1st Edition
Computer Intensive Methods in Statistics
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.
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
Biography
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.
"...The book is rich in content, excellent in coverage, highly informative, extremely reader friendly in style, and full of cartoon illustrations. The reader will find this book as a collection of the most important ideas and tools that are used in computer intensive methods for statistical analysis and data analytic investigations...The book can be used by upper undergraduate and graduate students as well as researchers and practitioners in statistics, data science, and users of all disciplines. The good news is that it is available in paperback.
- Subir Ghosh, Technometrics, Volume 62
