Portale di Ateneo - En.Unibs.it

Estimation
Population and Random Sample; Parameter Space; concepts of "statistics", "estimator" and "estimate".
Estimator and its properties (unbiasedness, consistency, efficiency). - Tchebycheff inequality.
Methods for the construction of estimators (least-squares (notes), moments, maximum likelihood).
Outline of Chi-Square, Student's t, Fisher-Snedecor’s F random variables.
Sampling Distributions of some estimators (mean, proportion, unbiased variance, difference between two means, difference between two proportions, the ratio of two variances).
Confidence Interval estimation for: Population Mean, Proportion, Difference between the Means of two populations, Difference between the proportions, Variance.

Hypothesis Testing
Statistical Hypothesis. Null and Alternative Hypothesis, Simple and Complex Hypothesis.
Statistical test. I and II Type Errors and their associated probabilities. Power Function.
Test of Hypotheses for the Mean of a Population, the Proportion of a Population, the Homogeneity of Variances of two Populations, the equality of Means of two Populations, equality of the Proportions of two Populations).
Hypothesis testing of adaptation (or compliance) of a theoretical model to an empirical distribution.
Jarque-Bera test of Normality
Chi-Square test of Indipendence

Simple Linear Regression
Determining the Simple Linear Regression
Measure of Variation
Assumptions
Residual Analysis
Inference about the Slope and Correlation Coeffecient
Estimation of Mean Value and Prediction of Individual Values
Durbin-Watson test

Multiple Regression Model
Developing a Multiple Regression Model
Multicollinarity
Overall F test
Residual Analysis
Inferences Concerning the Population Regression Coefficients
Using Dummy Variables and Interaction Terms in Regression Models
From OLS to ML estimators