paulinamoskwa / r-stats

Easy-to-use collection of statistical methods and techniques, all written in R 🗂

R-Stats

📖 About

This repository comes as a rearrangement of all the work done during my MSc in Mathematical Engineering @ Politecnico di Milano. The purpose of the repository is to put at reach an easy-to-use collection of statistical methods and techniques. Out of scope, on the other hand, is to address all the problems that these methods and techniques may encounter in a real-world data contest. In fact, all the datasets used are toy datasets, used only to introduce an application.

All the code is written in R.
A python correspondent will also exist in the future.

Mainly, the collection is divided into two sections:

• Standard Statistics - parametric statistics, classical approaches with, often, strong assumptions on data
• Nonparametric Statistics - modern approaches, free from heavy assumptions on data

I uploaded the files in .r (script version, easy to download and use directly with a custom dataset), in .rmd and in .html (for visualization purposes). Since GitHub does not provide a preview for .rmd (nor .html), I made use of an extension that allows the viewing of .html.

📁 Content

The files are viewable (code chuncks, outputs and plots) at the links below.

📈 Standard Statistics

• 01 - PCA
• 02 - Multivariate Gaussian, One Population - Test and CR for the Mean
• 03 - Paired Gaussian Data - Test for the Mean
• 04 - Repeated Measures
• 05 - Multivariate Gaussian, Two Populations - Test for the Mean
• 06 - One-way ANOVA (p=1, g=6)
• 07 - One-way MANOVA (p=4, g=3)
• 08 - Two-way ANOVA (p=1, g=2, b=2)
• 09 - Two-way MANOVA (p=3, g=2, b=2)
• 10 - Supervised learning - LDA (univariate, bivariate), QDA (bivariate), KNN, Fisher’s argument
• 11 - Unsupervised learning - Hierarchical, K-means clustering
• 12 - Linear Models - Model, IC, IP, PCA Regression, Ridge Regression, Lasso Regression
• 13 - Linear Models - Variables Selection
• 14 - Functional Data Analysis (FDA)
• 15 - Functional Data Analysis (FDA) - Example
• 16 - Geostatistics

📊 Nonparametric Statistics

• 01 - Depth Measures
• 02 - Sign Test
• 03 - Rank Test (Mann-Withney U Test)
• 04 - Signed Rank Test (Wilcoxon Signed Rank W Test)
• 05 - Permutation Test - Two Independent Samples (1-dim)
• 06 - Permutation Test - Two Independent Samples (n-dim)
• 07 - Permutation Test - Center of Simmetry
• 08 - Permutation Test - Regression
• 09 - Permutation Test - ANOVA, MANOVA
• 10 - Permutation Test - Confidence Intervals
• 11 - Bootstrap - Confidence Intervals
• 12 - Bootstrap - Regression
• 13 - Bootstrap - Two Independent Samples (1-dim)
• 14 - Bootstrap - One Sample (n-dim)
• 15 - Bootstrap - Test and p-values
• 16 - Nonparametric Regression
• 17 - Splines
• 18 - GAMs
• 19 - Full Conformal Prediction
• 20 - Split Conformal Prediction
• 21 - Conformal Prediction Intervals
• 22 - Survival Analysis

If any code is not working, or if any dataset is missing let me know.

🔜 Future developments

As a python fan, I plan to "translate" the work into python language (where I know that, with the right libraries it will take much less lines of code 😉). In addition, it would also be interesting to push beyond toy datasets and try some real-world applications.