Estimator bias in statistics refers to the discrepancy between an estimator's expected value and the true population parameter it aims to estimate. An unbiased estimator, like the sample mean, accurately reflects the parameter on average. However, some estimators, such as sample variance, require adjustments to eliminate bias. Understanding and correcting estimator bias is essential for valid statistical inference, confidence interval estimation, and hypothesis testing.
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An estimator is a statistic used to infer the value of a population parameter from sample data
An estimator whose expected value equals the true parameter value it is estimating
An estimator whose expected value does not match the true parameter value
Understanding estimator bias is crucial for conducting accurate statistical analyses and drawing reliable conclusions
The unbiased nature of the sample mean is a key reason for its widespread use in statistical inference
The bias of an estimator is a function of the sample size, highlighting the importance of sample size in determining accuracy
The estimator \(T = \frac{X_1 + 2X_2}{n}\) for the mean of a distribution is biased unless \(n = 3\)
The unbiased sample variance is calculated as \(\frac{\sum\limits_{i=1}^n (X_i - \bar{X})^2}{n - 1}\), where \(n - 1\) is used in the denominator to correct for bias introduced by the sample mean
Recognizing and adjusting for bias is vital to ensure the validity and reliability of statistical conclusions
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Definition of an unbiased estimator
An unbiased estimator has an expected value equal to the true parameter it estimates.
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Consequence of estimator bias
Biased estimators lead to inaccurate statistical analyses and unreliable conclusions.
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Expected value vs. true parameter
If an estimator's expected value does not equal the true parameter, the estimator is considered biased.
