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In statistics, a point estimator is a function or a statistic that is used to estimate an unknown population parameter. It is called a point estimator because it provides us a single-point "best guess" for the population parameter. There are different point estimators, and some are better than others because of their desirable characteristics.

Unbiasedness is an essential characteristic of a good point estimator. It means that, on average, the estimator gives the correct value for the population parameter. Formally, an estimator \(\hat{\theta}\) is unbiased for the population parameter \(\theta\) if its expected value \(E(\hat{\theta})\) is equal to the population parameter \(\theta\), that is, \(E(\hat{\theta}) = \theta\). In other words, in the long run, an unbiased estimator doesn't systematically overestimate or underestimate the population parameter.

Efficiency is another characteristic of a good point estimator. An efficient estimator has the smallest variance among all the unbiased estimators of the population parameter. In other words, an efficient estimator provides more precise (or less dispersed) estimates compared to other unbiased estimators. If we have two unbiased estimators, \(\hat{\theta}_1\) and \(\hat{\theta}_2\), for a population parameter \(\theta\), we say that \(\hat{\theta}_1\) is more efficient than \(\hat{\theta}_2\) if the variance of \(\hat{\theta}_1\) is smaller than the variance of \(\hat{\theta}_2\), that is, \(Var(\hat{\theta}_1) < Var(\hat{\theta}_2)\). So, to recap, the two main characteristics of the best point estimator for a population parameter are unbiasedness and efficiency.