Biased and unbiased estimate of the difference between the estimated
1. Definition:
Biased Estimator: Estimate the amount of mathematical expectation is equal to estimate the true value of the parameter, the estimator is said to be an unbiased estimate of the estimated parameters, ie the sample mean is equal to the expectations of the population mean, so the sample mean is unbiased.
Unbiased estimate: Estimated amount of mathematical expectation is not equal to the true value of the parameter to be estimated, this estimate is called the estimated parameters biased estimate.
Biased estimation and unbiased estimate of the advantages and disadvantages:
Biased estimate systematic error is present, but small variance; unbiased estimation system there is no difference, but a larger variance in some cases.
2, understand the actual project
Actual engineering data processing, assuming that there is a need to confirm the amount of X, often using multiple measurements to estimate, and this measure the presence of randomness. How true value estimated by statistical measurements, we used a biased estimate and unbiased.
When used in a mathematical model can accurately estimate a statistical measure Application Part X values need to confirm the amount, called unbiased. This estimate is the ideal state of the actual project.
But the actual project because of uncertainty, resulting in the use of mathematical models can not accurately estimate the amount of each of the required measurement of the amount of X, and part of the statistics of the expected value is not the true value of X, which is biased estimate. So many biased estimation algorithm appears to have offset the elimination of the model due to biased estimates.