Models: Estimand, estimator and estimation (skip)
- Estimand: Parameter in the population which is to be estimated in a statistical analysis
- Estimator: A rule for calculating an estimate of a given quantity based on observed data
- Function of the observations, i.e., how observations are put together
- Estimation:
- The process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable (value derived from the best information available)
- Rule (the estimator), its result (the estimate) and the quantity of interest (the estimand) are distinguished.
- Example 1: We rely on the observations in our sample and use a linear (regression) function (the estimator) to estimate the causal effect of education on income in our sample which is our estimate for the population-level causal effect (the estimand).
- Example 2: We rely on the observations in our sample and use the variance estimator \(s^2 = \sum(x_i - \bar{x})^2/(n-1)\) (the estimator) to obtain the variance in the sample (the estimate) which is our estimate of the population-level variance (the estimand).
- More on this here and in (???)