Estimand

An Estimand is a target parameter that is to be estimated from a data sample that is of interest.

Context:
- It can (typically) be an input to an Estimation Task.
- It can range from being a Theoretical Estimand to being an Empirical Estimand.
- …
Example(s):
- "the mean height of all male adults in the person database".
- a Clinical Trial Estimand.
- …
See: Estimate, Estimator.

References

(Wikipedia, 2022) ⇒ https://en.wikipedia.org/wiki/estimand Retrieved:2022-5-26.
- An estimand is a quantity that is to be estimated in a statistical analysis. The term is used to more clearly distinguish the target of inference from the method used to obtain an approximation of this target (i.e., the estimator) and the specific value obtained from a given method and dataset (i.e., the estimate). For instance, a normally distributed random variable [math]\displaystyle{ X }[/math] has two defining parameters, its mean [math]\displaystyle{ \mu }[/math] and variance [math]\displaystyle{ \sigma^{2} }[/math] . A variance estimator: [math]\displaystyle{ s^{2} = \sum_{i=1}^{n} \left. \left( x_{i} - \bar{x} \right)^{2} \right/ (n-1) }[/math] ,
  yields an estimate of 7 for a data set [math]\displaystyle{ x = \left\{ 2, 3, 7 \right\} }[/math] ; then [math]\displaystyle{ s^{2} }[/math] is called an estimator of [math]\displaystyle{ \sigma^{2} }[/math] , and [math]\displaystyle{ \sigma^{2} }[/math] is called the estimand.

https://www.appliedclinicaltrialsonline.com/view/estimand-framework-what-it-and-why-you-need-it
- QUOTE: ... An estimand is a precise description of the treatment effect to be estimated from a trial (the question) and is distinct from the methods of statistical analysis (how the question is to be answered). The potential use of estimands to improve trial research and reporting has been underpinned by the recent publication of the ICH E9(R1) Addendum on the use of estimands in clinical trials in 2019. We set out to assess how well estimands are described in published trial protocols. ...

https://trialsjournal.biomedcentral.com/articles/10.1186/s13063-021-05644-4
- QUOTTE: ... An estimand is a precise description of the treatment effect to be estimated from a trial (the question) and is distinct from the methods of statistical analysis (how the question is to be answered).Oct 9, 2021 ...

(Lundberg et al., 2021) ⇒ Ian Lundberg, Rebecca Johnson, and Brandon M. Stewart. (2021). “What is Your Estimand? Defining the Target Quantity Connects Statistical Evidence to Theory.” In: American Sociological Review, 86(3).
- ABSTRACT: ... Every quantitative study must be able to answer the question: what is your estimand? The estimand is the target quantity — the purpose of the statistical analysis. Much attention is already placed on how to do estimation; a similar degree of care should be given to defining the thing we are estimating. We advocate that authors state the central quantity of each analysis — the theoretical estimand — in precise terms that exist outside of any statistical model. In our framework, researchers do three things: (1) set a theoretical estimand, clearly connecting this quantity to theory; (2) link to an empirical estimand, which is informative about the theoretical estimand under some identification assumptions; and (3) learn from data. Adding precise estimands to research practice expands the space of theoretical questions, clarifies how evidence can speak to those questions, and unlocks new tools for estimation. By grounding all three steps in a precise statement of the target quantity, our framework connects statistical evidence to theory.

(Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/estimand Retrieved:2015-6-28.
- … The term has recently seen increased use in the clinical trials community in order to more clearly distinguish the target of inference from different possible estimators and estimates.

(Gentle, 2009) ⇒ James E. Gentle. (2009). “Computational Statistics." Springer. ISBN:978-0-387-98143-7
- QUOTE: There are three different types of inference related to the problem of determining the specific [math]\displaystyle{ P_θ \in \mathcal{P} }[/math]: point estimation, hypothesis tests, and confidence sets. In point estimation, the estimand is often some function of the basic parameter θ. We often denote the estimand in general as g(θ). Hypothesis tests and confidence sets are associated with probability statements that depend on Pθ. ...