Ebook: Computer intensive methods in statistics

Table of contents Introduction 1. Randfom Variable Generation Basic Methods Congruential Generators The KISS Generator Beyond Uniform Distributions Transformation Methods Accept-Reject Methods Envelope Accept-Reject Methods Problems 2. Monte Carlo Methods Independent Monte Carlo Methods Importance Sampling The Rule of Thumb for Importance Sampling Markov Chain Monte Carlo -- MCMC Metropolis-Hastings Algorithm Some Special Algorithms Adaptive MCMC Perfect Simulation The Gibbs Sampler Approximate Bayesian computation (ABC) methods Problems 3. Bootstrap General Principle Unified Bootstrap Framework Bootstrap and Monte Carlo Conditional and Unconditional Distribution Basic Bootstrap Plug-in Principle Why is Bootstrap Good? Example, where Bootstrap Fails Bootstrap Confidence Sets The Pivotal Method The Bootstrap Pivotal Methods Percentile Bootstrap Confidence Interval Basic Bootstrap Confidence Interval Studentized Bootstrap Confidence Interval Transformed Bootstrap Confidence Intervals Prepivoting Confidence Set BCa-Confidence Interval Bootstrap Hypothesis Tests Parametric Bootstrap Hypothesis Test Nonparametric Bootstrap Hypothesis Test Advanced Bootstrap Hypothesis Tests Bootstrap in Regression Model Based Bootstrap Parametric Bootstrap Regression Casewise Bootstrap In The Correlation Model Bootstrap For Time Series Problems 4. Simulation based Methods EM -- Algorithm SIMEX Problems 5. Density Estimation Background Histogram Kernel Density Estimator Statistical Properties Bandwidth Selection in Practice Nearest Neighbor Estimator Orthogonal Series Estimators Minimax Convergence Rates Problems 6. Nonparametric Regression Background Kernel Regression Smoothing Local Regression Classes of Restricted Estimators Ridge Regression Lasso Spline Estimators Base Splines Smoothing Splines Wavelets Estimators Wavelet Base Wavelet Smoothing Choosing the Smoothing Parameter Bootstrap in Regression Problems;This textbook gives an overview of statistical methods that have been developed during the last years due to increasing computer use, including random number generators, Monte Carlo methods, Markov Chain Monte Carlo (MCMC) methods, Bootstrap, EM algorithms, SIMEX, variable selection, density estimators, kernel estimators, orthogonal and local polynomial estimators, wavelet estimators, splines, and model assessment. Computer Intensive Methods in Statistics is written for students at graduate level, but can also be used by practitioners. Features Presents the main ideas of computer-intensive statistical methods Gives the algorithms for all the methods Uses various plots and illustrations for explaining the main ideas Features the theoretical backgrounds of the main methods. Includes R codes for the methods and examples Silvelyn Zwanzig is an Associate Professor for Mathematical Statistics at Uppsala University. She studied Mathematics at the Humboldt- University in Berlin. Before coming to Sweden, she was Assistant Professor at the University of Hamburg in Germany. She received her Ph.D. in Mathematics at the Academy of Sciences of the GDR. Since 1991, she has taught Statistics for undergraduate and graduate students. Her research interests have moved from theoretical statistics to computer intensive statistics. Behrang Mahjani is a postdoctoral fellow with a Ph.D. in Scientific Computing with a focus on Computational Statistics, from Uppsala University, Sweden. He joined the Seaver Autism Center for Research and Treatment at the Icahn School of Medicine at Mount Sinai, New York, in September 2017 and was formerly a postdoctoral fellow at the Karolinska Institutet, Stockholm, Sweden. His research is focused on solving large-scale problems through statistical and computational methods.