Mathematical Statistics with resampling and R: Mathematical statistics is the branch of statistics that deals with the theoretical underpinnings of statistical methods, including probability theory, statistical inference, hypothesis testing, and the design of experiments. Resampling is a technique used in statistics to estimate the sampling distribution of a statistic by repeatedly sampling from the original data set. R is a popular programming language and software environment used in statistics and data analysis. Resampling methods, such as bootstrapping and permutation tests, are widely used in modern statistical practice to estimate uncertainty in statistical inferences. In bootstrapping, a statistic is repeatedly calculated from resampled data sets, with replacement, to estimate the distribution of the statistic. Permutation tests involve repeatedly permuting the labels of observations in a data set to estimate the distribution of a statistic.
R provides a rich set of tools for statistical analysis and visualization, including functions for resampling methods and statistical modeling. The core R package, along with additional packages such as dplyr, ggplot2, and tidyr, provide a wide range of data manipulation, visualization, and modeling capabilities.
Some of the key topics in mathematical statistics with resampling and R include:
- Probability theory and distributions
- Sampling theory and inference
- Resampling methods, such as bootstrapping and permutation tests
- Hypothesis testing and statistical inference
- Linear models, including regression and ANOVA
- Non-parametric methods, such as kernel density estimation and rank-based tests
- Bayesian inference and computation
- Visualization of data and results using R graphics packages such as ggplot2.