This book 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. It is written for students at Master's and PhD level.

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