#### Overview of this book

Data Science with R aims to teach you how to begin performing data science tasks by taking advantage of Rs powerful ecosystem of packages. R being the most widely used programming language when used with data science can be a powerful combination to solve complexities involved with varied data sets in the real world. The book will provide a computational and methodological framework for statistical simulation to the users. Through this book, you will get in grips with the software environment R. After getting to know the background of popular methods in the area of computational statistics, you will see some applications in R to better understand the methods as well as gaining experience of working with real-world data and real-world problems. This book helps uncover the large-scale patterns in complex systems where interdependencies and variation are critical. An effective simulation is driven by data generating processes that accurately reflect real physical populations. You will learn how to plan and structure a simulation project to aid in the decision-making process as well as the presentation of results. By the end of this book, you reader will get in touch with the software environment R. After getting background on popular methods in the area, you will see applications in R to better understand the methods as well as to gain experience when working on real-world data and real-world problems.
Simulation for Data Science with R
Credits
www.PacktPub.com
Preface
Free Chapter
Introduction
R and High-Performance Computing
The Discrepancy between Pencil-Driven Theory and Data-Driven Computational Solutions
Simulation of Random Numbers
Monte Carlo Methods for Optimization Problems
Probability Theory Shown by Simulation
Resampling Methods
Applications of Resampling Methods and Monte Carlo Tests
The EM Algorithm
Simulation with Complex Data
System Dynamics and Agent-Based Models
Index

## The jackknife

The jackknife is – like the bootstrap – a resampling method. The jackknife can be used to determine bias and standard error of estimators. It is simpler and faster than the bootstrap, since we do not draw new (bootstrap) samples, but we leave out one value from the original sample (for each jackknife sample). We just make estimations with one observation excluded.

The jackknife method was originally proposed by Quenouille (1949). Almost a century later, John Tukey (1958) extended the use of the method by showing how to use it for reducing the bias and estimating the variance. He invented the name "jackknife". Like a pocket knife, this technique can be used as an easy to use and fast to calculate "quick and dirty" tool that can solve a variety of problems. While the jackknife was very popular in the past because of its simplicity and fast computation, it generally has lower quality than the bootstrap, and it should be used only in rare, specific cases.

Let be an estimator for...