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Faculty of Management, Economics and Social SciencesInstitute of Econometrics and Statistics

Content of the lecture

Statistical Inference and Econometrics

Part I: Probability

Random Variables and Distributions

  • Special Discrete Distributions
    • Binomial Distribution
    • Poisson Distribution
    • Geometric Distribution
    • Hypergeometric Distribution
    • Approximation of Discrete Distributions
  • Special Continuous Distributions
    • Rectangular Distribution
    • Exponential Distribution
    • Normal Distribution

Multivariate Distributions and Limit Theorems

  • Joint Distribution of Random Variables
    • Joint and Conditional Distribution of Random Variables
    • Covariance and Coefficient of Correlation
    • Sums of Random Variables
  • Limit Theorems
    • Weak Law of Large Numbers
    • Central Limit Theorem

Part II: Statistical Inference

Samples and Sample Functions

  • Random Sampling
  • Statistics (Functions of Random Samples)
  • Statisticas for Normally Distributed Samples
  • t-Distribution

Method of Estimation for Parameters

  • Estimation of Parameters
    • Point Estimation
    • Unbiasedness and Consistency
    • Maximum-Likelihood-Estimator
    • Estimation of Expected Values
    • Estimation of Probabilities
    • Estimation of Variances and Standard Deviations
  • Interval Estimation of Expected Values and Probabilities
    • Confidence Intervals of Expected Values
    • Confidence Intervals of Probabilities
    • Sample Size

Testing Procedure

  • Estimation of Parameters
    • Testing Problem, Hypotheses
    • Sampling Errors (Type 1 & 2)
    • p-Value
  • Testing of Expected Values
    • One Sample Tests for Expected Values and Probabilities
    • Two Sample Tests for Expected Values and Probabilities
  • Tests for Probabilites
    • Tests for one Probability or Fractile
    • Comparison of two Probabilites or Fractiles

 

Part III: Econometrics

Multiple linear Regression

  • The model of linear multiple regression
  • Point estimation
    • Point estimation of regression coefficients
    • Point estimation of the variance of the error terms
  • Interval estimation and hypothesis testing
    • Confidence intervals for the regression coefficients
    • Hypothesis tests for the regression coefficients
    • Test for overall correlation (F-test)
  • Forecast
  • Linear regression in R
  • Extension of the model
    • Binary and categorical regressors
    • Modeling of more general correlations

<- back to: probability and statistical inference