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An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator. Bias is a distinct concept from consistency: consistent estimators converge in probability to the true value of the parameter, but may be biased or unbiased (see bias versus consistency for more).
Detection bias occurs when a phenomenon is more likely to be observed for a particular set of study subjects. For instance, the syndemic involving obesity and diabetes may mean doctors are more likely to look for diabetes in obese patients than in thinner patients, leading to an inflation in diabetes among obese patients because of skewed detection efforts.
Under simple random sampling the bias is of the order O( n −1). An upper bound on the relative bias of the estimate is provided by the coefficient of variation (the ratio of the standard deviation to the mean). [2] Under simple random sampling the relative bias is O( n −1/2).
A typical measure of bias of forecasting procedure is the arithmetic mean or expected value of the forecast errors, but other measures of bias are possible. For example, a median-unbiased forecast would be one where half of the forecasts are too low and half too high: see Bias of an estimator .
Bias: The bootstrap distribution and the sample may disagree systematically, in which case bias may occur. If the bootstrap distribution of an estimator is symmetric, then percentile confidence-interval are often used; such intervals are appropriate especially for median-unbiased estimators of minimum risk (with respect to an absolute loss ...
The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator (how widely spread the estimates are from one data sample to another) and its bias (how far off the average estimated value is from the true value). [citation needed] For an unbiased estimator, the MSE is the variance of the ...
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Correction factor versus sample size n.. When the random variable is normally distributed, a minor correction exists to eliminate the bias.To derive the correction, note that for normally distributed X, Cochran's theorem implies that () / has a chi square distribution with degrees of freedom and thus its square root, / has a chi distribution with degrees of freedom.