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- Politecnico di Milano
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- Mathematical Engineering
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- Modelli e Metodi dell'Inferenza Statistica
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Modelli e metodi dell’inferenza statistica Corso tenuto da Anna Maria “Pagatauro” Paganoni 2019 - 2020 Indice 1 Campioni casuali e statistiche 3 1.1 Su cienza . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Famiglia esponenziale (EF) . . . . . . . . . . . . . . . . . . . . . 4 1.3 Minimalit` a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Completezza . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Stima puntuale 7 2.1 Metodo dei momenti . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Metodo di massima verosimiglianza . . . . . . . . . . . . . . . . . 7 2.3 Valutazione degli stimatori . . . . . . . . . . . . . . . . . . . . . 8 2.4 Uniform Minimum Variance Unbiased Estimator . . . . . . . . . 9 2.5 Informazione di Fisher . . . . . . . . . . . . . . . . . . . . . . . . 12 3 T est di ipotesi 14 3.1 Likelihood Ratio Test . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 Valutare i test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.3 Risultati notevoli sugli UMP . . . . . . . . . . . . . . . . . . . . 17 3.4 Test UI (IU) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.5p-values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4 Stima intervallare 21 4.1 Inversione di test . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.2 Quantit` a pivot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3 ScegliereCIa lunghezza minimale . . . . . . . . . . . . . . . . . 22 5 T eoria asintotica 24 6 T est di gaussianit` a 27 6.1 Shapiro-Wilk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 6.2 QQ-plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 1 7 Modelli lineari di regressione 28 7.1 Regressione . . . . . . . . . . . .…
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