Computer Intensive Methods in Statistics: 1st Edition (Paperback) book cover

Computer Intensive Methods in Statistics

1st Edition

By Silvelyn Zwanzig, Behrang Mahjani

Chapman and Hall/CRC

215 pages

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Paperback: 9780367194239
pub: 2019-12-13
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Hardback: 9780367194253
pub: 2019-12-13
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Description

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.

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

About the Authors

Arvind Bansal is a full professor of Computer Science at Kent State University, Kent, Ohio, USA. He received his PhD (1988) from Case Western Reserve University, Cleveland, Ohio, USA. His research publications, and undergraduate and graduate teaching are in artificial intelligence, multimedia systems and languages, bioinformatics, and computational health informatics.

Javed Khan is a full professor of Computer Science at Kent State University, Kent, Ohio, USA. He received his PhD (1995) from University of Hawaii at Manoa, USA. His research publications, and undergraduate and graduate teachings are in artificial intelligence, computer networking protocols, educational networks, medical image processing and communication, perceptual enhancement, and automated knowledge acquisition. He has been a long-term Fulbright area expert.

S. Kaisar Alam received his PhD (1996) in Electrical Engineering from University of Rochester, Rochester NY, USA. His research publications and teaching are in medical image analysis and genome analysis. He was a member of the research staff in Biomedical Engineering Laboratories during 1998-2013. He has been a Fullbright scholar and a visiting professor at RUTGERS University, NY, USA. Currently, he runs his company for medical image analysis.

Subject Categories

BISAC Subject Codes/Headings:
BUS061000
BUSINESS & ECONOMICS / Statistics
COM021030
COMPUTERS / Database Management / Data Mining
MAT029000
MATHEMATICS / Probability & Statistics / General