Computational statistics: an introduction to R

1 Basic data analysis R programming conventions Generation of random numbers and patterns Random numbers Patterns Case study: distribution diagnostics Distribution functions Histograms Barcharts Statistics of distribution functions; Kolmogorov-Smirnov tests Monte Carlo confidence bands Statistics of histograms and related plots; X2-tests Moments and quantiles R complements Random numbers Graphical comparisons Functions Enhancing graphical displays R internals parse eval print Executing files Packages Statistical summary Literature and additional references 2 Regression General regression model Linear model Factors Least squares estimation Regression diagnostics More examples for linear models Model formulae Gauss-Markov estimator and residuals Variance decomposition and analysis of variance Simultaneous inference Scheff́e's confidence bands Tukey's confidence intervals Case study: titre plates Beyond linear regression Transformations Generalised linear models Local regression R complements Discretisation External data Testing software R data types Classes and polymorphic functions Extractor functions Statistical summary Literature and additional references

3 Comparisons

Shift/scale families, and stochastic order

QQ plot, PP plot, and comparison of distributions

Kolmogorov-Smirnov tests

Tests for shift alternatives

Road map

Power and confidence

Theoretical power and confidence

Simulated power and confidence

Quantile estimation

Qualitative features of distributions

Statistical summary

Literature and additional references

4 Dimensions 1, 2, 3, ..., c

R Complements

Dimensions

Selections

Projections

Marginal distributions and scatter plot matrices

Projection pursuit

Projections for dimensions 1, 2, 3, ... 7

Parallel coordinates

Sections, conditional distributions and coplots

Transformations and dimension reduction

Higher dimensions

Linear case

Partial residuals and added variable plots

Non-linear case

Example: cusp non-linearity

Case study: Melbourne temperature data

Curse of dimensionality

Case study: body fat

High dimensions

Statistical summary

R as a programming language and environment

Help and information

Names and search paths

Administration and customisation

Basic data types

Output for objects

Object inspection

System inspection

Complex data types

Accessing components

Data manipulation

Operators

Functions

Debugging and profiling

Control structures

Input and output to data streams; external data

Libraries, packages

Mathematical operators and functions; linear algebra

Model descriptions

Graphic functions

High-level graphics

Low-level graphics

Annotations and legends

Graphic parameters and Llyout

Elementary statistical functions

Distributions, random numbers, densities...

Computing on the language.