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Statistical Data Analysis (Basic Stochastics and Statistics (Univariate…
Statistical Data Analysis
Basic Stochastics and Statistics
Random Vectors
Marginal PDF
Expectation
Covariance
Independence
Variance
Univariate Distributions
Normal
Standard Normal
Poisson
Beta
Moments
Gamma
Binomial
Random Variables
Distribution Functions
PDF
CDF
Joint PDF
Conditional PDF
Independence
Functions of Random Variables
Variance
Expectation
Moments
Standard Deviation
Characteristic Functions
Multivariate Distributions
Normal
Linear Transformation
Central Limit Theorem
Random Samples and Estimators
Estimation
Estimator
Consistency
Effectivity
MSE
Examples
Sample Mean
Standard error
Empirical Variance
Maximum Likelihood Estimation
Method of Moments
Samples
Gaussian Distribution
Xi Squared Distribution
Normal Distribution
Student's t-Distribution
Empirical Distribution Functions
Quantiles
Confidence Intervals
One-Sided Intervals
Two Sided Intervals
Confidence Regions
Classification
Logistic Regression
Multicategorical Classification
Regression
Non-Linear Regression
Logistic Regression
Model
Non-Linear Least Squares
Gauss-Newton Method
Newtons Method
Gradient Descent
Confidence Intervals for Parameters
Linear Regression
Simple Linear Regression
Estimating the Parameters
Method of Least Squares
Least Squares Estimator
Error and Residuals
Estimating the Variance
Normal Equations
BLUE Estimators
Confidence Intervals for the Parameters
Regression Function
Multiple Linear Regression
Design Matrix
Response Variable
Method of Least Squares
Distribution of the Parameters
Properties of LS Estimator
Statistical Tests for Coefficients
Test Statistic
F-Statistic
F-Distribution
Confidence Interval
T-Statistic
T-Distribtuion
Confidence Interval
Variability of Data
SST
SSE
SSR
Weighted Least Squares
Regularization
Ridge Regression
Tikkonov Regularization
Singular Value Decomposition
Cross Validation
Lasso Regression
Principal Component Regression
Principal Component Analysis
Truncated SVD
Principal Components
Analysis of Variance
Linear Model
ANOVA
Tests
General Inverse
Non-Parametric Regression
Nonparametric Density Estimation
Histograms
Bin-Width
Sliding Window
Kernel Density Estimators
Kernel Functions
Bandwidth
Nearest Neighbour Estimator
Multivariate KDE
Gaussian Kernel
Nadaraya-Watson-Estimator
Local Polynomial Estimator
Regressogramm
Multivariate Kernel Regression
Local Linear Estimator