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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). All else being equal, an unbiased estimator is preferable to a biased estimator, although in practice, biased estimators (with generally small bias ...
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.
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.
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.
The MSE can be written as the sum of the variance of the estimator and the squared bias of the estimator, providing a useful way to calculate the MSE and implying that in the case of unbiased estimators, the MSE and variance are equivalent. [5]
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).
When interpreting the floating-point number, the bias is subtracted to retrieve the actual exponent. For a half-precision number, the exponent is stored in the range 1 .. 30 (0 and 31 have special meanings), and is interpreted by subtracting the bias for an 5-bit exponent (15) to get an exponent value in the range −14 .. +15.
However, there is also a more subtle form of bias that can occur even if the input, measured, quantities are unbiased; all terms after the first in Eq(14) represent this bias. It arises from the nonlinear transformations of random variables that often are applied in obtaining the derived quantity.