Introduction to descriptive and parametric statistics for univariate and multivariate data with the software R.

1.  Descriptive statistic for univariate and bivariate data

• Repartition of the data (histogram, kernel density, distribution function)
• Order statistic and quantile
• Statistics for location and variability, boxplot
• Scatter plot, QQplot
• Covariance and correlation
• Simple linear regression

2.  Descriptive statistic for multivariate data

• Least squares and multiple linear and non-linear regression models
• Principal component analysis and principal component regression
• Clustering methods (K-means, hierarchical, density-based)
• Linear discriminant analysis
• Bootstrap technique
• Artificial neural network

3.  Parametric statistic

• Notion of Likelihood
• Estimator: Definition and main properties (bias, convergence)
• Punctual estimate (maximum likelihood estimation, Bayesian estimation)
• Confidence and credible intervals
• Information criteria
• Test of hypothesis
• Parametric clustering