Topics for the Statistics Curriculum

Topics related to the basic preparation of the candidate


Data analysis

  • Types of statistical survey
  • Units and variables
  • Classifications of variables
  • Bar charts and histograms
  • Empirical distribution function
  • Median and quantiles
  • Mean and properties
  • Variance and properties
  • Outliers and robustness


Elementary time series analysis

  • Measures of change in a time series
  • Simple index numbers
  • Complex index numbers


Multivariate data analysis

  • Scatter and scatter matrix
  • Covariance, correlation and properties
  • Covariance and correlation matrix and properties
  • Least squares line
  • Missing data
  • Principal components
  • Double and multiple contingency tables
  • Conditional distributions
  • Association indices for 2x2 tables
  • Sample and structural zeros


Probability distributions

  • Probability spaces
  • Random variables (Binomial, Hypergeometric, Poisson, Uniform, Exponential, Normal)
  • Expected value and moments from the origin
  • Variance and central moments
  • Indices of position, variance, skewness and kurtosis
  • Chebyshev's inequality
  • Law of large numbers
  • Central limit theorem
  • Multivariate distributions
  • Mutivariate normal
  • Multinomial


Sampling from finite populations

  • Terminology: observation unit, target population, sampling unit, sampling frame
  • Selection bias
  • Measurement errors
  • Sampling and non-sampling errors
  • Random samples
  • Simple random sampling
  • Stratified sampling
  • Cluster sampling


Plan of experiments

  • Terminology of the plan of experiments: experimental combination, replication, randomisation, source of variability
  • Role of factors
  • Complete factor design
  • Concept of interaction


Statistical models

  • Parametric and non-parametric models
  • Independent and identically distributed observations
  • The normal model
  • The Bernoulli model
  • Independent but not identically distributed observations
  • The analysis of variance model
  • The simple linear regression model


Estimation methods

  • Empirical distribution function
  • Quantile-quantile graphs
  • Method of moments
  • Method of least squares
  • Method of maximum likelihood


Frequentist inference

  • Statistics and estimators
  • Sample distributions in the normal model
  • Non-bias
  • Mean square error and its breakdown
  • Efficiency and accuracy


Elementary asymptotic theory

  • Consistency
  • Asymptotic normality
  • Asymptotic properties of maximum likelihood estimators and likelihood ratios


Confidence intervals

  • Estimation intervals and coverage probabilities
  • Pivot quantity method
  • Likelihood intervals


Bayesian inference

  • Conditional probability
  • The generalised Bayes formula
  • A priori parameter distributions
  • A posteriori distribution
  • Credibility intervals
  • Comparison of confidence intervals and credibility intervals


Hypothesis testing

  • Neyman-Pearson approach
  • Test level
  • Test statistics and level of significance of data (p-value)
  • Uniformly most powerful tests
  • Tests and confidence intervals
  • Chi-square test of independence


Regression models

  • Multiple linear regression
  • Estimators of regression coefficients and standard errors
  • Deviance analysis
  • Future value prediction
  • Residue diagnostics
  • Weighted least squares
  • Selection of variables
  • Linear logistic regression model
  • Goodness of fit in models with binomial data



  • Experimental and observational studies
  • Cohort and case-control studies
  • Prevalence and incidence
  • Risk measures
  • Effect measures
  • Duration data analysis
  • Censored data
  • Survival function and its estimation
  • Mortality tables
  • Risk function (force of mortality, failure rate)
  • Diagnostic tests
  • Sensitivity and specificity


Baldi, P. (2007). Calcolo delle probabilità. McGraw-Hill

Chiandotto, B. (2014). Inferenza statistica. Dispense, DISIA

Cicchitelli (2015). Statistica: principi e metodi. Pearson

Conti, P. L. & Marella, A. (2012). Campionamento da popolazione finite. Milan: Springer-Verlag Italia

Di Ciaccio, A. & Borra S. (2008). Statistica - metodologie per le scienze economiche e sociali. 2/ed. McGraw-Hill

Di Fonzo, T. Lisi, F. (2005). Serie storiche economiche. Carocci

Härdle, W. & Simar A. (2007). Applied Multivariate Statistical Analysis. Berlin: Springer

Liseo, B. (2008). Introduzione alla statistica bayesiana. Dispense

Montgomery, D. C. (2005). Progettazione e analisi degli esperimenti. McGraw-Hill

Pace, L. & Salvan, A. (2001). Introduzione alla statistica-II. Inferenza, verosimiglianza, modelli. Padua: CEDAM.

Pagano, M. & Gavreau, K. (2003). Biostatistica. Idelson Gnocchi

Santini, A. (2005). Appunti di analisi demografica. Dispense, DISIA.

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