However, this is a biased estimator, as the estimates are generally too low.

However, we can achieve a lower mean squared error using a biased estimator.

When a biased estimator is used, the bias is also estimated.

Omitting a relevant variable may lead to biased estimators for the remaining coefficients.

Therefore the absolute deviation is a biased estimator.

The statistic is a biased estimator of .

Each measure of location has its own form of unbiasedness (see entry on biased estimator).

An alternative less biased estimator of population size is given by the Chapman estimator:

The requirement that the estimator be unbiased cannot be dropped, since biased estimators exist with lower variance.

Because of this the usual sample mean (arithmetic mean) is a biased estimator of the true mean.

In fact, if we use mean squared error as a selection criterion, many biased estimators will slightly outperform the "best" unbiased ones.

This use of "biased" distributions will result in a biased estimator if it is applied directly in the simulation.

However, a biased estimator may have lower MSE; see estimator bias.

But this estimator, when applied to a small or moderately sized sample, tends to be too low: it is a biased estimator.

A far more extreme case of a biased estimator being better than any unbiased estimator arises from the Poisson distribution.

In consequence, each ODE should create a less biased estimator than naive Bayes.

The Cramér-Rao bound can also be used to bound the variance of biased estimators of given bias.

However, the authors rejected this possibility of testing the CAPM as the data could produce biased estimators in certain cases.

The variance of the biased estimator was always smaller than the variance of the unbiased estimator.

However it can be shown that the biased estimator is "better" than the s in terms of the mean squared error (MSE) criterion.

Conversely, MSE can be minimized by dividing by a different number (depending on distribution), but this results in a biased estimator.

The James-Stein estimator is a biased estimator of the mean of Gaussian random vectors.

Lagrangian strain is a non-linear and biased estimator of strain but it is currently the most widely used estimator.

In general, the ratios and are both biased estimators of the population skewness ; their expected values can even have the opposite sign from the true skewness.

Biased estimators of lengths of boundaries between forest conditions and unbiased but inefficient estimators of areas in these conditions are available.