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\chapter{Unbiased Estimators}
\section{intro}An unbiased estimator is a statistical measure that accurately estimates the true value of a population parameter without any systematic error or bias. It means that on average, the estimator will produce estimates that are close to the true value.
An unbiased estimator does not have any systematic error or bias, whereas a biased estimator consistently produces estimates that are either too high or too low from the true value. This can lead to inaccurate conclusions and misleading results.
To determine if an estimator is unbiased, we need to compare its expected value to the true value of the parameter. If the expected value of the estimator is equal to the true value, then it is considered unbiased. This can be verified through mathematical calculations or simulations.
Some examples of unbiased estimators include the sample mean, sample variance, and sample proportion. These estimators are commonly used to estimate the population mean, variance, and proportion, respectively, and are known to be unbiased under certain conditions.
The accuracy of an unbiased estimator can be improved by increasing the sample size. This reduces the variability of the estimator and makes it more likely to produce estimates that are close to the true value. Additionally, using more advanced statistical techniques and methods can also help improve the accuracy of an unbiased estimator.