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Nonparametric Statistics with Applications to Science and Engineering with R


Nonparametric Statistics with Applications to Science and Engineering with R


Wiley Series in Probability and Statistics, Band 1 2. Aufl.

von: Paul Kvam, Brani Vidakovic, Seong-joon Kim

107,99 €

Verlag: Wiley
Format: EPUB
Veröffentl.: 06.10.2022
ISBN/EAN: 9781119268161
Sprache: englisch
Anzahl Seiten: 448

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Beschreibungen

<B>NONPARAMETRIC STATISTICS WITH APPLICATIONS TO SCIENCE AND ENGINEERING WITH R</B> <P><B>Introduction to the methods and techniques of traditional and modern nonparametric statistics, incorporating R code</B> <p><i>Nonparametric Statistics with Applications to Science and Engineering with R</i> presents modern nonparametric statistics from a practical point of view, with the newly revised edition including custom R functions implementing nonparametric methods to explain how to compute them and make them more comprehensible. <p>Relevant built-in functions and packages on CRAN are also provided with a sample code. R codes in the new edition not only enable readers to perform nonparametric analysis easily, but also to visualize and explore data using R’s powerful graphic systems, such as ggplot2 package and R base graphic system. <p>The new edition includes useful tables at the end of each chapter that help the reader find data sets, files, functions, and packages that are used and relevant to the respective chapter. New examples and exercises that enable readers to gain a deeper insight into nonparametric statistics and increase their comprehension are also included. <p>Some of the sample topics discussed in <i>Nonparametric Statistics with Applications to Science and Engineering with R include</i>: <ul><li> Basics of probability, statistics, Bayesian statistics, order statistics, Kolmogorov–Smirnov test statistics, rank tests, and designed experiments</li> <li> Categorical data, estimating distribution functions, density estimation, least squares regression, curve fitting techniques, wavelets, and bootstrap sampling</li> <li> EM algorithms, statistical learning, nonparametric Bayes, WinBUGS, properties of ranks, and Spearman coefficient of rank correlation</li> <li> Chi-square and goodness-of-fit, contingency tables, Fisher exact test, MC Nemar test, Cochran’s test, Mantel–Haenszel test, and Empirical Likelihood </li></ul> <p><i>Nonparametric Statistics with Applications to Science and Engineering with R</i> is a highly valuable resource for graduate students in engineering and the physical and mathematical sciences, as well as researchers who need a more comprehensive, but succinct understanding of modern nonparametric statistical methods.
<p>Preface xi</p> <p><b>1 Introduction 1</b></p> <p>1.1 Efficiency of Nonparametric Methods 2</p> <p>1.2 Overconfidence Bias 4</p> <p>1.3 Computing with R 5</p> <p>1.4 Exercises 6</p> <p>References 7</p> <p><b>2 Probability Basics 9</b></p> <p>2.1 Helpful Functions 10</p> <p>2.2 Events, Probabilities and Random Variables 12</p> <p>2.3 Numerical Characteristics of Random Variables 13</p> <p>2.4 Discrete Distributions 14</p> <p>2.5 Continuous Distributions 18</p> <p>2.6 Mixture Distributions 24</p> <p>2.7 Exponential Family of Distributions 26</p> <p>2.8 Stochastic Inequalities 26</p> <p>2.9 Convergence of Random Variables 28</p> <p>2.10 Exercises 32</p> <p>References 34</p> <p><b>3 Statistics Basics 35</b></p> <p>3.1 Estimation 36</p> <p>3.2 Empirical Distribution Function 36</p> <p>3.3 Statistical Tests 38</p> <p>3.4 Confidence Intervals 41</p> <p>3.5 Likelihood 45</p> <p>3.6 Exercises 49</p> <p>References 51</p> <p><b>4 Bayesian Statistics 53</b></p> <p>4.1 The Bayesian Paradigm 53</p> <p>4.2 Ingredients for Bayesian Inference 54</p> <p>4.3 Point Estimation 58</p> <p>4.4 Interval Estimation: Credible Sets 60</p> <p>4.5 Bayesian Testing 62</p> <p>4.6 Bayesian Prediction 65</p> <p>4.7 Bayesian Computation and Use of WinBUGS 67</p> <p>4.8 Exercises 69</p> <p>References 73</p> <p><b>5 Order Statistics 75</b></p> <p>5.1 Joint Distributions of Order Statistics 77</p> <p>5.2 Sample Quantiles 79</p> <p>5.3 Tolerance Intervals 79</p> <p>5.4 Asymptotic Distributions of Order Statistics 81</p> <p>5.5 Extreme Value Theory 82</p> <p>5.6 Ranked Set Sampling 83</p> <p>5.7 Exercises 84</p> <p>References 87</p> <p><b>6 Goodness of Fit 89</b></p> <p>6.1 KolmogorovSmirnov Test Statistic 90</p> <p>6.2 Smirnov Test to Compare Two Distributions 96</p> <p>6.3 Specialized Tests 99</p> <p>6.4 Probability Plotting 106</p> <p>6.5 Runs Test 112</p> <p>6.6 Meta Analysis 117</p> <p>6.7 Exercises 121</p> <p>References 125</p> <p><b>7 Rank Tests 127</b></p> <p>7.1 Properties of Ranks 128</p> <p>7.2 Sign Test 130</p> <p>7.3 Spearman Coefficient of Rank Correlation 135</p> <p>7.4 Wilcoxon Signed Rank Test 139</p> <p>7.5 Wilcoxon (TwoSample) Sum Rank Test 142</p> <p>7.6 MannWhitney U Test 144</p> <p>7.7 Test of Variances 146</p> <p>7.8 Walsh Test for Outliers 147</p> <p>7.9 Exercises 148</p> <p>References 153</p> <p><b>8 Designed Experiments 155</b></p> <p>8.1 KruskalWallis Test 156</p> <p>8.2 Friedman Test 160</p> <p>8.3 Variance Test for Several Populations 165</p> <p>8.4 Exercises 166</p> <p>References 169</p> <p><b>9 Categorical Data 171</b></p> <p>9.1 ChiSquare and GoodnessofFit 172</p> <p>9.2 Contingency Tables 178</p> <p>9.3 Fisher Exact Test 183</p> <p>9.4 Mc Nemar Test 184</p> <p>9.5 Cochran’s Test 186</p> <p>9.6 MantelHaenszel Test 188</p> <p>9.7 CLT for Multinomial Probabilities 190</p> <p>9.8 Simpson’s Paradox 191</p> <p>9.9 Exercises 193</p> <p>References 200</p> <p><b>10 Estimating Distribution Functions 203</b></p> <p>10.1 Introduction 203</p> <p>10.2 Nonparametric Maximum Likelihood 204</p> <p>10.3 KaplanMeier Estimator 205</p> <p>10.4 Confidence Interval for F 213</p> <p>10.5 Plugin Principle 214</p> <p>10.6 SemiParametric Inference 215</p> <p>10.7 Empirical Processes 217</p> <p>10.8 Empirical Likelihood 218</p> <p>10.9 Exercises 221</p> <p>References 223</p> <p><b>11 Density Estimation 225</b></p> <p>11.1 Histogram 226</p> <p>11.2 Kernel and Bandwidth 228</p> <p>11.3 Exercises 235</p> <p>References 236</p> <p><b>12 Beyond Linear Regression 237</b></p> <p>12.1 Least Squares Regression 238</p> <p>12.2 Rank Regression 239</p> <p>12.3 Robust Regression 243</p> <p>12.4 Isotonic Regression 249</p> <p>12.5 Generalized Linear Models 252</p> <p>12.6 Exercises 259</p> <p>References 261</p> <p><b>13 Curve Fitting Techniques 263</b></p> <p>13.1 Kernel Estimators 265</p> <p>13.2 Nearest Neighbor Methods 269</p> <p>13.3 Variance Estimation 272</p> <p>13.4 Splines 273</p> <p>13.5 Summary 279</p> <p>13.6 Exercises 279</p> <p>References 282</p> <p><b>14 Wavelets 285</b></p> <p>14.1 Introduction to Wavelets 285</p> <p>14.2 How Do the Wavelets Work? 288</p> <p>14.3 Wavelet Shrinkage 295</p> <p>14.4 Exercises 304</p> <p>References 305</p> <p><b>15 Bootstrap 307</b></p> <p>15.1 Bootstrap Sampling 307</p> <p>15.2 Nonparametric Bootstrap 309</p> <p>15.3 Bias Correction for Nonparametric Intervals 315</p> <p>15.4 The Jackknife 317</p> <p>15.5 Bayesian Bootstrap 318</p> <p>15.6 Permutation Tests 320</p> <p>15.7 More on the Bootstrap 324</p> <p>15.8 Exercises 325</p> <p>References 327</p> <p><b>16 EM Algorithm 329</b></p> <p>16.1 Fisher’s Example 331</p> <p>16.2 Mixtures 333</p> <p>16.3 EM and Order Statistics 338</p> <p>16.4 MAP via EM 339</p> <p>16.5 Infection Pattern Estimation 341</p> <p>16.6 Exercises 342</p> <p>References 343</p> <p><b>17 Statistical Learning 345</b></p> <p>17.1 Discriminant Analysis 346</p> <p>17.2 Linear Classification Models 349</p> <p>17.3 Nearest Neighbor Classification 353</p> <p>17.4 Neural Networks 355</p> <p>17.5 Binary Classification Trees 361</p> <p>17.6 Exercises 368</p> <p>References 369</p> <p><b>18 Nonparametric Bayes 371</b></p> <p>18.1 Dirichlet Processes 372</p> <p>18.2 Bayesian Categorical Models 380</p> <p>18.3 Infinitely Dimensional Problems 383</p> <p>18.4 Exercises 387</p> <p>References 389</p> <p><b>A WinBUGS 392</b></p> <p>A.1 Using WinBUGS 393</p> <p>A.2 Builtin</p> <p>Functions 396</p> <p><b>B R Coding 400</b></p> <p>B.1 Programming in R 400</p> <p>B.2 Basics of R 402</p> <p>B.3 R Commands 403</p> <p>B.4 R for Statistics 405</p> <p><b>R Index 411</b></p> <p>Author Index 414</p> <p>Subject Index 418</p>
<p><b>Paul Kvam</b> is professor in the Department of Mathematics, University of Richmond, USA. He received his Ph.D. from University of California, Davis. <p><b>Brani Vidakovic</b> is professor in the Department of Statistics, Texas A&M University, USA. He received his Ph.D from Purdue University. <p><b>Seong-joon Kim</b> is assistant professor in Department of Industrial Engineering, Chosun University, South Korea. He received his Ph.D. from Hanyang University.
<P><B>Introduction to the methods and techniques of traditional and modern nonparametric statistics, incorporating R code</B> <p><i>Nonparametric Statistics with Applications to Science and Engineering with R</i> presents modern nonparametric statistics from a practical point of view, with the newly revised edition including custom R functions implementing nonparametric methods to explain how to compute them and make them more comprehensible. <p>Relevant built-in functions and packages on CRAN are also provided with a sample code. R codes in the new edition not only enable readers to perform nonparametric analysis easily, but also to visualize and explore data using R’s powerful graphic systems, such as ggplot2 package and R base graphic system. <p>The new edition includes useful tables at the end of each chapter that help the reader find data sets, files, functions, and packages that are used and relevant to the respective chapter. New examples and exercises that enable readers to gain a deeper insight into nonparametric statistics and increase their comprehension are also included. <p>Some of the sample topics discussed in <i>Nonparametric Statistics with Applications to Science and Engineering with R include</i>: <ul><li> Basics of probability, statistics, Bayesian statistics, order statistics, Kolmogorov–Smirnov test statistics, rank tests, and designed experiments</li> <li> Categorical data, estimating distribution functions, density estimation, least squares regression, curve fitting techniques, wavelets, and bootstrap sampling</li> <li> EM algorithms, statistical learning, nonparametric Bayes, WinBUGS, properties of ranks, and Spearman coefficient of rank correlation</li> <li> Chi-square and goodness-of-fit, contingency tables, Fisher exact test, MC Nemar test, Cochran’s test, Mantel–Haenszel test, and Empirical Likelihood </li></ul> <p><i>Nonparametric Statistics with Applications to Science and Engineering with R</i> is a highly valuable resource for graduate students in engineering and the physical and mathematical sciences, as well as researchers who need a more comprehensive, but succinct understanding of modern nonparametric statistical methods.

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