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An estimator is a statistical tool used to estimate the value of an unknown parameter in a statistical model. It is a function of the observed data and is designed to provide a reasonable approximation of the true parameter value. Estimators are fundamental in statistical inference, where the goal is to make inferences about population parameters based on sample data.

There are various types of estimators, each with its own properties and applications. The most common types include:

1. Point Estimators: These provide a single value estimate of the parameter. Examples include the sample mean and sample variance.

2. Interval Estimators: These provide a range of values within which the parameter is expected to lie, along with a measure of confidence. An example is the confidence interval.

3. Maximum Likelihood Estimators (MLEs): These are point estimators that maximize the likelihood function, which is the probability of observing the given data under the assumed statistical model.

The performance of an estimator is typically evaluated using criteria such as bias, variance, and mean squared error. An estimator is considered unbiased if its expected value is equal to the true parameter value. The variance of an estimator measures its consistency, with lower variance indicating more reliable estimates. The mean squared error combines both bias and variance to provide a comprehensive measure of an estimator's performance.

In practice, the choice of estimator depends on the specific problem, the available data, and the desired properties of the estimate. Estimators are widely used in various fields, including economics, engineering, and the natural sciences, to make data-driven decisions and draw meaningful conclusions from observed data.