Biased Estimator

In many scientific research fields, statistical models are used to describe a system or a population, to interpret a phenomenon, or to investigate the [Page 85]relationship among various measurements. These statistical models often contain one or multiple components, called parameters, that are unknown and thus need to be estimated from the data (sometimes also called the sample). An estimator, which is essentially a function of the observable data, is biased if its expectation does not equal the parameter to be estimated.

To formalize this concept, suppose θ is the parameter of interest in a statistical model. Let be its estimator based on an observed sample. Then is a biased estimator if , where E denotes the expectation operator. Similarly, one may say that ...