Mathematical Statistics and Data Analysis, Second Edition

Contents V......Page p0005.djvu
Preface XIII......Page p0013.djvu
1.1 Introduction 1......Page p0019.djvu
1.2 Sample Spaces 2......Page p0020.djvu
1.3 Probability Measures 4......Page p0022.djvu
1.4 Computing Probabilities: Counting Methods 7......Page p0025.djvu
1.4.1 The Multiplication Principle 8......Page p0026.djvu
1.4.2 Permutations and Combinations 9......Page p0027.djvu
1.5 Conditional Probability 15......Page p0033.djvu
1.6 Independence 21......Page p0039.djvu
1.8 Problems 24......Page p0042.djvu
2.1 Discrete Random Variables 33......Page p0051.djvu
2.1.1 Bernoulli Random Variables 35......Page p0053.djvu
2.1.2 The Binomial Distribution 36......Page p0054.djvu
2.1.3 The Geometric and Negative Binomial Distributions 38......Page p0056.djvu
2.1.4 The Hypergeometric Distribution 39......Page p0057.djvu
2.1.5 The Poisson Distribution 41......Page p0059.djvu
2.2 Continuous Random Variables 46......Page p0064.djvu
2.2.1 The Exponential Density 48......Page p0066.djvu
2.2.2 The Gamma Density 50......Page p0068.djvu
2.2.3 The Normal Distribution 53......Page p0071.djvu
2.3 Functions of a Random Variable 57......Page p0075.djvu
2.4 Concluding Remarks 61......Page p0079.djvu
2.5 Problems 62......Page p0080.djvu
3.1 Introduction 69......Page p0087.djvu
3.2 Discrete Random Variables 71......Page p0089.djvu
3.3 Continuous Random Variables 73......Page p0091.djvu
3.4 Independent Random Variables 83......Page p0101.djvu
3.5.1 The Discrete Case 85......Page p0103.djvu
3.5.2 The Continuous Case 86......Page p0104.djvu
3.6.1 Sums and Quotients 92......Page p0110.djvu
3.6.2 The General Case 95......Page p0113.djvu
3.7 Extrema and Order Statistics 100......Page p0118.djvu
3.8 Problems 103......Page p0121.djvu
4.1 The Expected Value of a Random Variable 111......Page p0129.djvu
4.1.1 Expectations of Functions of Random Variables 116......Page p0134.djvu
4.1.2 Expectations of Linear Combinations of Random Variables 119......Page p0137.djvu
4.2 Variance and Standard Deviation 122......Page p0140.djvu
4.2.1 A Model for Measurement Error 126......Page p0144.djvu
4.3 Covariance and Correlation 129......Page p0147.djvu
4.4.1 Definitions and Examples 135......Page p0153.djvu
4.4.2 Prediction 140......Page p0158.djvu
4.5 The Moment-Generating Function 142......Page p0160.djvu
4.6 Approximate Methods 149......Page p0167.djvu
4.7 Problems 154......Page p0172.djvu
5.2 The Law of Large Numbers 163......Page p0181.djvu
5.3 Convergence in Distribution and the Central Limit Theorem 166......Page p0184.djvu
5.4 Problems 173......Page p0191.djvu
6.2 chi^2, t, and F Distributions 177......Page p0195.djvu
6.3 The Sample Mean and the Sample Variance 179......Page p0197.djvu
6.4 Problems 182......Page p0200.djvu
7.1 Introduction 185......Page p0203.djvu
7.2 Population Parameters 186......Page p0204.djvu
7.3 Simple Random Sampling 188......Page p0206.djvu
7.3.1 The Expectation and Variance of the Sample Mean 189......Page p0207.djvu
7.3.2 Estimation of the Population Variance 196......Page p0214.djvu
7.3.3 The Normal Approximation to the Sampling Distribution of X-bar 199......Page p0217.djvu
7.4 Estimation of a Ratio 206......Page p0224.djvu
7.5.1 Introduction and Notation 213......Page p0231.djvu
7.5.2 Properties of Stratified Estimates 214......Page p0232.djvu
7.5.3 Methods of Allocation 218......Page p0236.djvu
7.6 Concluding Remarks 223......Page p0241.djvu
7.7 Problems 225......Page p0243.djvu
8.2 Fitting the Poisson Distribution to Emissions of Alpha Particles 239......Page p0257.djvu
8.3 Parameter Estimation 243......Page p0261.djvu
8.4 The Method of Moments 246......Page p0264.djvu
8.5 The Method of Maximum Likelihood 253......Page p0271.djvu
8.5.1 Maximum Likelihood Estimates of Multinomial Cell Probabilities 259......Page p0277.djvu
8.5.2 Large Sample Theory for Maximum Likelihood Estimates 261......Page p0279.djvu
8.5.3 Confidence Intervals for Maximum Likelihood Estimates 266......Page p0284.djvu
8.6 Efficiency and the Cramer-Rao Lower Bound 273......Page p0291.djvu
8.6.1 An Example: The Negative Binomial Distribution 277......Page p0295.djvu
8.7 Sufficiency 280......Page p0298.djvu
8.7.1 A Factorization Theorem 281......Page p0299.djvu
8.7.2 The Rao-Blackwell Theorem 284......Page p0302.djvu
8.8 Concluding Remarks 285......Page p0303.djvu
8.9 Problems 286......Page p0304.djvu
9.1 Introduction 299......Page p0317.djvu
9.2 The Neyman-Pearson Paradigm 300......Page p0318.djvu
9.3 Optimal Tests: The Neyman-Pearson Lemma 303......Page p0321.djvu
9.4 The Duality of Confidence Intervals and Hypothesis Tests 306......Page p0324.djvu
9.5 Generalized Likelihood Ratio Tests 308......Page p0326.djvu
9.6 Likelihood Ratio Tests for the Multinomial Distribution 310......Page p0328.djvu
9.7 The Poisson Dispersion Test 316......Page p0334.djvu
9.8 Hanging Rootograms 318......Page p0336.djvu
9.9 Probability Plots 321......Page p0339.djvu
9.10 Tests for Normality 327......Page p0345.djvu
9.11 Concluding Remarks 330......Page p0348.djvu
9.12 Problems 331......Page p0349.djvu
10.1 Introduction 345......Page p0363.djvu
10.2.1 The Empirical Cumulative Distribution Function 346......Page p0364.djvu
10.2.2 The Survival Function 348......Page p0366.djvu
10.2.3 Quantile-Quantile Plots 353......Page p0371.djvu
10.3 Histograms, Density Curves, and Stem-and-Leaf Plots 357......Page p0375.djvu
10.4.1 The Arithmetic Mean 361......Page p0379.djvu
10.4.2 The Median 364......Page p0382.djvu
10.4.3 The Trimmed Mean 365......Page p0383.djvu
10.4.4 M Estimates 366......Page p0384.djvu
10.4.6 Estimating Variability of Location Estimates by the Bootstrap 367......Page p0385.djvu
10.5 Measures of Dispersion 370......Page p0388.djvu
10.6 Boxplots 372......Page p0390.djvu
10.7 Concluding Remarks 374......Page p0392.djvu
10.8 Problems 375......Page p0393.djvu
11.1 Introduction 387......Page p0405.djvu
11.2.1 Methods Based on the Normal Distribution 388......Page p0406.djvu
11.2.1.1 An Example - A Study of Iron Retention 396......Page p0414.djvu
11.2.2 Power 400......Page p0418.djvu
11.2.3 A Nonparametric Method - The Mann-Whitney Test 402......Page p0420.djvu
11.3 Comparing Paired Samples 410......Page p0428.djvu
11.3.1 Methods Based on the Normal Distribution 411......Page p0429.djvu
11.3.2 A Nonparametric Method - The Signed Rank Test 413......Page p0431.djvu
11.3.3 An Example - Measuring Mercury Levels in Fish 415......Page p0433.djvu
11.4.1 Mammary Artery Ligation 417......Page p0435.djvu
11.4.2 The Placebo Effect 418......Page p0436.djvu
11.4.4 The Portocaval Shunt 419......Page p0437.djvu
11.4.5 FD&C Red No. 40 420......Page p0438.djvu
11.4.6 Further Remarks on Randomization 421......Page p0439.djvu
11.4.7 Observational Studies, Confounding, and Bias in Graduate Admissions 422......Page p0440.djvu
11.4.8 Fishing Expeditions 423......Page p0441.djvu
11.5 Concluding Remarks 424......Page p0442.djvu
11.6 Problems 425......Page p0443.djvu
12.2 The One-Way Layout 443......Page p0461.djvu
12.2.1 Normal Theory; the F Test 445......Page p0463.djvu
12.2.2.1 Tukey's Method 451......Page p0469.djvu
12.2.3 A Nonparametric Method - The Kruskal-Wallis Test 453......Page p0471.djvu
12.3.1 Additive Parametrization 455......Page p0473.djvu
12.3.2 Normal Theory for the Two-Way Layout 458......Page p0476.djvu
12.3.3 Randomized Block Designs 465......Page p0483.djvu
12.3.4 A Nonparametric Method - Friedman's Test 469......Page p0487.djvu
12.4 Concluding Remarks 471......Page p0489.djvu
12.5 Problems 472......Page p0490.djvu
13.2 Fisher's Exact Test 483......Page p0501.djvu
13.3 The Chi-Square Test of Homogeneity 485......Page p0503.djvu
13.4 The Chi-Square Test of Independence 489......Page p0507.djvu
13.5 Matched-Pairs Designs 492......Page p0510.djvu
13.6 Odds Ratios 494......Page p0512.djvu
13.8 Problems 498......Page p0516.djvu
14.1 Introduction 507......Page p0525.djvu
14.2.1 Statistical Properties of the Estimated Slope and Intercept 511......Page p0529.djvu
14.2.2 Assessing the Fit 515......Page p0533.djvu
14.2.3 Correlation and Regression 526......Page p0544.djvu
14.3 The Matrix Approach to Linear Least Squares 529......Page p0547.djvu
14.4.1 Vector-Valued Random Variables 532......Page p0550.djvu
14.4.2 Mean and Covariance of Least Squares Estimates 537......Page p0555.djvu
14.4.3 Estimation of sigma^2 539......Page p0557.djvu
14.4.4 Residuals and Standardized Residuals 541......Page p0559.djvu
14.4.5 Inference about beta 542......Page p0560.djvu
14.5 Multiple Linear Regression - An Example 544......Page p0562.djvu
14.6 Conditional Inference, Unconditional Inference, and the Bootstrap 548......Page p0566.djvu
14.7 Concluding Remarks 551......Page p0569.djvu
14.8 Problems 552......Page p0570.djvu
15.2 Decision Theory 571......Page p0589.djvu
15.2.1 Bayes Rules and Minimax Rules 573......Page p0591.djvu
15.2.2 Posterior Analysis 578......Page p0596.djvu
15.2.3 Classification and Hypothesis Testing 580......Page p0598.djvu
15.2.4 Estimation 584......Page p0602.djvu
15.3 The Subjectivist Point of View 587......Page p0605.djvu
15.3.1 Bayesian Inference for the Normal Distribution 589......Page p0607.djvu
15.3.2 Bayesian Analysis for the Binomial Distribution 592......Page p0610.djvu
15.5 Problems 597......Page p0615.djvu
A Common Distributions A1......Page p0621.djvu
1 Binomial Probabilities A4......Page p0624.djvu
2 Cumulative Normal Distribution A7......Page p0627.djvu
3 Percentiles of the chi^2 Distribution A8......Page p0628.djvu
4 Percentiles of the t Distribution A9......Page p0629.djvu
5 Percentiles of the F Distribution A10......Page p0630.djvu
6 Percentiles of the Studentized Range A14......Page p0634.djvu
7 Percentage Points of the Bonferroni t Statistic A20......Page p0640.djvu
8 Critical Values of the Smaller Rank Sum for the WMW Test A21......Page p0641.djvu
9 Critical Values of W_alpha(n) for the Wilcoxon Signed-Ranks Test A24......Page p0644.djvu
Bibliography A25......Page p0645.djvu
Answers to Selected Problems A31......Page p0651.djvu
Author Index A43......Page p0663.djvu
Index to Data Sets A45......Page p0665.djvu
Subject Index A46......Page p0666.djvu