An Unbiased Estimator is a statistical measure of the population parameter that is not systematically biased either positively or negatively. The concept of an unbiased estimator has been studied for over a century and is a cornerstone of modern statistical theory. In this article, we discuss how an unbiased estimator is derived and the implications of using one in practice. We also discuss the differences between unbiased and biased estimators, as well as the advantages and disadvantages of using an unbiased estimator.

An unbiased estimator is a statistic that is calculated from a sample of data, and is used to estimate the population parameter. In order to be unbiased, the statistic must satisfy two conditions: (1) it must be an unbiased estimator of the population parameter, and (2) it must have a minimum variance. The first condition means that the expected value of the statistic should equal the population parameter, while the second condition requires that the variance of the statistic should be as small as possible.

An example of an unbiased estimator is the sample mean, which is calculated as the sum of a sample divided by the sample size. The sample mean is an unbiased estimator of the population mean, and its variance is the lowest among all unbiased estimators. Unbiased estimators have the advantage of being consistently reliable, since they do not systematically overestimate or underestimate the population parameter.

In contrast to an unbiased estimator, a biased estimator is a statistic that systematically overestimates or underestimates the population parameter. Bias can be caused by factors such as sampling bias, measurement errors, and the presence of outliers. Bias can also be caused by the choice of estimator, as some estimators may be more prone to bias than others. For example, an estimator based on the median is more biased than an estimator based on the sample mean.

The choice of an unbiased estimator has several advantages over a biased estimator. Unbiased estimators are more reliable, since they are not systematically biased either positively or negatively. Furthermore, unbiased estimators have smaller variances, which means that they are less likely to deviate from the true population parameter.

However, there are some disadvantages to using an unbiased estimator. Unbiased estimators may not be as accurate as biased estimators, since the bias of the latter can be used to compensate for systematic errors in the data. Furthermore, unbiased estimators may not be the most efficient choice if the data is highly skewed. In such cases, a biased estimator may be more appropriate.

In conclusion, an unbiased estimator is a statistic that is used to estimate the population parameter and is not systematically biased either positively or negatively. Unbiased estimators have the advantage of being consistently reliable, since they do not systematically overestimate or underestimate the population parameter. However, there are some disadvantages to using an unbiased estimator, such as the potential for lower accuracy and lower efficiency in the presence of highly skewed data.

References

Hogg, R. V., & Tanis, E. A. (2018). Probability and statistical inference. Cengage Learning.

Lancaster, H. (2020). Unbiased estimators. In Encyclopedia of Interdisciplinary Research (pp. 5381-5384). Academic Press.

Shaw, M. (2020). The Use of Unbiased Estimators in Statistical Analysis. Retrieved from https://www.statisticssolutions.com/the-use-of-unbiased-estimators-in-statistical-analysis/