Estimand

An estimand is a parameter which is to be estimated in a statistical analysis. The term is used to more clearly distinguish the target of inference from the function to obtain this parameter (i.e., the estimator) and the specific value obtained from a given data set (i.e., the estimate). For instance, a normally distributed random variable X {displaystyle X} has two parameters, its mean μ {displaystyle mu } and variance σ 2 {displaystyle sigma ^{2}} . The variance estimator, s 2 = ∑ i = 1 n ( x i − x ¯ ) 2 / ( n − 1 ) {displaystyle s^{2}=sum _{i=1}^{n}left.left(x_{i}-{ar {x}} ight)^{2} ight/(n-1)} , yields an estimate of 7 for a data set x = { 2 , 3 , 7 } {displaystyle x=left{2,3,7 ight}} ; then s 2 {displaystyle s^{2}} is called an estimator of σ 2 {displaystyle sigma ^{2}} , and σ 2 {displaystyle sigma ^{2}} is called the estimand. An estimand is a parameter which is to be estimated in a statistical analysis. The term is used to more clearly distinguish the target of inference from the function to obtain this parameter (i.e., the estimator) and the specific value obtained from a given data set (i.e., the estimate). For instance, a normally distributed random variable X {displaystyle X} has two parameters, its mean μ {displaystyle mu } and variance σ 2 {displaystyle sigma ^{2}} . The variance estimator, s 2 = ∑ i = 1 n ( x i − x ¯ ) 2 / ( n − 1 ) {displaystyle s^{2}=sum _{i=1}^{n}left.left(x_{i}-{ar {x}} ight)^{2} ight/(n-1)} , yields an estimate of 7 for a data set x = { 2 , 3 , 7 } {displaystyle x=left{2,3,7 ight}} ; then s 2 {displaystyle s^{2}} is called an estimator of σ 2 {displaystyle sigma ^{2}} , and σ 2 {displaystyle sigma ^{2}} is called the estimand. An estimand is closely linked to the purpose or objective of an analysis. It describes what is to be estimated based on the question of interest. This is in contrast to an estimator, which defines the specific rule according to which the estimand is to be estimated. While the estimand will often be free of the specific assumptions e.g. regarding missing data, such assumption will typically have to be made when defining the specific estimator. For this reason, it is logical to conduct sensitivity analyses using different estimators for the same estimand, in order to test the robustness of inference to different assumptions.