The chapter starts building the first leg of the relation between the empirical world of experiments and the theoretical world of models. If we consider a statistical variable as the catalogue of repetitions (sampling) of an experiment described by a probabilistic model (here parametric), we can build a composite model for the sampling, namely a likelihood function. Estimation theory is exactly the tool to go from empirical numbers to estimates of the parameters. Maximum likelihood and Least Squares are analyzed recalling the main properties of the corresponding estimators. Widening the probabilistic model including the parameters as random variables , opens the way to Bayesian Theory, and its approach to estimation, that, more properly, in this context becomes prediction.

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Statistical Inference: The Theory of Estimation

  • Fernando Sansò,
  • Alberta Albertella

摘要

The chapter starts building the first leg of the relation between the empirical world of experiments and the theoretical world of models. If we consider a statistical variable as the catalogue of repetitions (sampling) of an experiment described by a probabilistic model (here parametric), we can build a composite model for the sampling, namely a likelihood function. Estimation theory is exactly the tool to go from empirical numbers to estimates of the parameters. Maximum likelihood and Least Squares are analyzed recalling the main properties of the corresponding estimators. Widening the probabilistic model including the parameters as random variables , opens the way to Bayesian Theory, and its approach to estimation, that, more properly, in this context becomes prediction.