Maximum-likelihood estimators are often inefficient and biased for finite samples.

The previous definitions can easily be extended to finite samples.

However, the asymptotic theory of limiting distributions is often invoked for work with finite samples.

The bounds these inequalities give on a finite sample are less tight than those the Chebyshev inequality gives for a distribution.

It is likely that better bounds for finite samples than these exist.

For practical problems with finite samples, other estimators may be preferable.

Recurrence relations for the distribution of the test statistic in finite samples are available.

It is sometimes used, incorrectly, to mean sample variance - the difference between different finite samples of the same parent population.

In finite samples both s and have scaled chi-squared distribution with (n 1) degrees of freedom:

Maximum likelihood provides reasonably precise estimates in finite samples.