ELEMENTS OF STATISTICAL INFERENCE

International Teaching ELEMENTS OF STATISTICAL INFERENCE

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8861200012
DEPARTMENT OF ECONOMICS AND STATISTICS
Corso di Dottorato (D.M.226/2021)
ECONOMICS AND POLICY ANALYSIS OF MARKETS AND FIRMS
2023/2024



Objectives
THE AIM OF THE COURSE IS TO INTRODUCE THE ESSENTIAL ELEMENTS OF STATISTICAL INFERENCE AND THE LINEAR REGRESSION MODEL. REFERENCES TO ELEMENTS OF PROBABILITY THEORY AND KNOWN MODELS OF RANDOM VARIABLES WILL BE PREPARATORY TO THE ILLUSTRATION OF THE MAIN ESTIMATION METHODS, THE PROPERTIES OF THE ESTIMATORS AND THE TESTS OF HYPOTHESES. THE MAIN INFERENCE TECHNIQUES, SUCH AS POINT ESTIMATION, INTERVAL ESTIMATION AND HYPOTHESIS TESTING, WILL ALSO BE TREATED AND ILLUSTRATED WITH PRACTICAL APPLICATION EXAMPLES ON REAL ECONOMIC DATA AND COMPUTATIONAL EXAMPLES WITH THE R SOFTWARE.
Prerequisites
BASIC ALGEBRA, DESCRIPTIVE STATISTICS
Contents
INTRODUCTORY CONCEPTS.
THE STATISTICAL INVESTIGATION. TYPES OF INFORMATION AND MEASUREMENT SCALES. CENSUS AND SAMPLING. SAMPLING ERRORS AND SOURCES OF DISTORTIONS. ORGANIZE DATA INTO TABLE.

DESCRIPTIVE STATISTICS
FREQUENCY DISTRIBUTIONS. GRAPHICAL REPRESENTATIONS: BAR CHARTS, PIES, HISTOGRAMS, TIME SERIES CHARTS.
INDEXES OF POSITION, VARIABILITY AND SHAPE. DATA TRANSFORMATION. Z-SCORES. BOXPLOT. RELATIONSHIPS BETWEEN VARIABLES. CORRELATION.

PROBABILITY THEORY. OUTLINE OF COMBINATORY CALCULUS. MAIN MODELS OF DISCRETE RANDOM VARIABLES: UNIFORM, BERNOULLI, BINOMIAL. CONTINUOUS RANDOM VARIABLES. THE NORMAL RANDOM VARIABLE. T STUDENT'S AND CHI-SQUARE RANDOM VARIABLES . THE CENTRAL LIMIT THEOREM.

POINT ESTIMATE.
ESTIMATORS OF THE MEAN, VARIANCE AND PROPORTION.

INTERVAL ESTIMATION.
CONFIDENCE INTERVALS. CONFIDENCE LEVEL. CONFIDENCE INTERVALS FOR THE MEAN AND FOR THE PROPORTION.

HYPOTHESIS TESTING.
THE LOGIC OF HYPOTHESIS TESTING. TESTING HYPOTHESES ON THE MEAN AND PROPORTION. LINK BETWEEN HYPOTHESIS TESTING AND CONFIDENCE INTERVALS.

NON-PARAMETRIC TESTS
CHI-SQUARE TEST. GOODNESS OF FIT AND INDEPENDENCE BETWEEN VARIABLES.
Teaching Methods
THE COURSE CONSISTS OF 10 HOURS OF LECTURED TEACHING. EACH LESSON IS STRUCTURED INTO A THEORETICAL PART AND A PART OF APPLICATIONS TO CASE STUDIES.
Verification of learning
THE EVALUATION CONSISTS OF THE DRAFTING AND DISCUSSION OF A STATISTICAL REPORT ON A REAL DATASET AGREED WITH THE TEACHER.

THE ORAL EXAM, CONSISTING OF THE DISCUSSION OF THE REPORT, LASTS ABOUT 20
MINUTES AND FOCUS ON THE TOPICS COVERED IN THE WRITTEN TEST AND THE
THEORETICAL TOPICS OF THE COURSE.
THE FINAL ASSESSMENT RESULTS FROM THE SUM OF THE SCORES ACHIEVED IN THE REPORT AND IN THE ORAL: THIS OVERALL SCORE REPRESENTS THE FINAL MARK (IN THIRTIETH) AND THE EXAM IS PASSED IF IT REACHES THE MINIMUM THRESHOLD OF 18.
IN THE ASSESSMENT OF THE ORAL EXAM, AS WELL AS THE KNOWLEDGE OF THE MATTER COVERED, THE EXPRESSION ABILITY, THE ACCURACY OF THE LANGUAGE AND THE ABILITY TO CRITICALLY USE THE ACQUIRED STATISTICAL TOOLS WILL BE TAKEN INTO ACCOUNT.
Texts
HANDOUTS PROVIDED BY THE TEACHER
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