Statistics

• Statistical Inference
  • Statistical Model
    • Types of Statistical Model
      • Parametric Model
      • Non-parametric Model
  • Different Approaches to Inference
    • Bayesian Inference
    • Frequentist (Classical) Inference
  • Types of Inference
    • Point Estimation
      • Some useful terminology
    • Confidence Set Estimation
      • Some useful terminology
    • Hypothesis Testing
  • Machine Learning as a Statistical Inference
• Non-Parametric Methods
  • Estimation of CDF
    • Empirical distribution function as an estimator
    • Confidence interval for CDF estimator
  • Plug-in Estimator for Statistical Functionals
    • Estimator for mean
    • Estimtor for variance
    • Estimator for other functionals
  • Variance Estimation of a Statistic for CI
    • Bootstrap
      • Key Idea
      • Obtaining the variance of an estimator
    • Jack knife
• Parametric Point Estimation
  • Classical Infernece
    • Method of Moments Estimator (MOM)
      • Properties
      • Common Estimators
        • Bernoulli
        • Normal
    • Maximum Likelihood Estimator (MLE)
      • Likelihood function
      • Log likelihood
      • Properties
      • Computing CI for MLE
      • Common Estimators
        • Bernoulli
        • Uniform
        • Binomial
        • Geometric
        • Multinomial
        • Exponential
        • Normal
      • Iterative Method of Computation
        • Newton Raphson
        • The EM Algorithm
  • Bayesian Inference
    • Maximum A Posterior Estimator (MAP)
      • Common Estimators
        • Bernoulli
        • Normal
    • Minimum Mean Squared Error Estimator (MMSE)
• Hypothesis Testing
  • Classical Inference
    • Generic Setup
      • Likelihood Ratio Test (LRT)
    • Specific Setup
      • Mean Difference : Wald Test
      • Multinomial Parameter Value : Chi-Squared Test
      • Two Sample Test : Permutation Test
  • Bayesian Inference