An Unbiased Estimator: What it is and Why it Matters

What is an Unbiased Estimator?

In statistics, an unbiased estimator is a statistic whose mathematical expectation equals the true parameter being estimated. In simpler terms, it is a method of estimating a parameter that, on average, produces an estimate that is equal to the true value of the parameter.

Unbiased in the Mean

An unbiased estimator is also referred to as an unbiased in the mean estimator. This means that over multiple trials, the average of the estimates produced by the estimator will converge to the true value of the parameter.

Why Unbiased Estimators are Important

Unbiased estimators are desirable because they provide a reliable and accurate way to estimate parameters. When an estimator is unbiased, it is less likely to overestimate or underestimate the true value of the parameter. This leads to more precise and reliable statistical inferences.

Unbiased estimators are particularly important in hypothesis testing and confidence interval estimation. By using unbiased estimators, researchers can have greater confidence in the conclusions drawn from their statistical analyses.