Advanced Statistical Methods and Optimization
Preface
This is the script for the lecture “Advanced Statistical Methods and Optimization” at the DIT/Campus Cham. I do realize, that this body of knowledge has been repeated over and over, but have decided to do my own nonetheless so I can add my own flavor to the realms of statistics. This work is heavily inspired by (Wickham and Grolemund 2016). Please note that this material is copyrighted, you are not allowed to copy, at least ask for permission - you are likely to get it.
Content is subject to change.
Tim Weber, Oct. 2024
Glossary
List Of Acronyms
- ANOVA
- Analysis of Variance
- CDF
- Cumulative Density Function
- CI
- Confidence Interval
- CLT
- Central Limit Theorem
- H0
- Null-Hypothesis
- Ha
- alternative Hypothesis
- IQR
- Interquartile Range
- LLN
- Law of Large Numbers
- Probability Density Function
- PMF
- Probability Mass Function
- PoI
- Parameter of Interest
- QC
- Quality Control
- SE
- Standard Error
- Z
- Standard Score / Z-Score
- cl
- confidence level
- dof
- degree of freedom
- wrt
- with respect to
Symbol Abbreviations
Greek
\(\alpha\): significance level
\(\beta\): false negative risk, \(\beta\)-risk
\(\epsilon\): residuals
\(\mu_0\), \(\mu\): the true mean of a population
\(\varphi(x)\): probability density function
\(\phi(x)\): cumulative probability density function or cumulative distribution function
Latin
\(C_g\): potential Measurement System Capability Index
\(C_{gk}\): Measurement Capability Index with systematic error
\(C_p\): potential process capability
\(C_{pk}\): actual process capability including centering
\(\mathbb{E}[X]\): expected value of random variable \(X\)
\(k\): number of predictors in a model
\(n\): number of data points/observations in the sample
\(N\): number of datapoints/observations in the population
\(MSE\): mean squared error
\(P\): Probabilities
\(r\): range of values
\(r^2\): Coefficient of determination
\(r^2_{adjusted}\): adjusted Coefficient of determination
\(sd\): the standard deviation of a dataset
\(SSE\): Sum of squared errors as calculated by
\(\mathrm{Var}\): Variance