Home page for accesible maths 2 Statistical estimation and uncertainty

Style control - access keys in brackets

Font (2 3) - + Letter spacing (4 5) - + Word spacing (6 7) - + Line spacing (8 9) - +

2.3 Summary

{mdframed}
  • A statistical model assumes that data are realisations of random variables. For a parametric model, a set of assumptions are then made about the probability distributions of these random variables.

  • The simplest assumptions are that the random variables are

    • Independent and

    • Identically distributed, according to a probability distribution with unknown parameter values.

  • Statistical inference involves the estimation of the unknown parameters in the probability distribution.

  • An estimator of a parameter is a random variable. An estimate of a parameter is a number.

  • A good estimator should be unbiased and consistent.

  • The sampling distribution of an estimator displays the distribution of the estimator across repeated samples of a given size.