u003cp\u003e5.3 Comparison of Methods \/ 199\u003c\/p\u003e \u003cp\u003e5.4 A Primer on Shrinkage Estimation \/ 200\u003c\/p\u003e \u003cp\u003e5.5 Problems \/ 202\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART II FURTHER FUNDAMENTAL CONCEPTS IN STATISTICS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Q-Q Plots and Distribution Testing 209\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 P-P Plots and Q-Q Plots \/ 209\u003c\/p\u003e \u003cp\u003e6.2 Null Bands \/ 211\u003c\/p\u003e \u003cp\u003e6.2.1 Definition and Motivation \/ 211\u003c\/p\u003e \u003cp\u003e6.2.2 Pointwise Null Bands via Simulation \/ 212\u003c\/p\u003e \u003cp\u003e6.2.3 Asymptotic Approximation of Pointwise Null Bands \/ 213\u003c\/p\u003e \u003cp\u003e6.2.4 Mapping Pointwise and Simultaneous Significance Levels \/ 215\u003c\/p\u003e \u003cp\u003e6.3 Q-Q Test \/ 217\u003c\/p\u003e \u003cp\u003e6.4 Further P-P and Q-Q Type Plots \/ 219\u003c\/p\u003e \u003cp\u003e6.4.1 (Horizontal) Stabilized P-P Plots \/ 219\u003c\/p\u003e \u003cp\u003e6.4.2 Modified S-P Plots \/ 220\u003c\/p\u003e \u003cp\u003e6.4.3 MSP Test for Normality \/ 224\u003c\/p\u003e \u003cp\u003e6.4.4 Modified Percentile (Fowlkes-MP) Plots \/ 228\u003c\/p\u003e \u003cp\u003e6.5 Further Tests for Composite Normality \/ 231\u003c\/p\u003e \u003cp\u003e6.5.1 Motivation \/ 232\u003c\/p\u003e \u003cp\u003e6.5.2 Jarque–Bera Test \/ 234\u003c\/p\u003e \u003cp\u003e6.5.3 Three Powerful (and More Recent) Normality Tests \/ 237\u003c\/p\u003e \u003cp\u003e6.5.4 Testing Goodness of Fit via Binning: Pearson’s \u003ci\u003eX\u003csub\u003e P\u003c\/sub\u003e\u003csup\u003e2\u003c\/sup\u003e\u003c\/i\u003e Test \/ 240\u003c\/p\u003e \u003cp\u003e6.6 Combining Tests and Power Envelopes \/ 247\u003c\/p\u003e \u003cp\u003e6.6.1 Combining Tests \/ 248\u003c\/p\u003e \u003cp\u003e6.6.2 Power Comparisons for Testing Composite Normality \/ 252\u003c\/p\u003e \u003cp\u003e6.6.3 Most Powerful Tests and Power Envelopes \/ 252\u003c\/p\u003e \u003cp\u003e6.7 Details of a Failed Attempt \/ 255\u003c\/p\u003e \u003cp\u003e6.8 Problems \/ 260\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Unbiased Point Estimation and Bias Reduction 269\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Sufficiency \/ 269\u003c\/p\u003e \u003cp\u003e7.1.1 Introduction \/ 269\u003c\/p\u003e \u003cp\u003e7.1.2 Factorization \/ 272\u003c\/p\u003e \u003cp\u003e7.1.3 Minimal Sufficiency \/ 276\u003c\/p\u003e \u003cp\u003e7.1.4 The Rao–Blackwell Theorem \/ 283\u003c\/p\u003e \u003cp\u003e7.2 Completeness and the Uniformly Minimum Variance Unbiased Estimator \/ 286\u003c\/p\u003e \u003cp\u003e7.3 An Example with i.i.d. Geometric Data \/ 289\u003c\/p\u003e \u003cp\u003e7.4 Methods of Bias Reduction \/ 293\u003c\/p\u003e \u003cp\u003e7.4.1 The Bias-Function Approach \/ 293\u003c\/p\u003e \u003cp\u003e7.4.2 Median-Unbiased Estimation \/ 296\u003c\/p\u003e \u003cp\u003e7.4.3 Mode-Adjusted Estimator \/ 297\u003c\/p\u003e \u003cp\u003e7.4.4 The Jackknife \/ 302\u003c\/p\u003e \u003cp\u003e7.5 Problems \/ 305\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Analytic Interval Estimation 313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Definitions \/ 313\u003c\/p\u003e \u003cp\u003e8.2 Pivotal Method \/ 315\u003c\/p\u003e \u003cp\u003e8.2.1 Exact Pivots \/ 315\u003c\/p\u003e \u003cp\u003e8.2.2 Asymptotic Pivots \/ 318\u003c\/p\u003e \u003cp\u003e8.3 Intervals Associated with Normal Samples \/ 319\u003c\/p\u003e \u003cp\u003e8.3.1 Single Sample \/ 319\u003c\/p\u003e \u003cp\u003e8.3.2 Paired Sample \/ 320\u003c\/p\u003e \u003cp\u003e8.3.3 Two Independent Samples \/ 322\u003c\/p\u003e \u003cp\u003e8.3.4 Welch’s Method for 𝜇\u003csub\u003e1\u003c\/sub\u003e − 𝜇\u003csub\u003e2\u003c\/sub\u003e when 𝜎\u003csub\u003e1\u003c\/sub\u003e\u003csup\u003e2\u003c\/sup\u003e ≠ 𝜎\u003csub\u003e2\u003c\/sub\u003e\u003csup\u003e2 \u003c\/sup\u003e\/ 323\u003c\/p\u003e \u003cp\u003e8.3.5 Satterthwaite’s Approximation \/ 324\u003c\/p\u003e \u003cp\u003e8.4 Cumulative Distribution Function Inversion \/ 326\u003c\/p\u003e \u003cp\u003e8.4.1 Continuous Case \/ 326\u003c\/p\u003e \u003cp\u003e8.4.2 Discrete Case \/ 330\u003c\/p\u003e \u003cp\u003e8.5 Application of the Nonparametric Bootstrap \/ 334\u003c\/p\u003e \u003cp\u003e8.6 Problems \/ 337\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART III ADDITIONAL TOPICS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Inference in a Heavy-Tailed Context 341\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Estimating the Maximally Existing Moment \/ 342\u003c\/p\u003e \u003cp\u003e9.2 A Primer on Tail Estimation \/ 346\u003c\/p\u003e \u003cp\u003e9.2.1 Introduction \/ 346\u003c\/p\u003e \u003cp\u003e9.2.2 The Hill Estimator \/ 346\u003c\/p\u003e \u003cp\u003e9.2.3 Use with Stable Paretian Data \/ 349\u003c\/p\u003e \u003cp\u003e9.3 Noncentral Student’s \u003ci\u003et\u003c\/i\u003e Estimation \/ 351\u003c\/p\u003e \u003cp\u003e9.3.1 Introduction \/ 351\u003c\/p\u003e \u003cp\u003e9.3.2 Direct Density Approximation \/ 352\u003c\/p\u003e \u003cp\u003e9.3.3 Quantile-Based Table Lookup Estimation \/ 353\u003c\/p\u003e \u003cp\u003e9.3.4 Comparison of NCT Estimators \/ 354\u003c\/p\u003e \u003cp\u003e9.4 Asymmetric Stable Paretian Estimation \/ 358\u003c\/p\u003e \u003cp\u003e9.4.1 Introduction \/ 358\u003c\/p\u003e \u003cp\u003e9.4.2 The Hint Estimator \/ 359\u003c\/p\u003e \u003cp\u003e9.4.3 Maximum Likelihood Estimation \/ 360\u003c\/p\u003e \u003cp\u003e9.4.4 The McCulloch Estimator \/ 361\u003c\/p\u003e \u003cp\u003e9.4.5 The Empirical Characteristic Function Estimator \/ 364\u003c\/p\u003e \u003cp\u003e9.4.6 Testing for Symmetry in the Stable Model \/ 366\u003c\/p\u003e \u003cp\u003e9.5 Testing the Stable Paretian Distribution \/ 368\u003c\/p\u003e \u003cp\u003e9.5.1 Test Based on the Empirical Characteristic Function \/ 368\u003c\/p\u003e \u003cp\u003e9.5.2 Summability Test and Modification \/ 371\u003c\/p\u003e \u003cp\u003e9.5.3 ALHADI: The 𝛼-Hat Discrepancy Test \/ 375\u003c\/p\u003e \u003cp\u003e9.5.4 Joint Test Procedure \/ 383\u003c\/p\u003e \u003cp\u003e9.5.5 Likelihood Ratio Tests \/ 384\u003c\/p\u003e \u003cp\u003e9.5.6 Size and Power of the Symmetric Stable Tests \/ 385\u003c\/p\u003e \u003cp\u003e9.5.7 Extension to Testing the Asymmetric Stable Paretian Case \/ 395\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 The Method of Indirect Inference 401\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction \/ 401\u003c\/p\u003e \u003cp\u003e10.2 Application to the Laplace Distribution \/ 403\u003c\/p\u003e \u003cp\u003e10.3 Application to Randomized Response \/ 403\u003c\/p\u003e \u003cp\u003e10.3.1 Introduction \/ 403\u003c\/p\u003e \u003cp\u003e10.3.2 Estimation via Indirect Inference \/ 406\u003c\/p\u003e \u003cp\u003e10.4 Application to the Stable Paretian Distribution \/ 409\u003c\/p\u003e \u003cp\u003e10.5 Problems \/ 416\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Review of Fundamental Concepts in Probability Theory 419\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Combinatorics and Special Functions \/ 420\u003c\/p\u003e \u003cp\u003eA.2 Basic Probability and Conditioning \/ 423\u003c\/p\u003e \u003cp\u003eA.3 Univariate Random Variables \/ 424\u003c\/p\u003e \u003cp\u003eA.4 Multivariate Random Variables \/ 427\u003c\/p\u003e \u003cp\u003eA.5 Continuous Univariate Random Variables \/ 430\u003c\/p\u003e \u003cp\u003eA.6 Conditional Random Variables \/ 432\u003c\/p\u003e \u003cp\u003eA.7 Generating Functions and Inversion Formulas \/ 434\u003c\/p\u003e \u003cp\u003eA.8 Value at Risk and Expected Shortfall \/ 437\u003c\/p\u003e \u003cp\u003eA.9 Jacobian Transformations \/ 451\u003c\/p\u003e \u003cp\u003eA.10 Sums and Other Functions \/ 453\u003c\/p\u003e \u003cp\u003eA.11 Saddlepoint Approximations \/ 456\u003c\/p\u003e \u003cp\u003eA.12 Order Statistics \/ 460\u003c\/p\u003e \u003cp\u003eA.13 The Multivariate Normal Distribution \/ 462\u003c\/p\u003e \u003cp\u003eA.14 Noncentral Distributions \/ 465\u003c\/p\u003e \u003cp\u003eA.15 Inequalities and Convergence \/ 467\u003c\/p\u003e \u003cp\u003eA.15.1 Inequalities for Random Variables \/ 467\u003c\/p\u003e \u003cp\u003eA.15.2 Convergence of Sequences of Sets \/ 469\u003c\/p\u003e \u003cp\u003eA.15.3 Convergence of Sequences of Random Variables \/ 473\u003c\/p\u003e \u003cp\u003eA.16 The Stable Paretian Distribution \/ 483\u003c\/p\u003e \u003cp\u003eA.17 Problems \/ 492\u003c\/p\u003e \u003cp\u003eA.18 Solutions \/ 509\u003c\/p\u003e \u003cp\u003eReferences 537\u003c\/p\u003e \u003cp\u003eIndex 561\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49407049367895,"sku":"9781119417866","price":94.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781119417866.jpg?v=1730498002","url":"https:\/\/bookcurl.com\/products\/fundamental-statistical-inference-9781119417866","provider":"Book Curl","version":"1.0","type":"link"}