Exercises A

Statistical Inference - Ph.D. in Economics, Statistics, and Data Science

Author
Affiliation

Tommaso Rigon

UniversitĂ  degli Studi di Milano-Bicocca

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Preliminaries

  • Davison (2003), Exercise 8, pag. 109 (Sufficiency)
  • Davison (2003), Problem 2, pag. 156. (Reparametrizations and likelihood quantities)
  • Davison (2003), Problem 11, pag. 159. (Exponential model with censored data, practical implementation)
  • Casella & Berger (2002), Exercise 7.6. (MLE and MoM for a non-regular model)

Risk and Bayes Estimation

  • Casella & Berger (2002), Exercise 7.62. (Risk and Bayes risk for a Gaussian distribution)
  • Casella & Berger (2002), Exercise 7.65. (LINEX loss, Bayes estimators)

Unbiasedness and efficiency

  • Davison (2003), Problem 1, pag. 156. (Logistic density and expected information)
  • Casella & Berger (2002), Exercise 7.46. (Unbiasedeness, MoM, uniform non-regular model, UMVUE)
  • Casella & Berger (2002), Exercise 7.44. (Attaining the Cramer-Rao lower bound, UMVUE)
  • Casella & Berger (2002), Exercise 7.66. (Jacknife estimator, UMVUE)

Asymptotics

  • Davison (2003), Exercise 5, pag. 125. (Exponential model, asymptotics of the MLE)
  • Davison (2003), Exercise 5, pag. 149. (Non-regular models, asymptotics of the MLE)

Robustness