[Machine Learning] Unbiased Estimation and Biased Estimation and Formula Proof

On Unbiased Estimation

Unbiased estimation: For the population, the sample mean is an unbiased estimate of the population mean. If the k-order origin distance expectation exists, the k-order origin moment of the sample is also an unbiased estimate, but the center distance is not.

Biased Variance and Unbiased Variance

Biased estimator variance
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Unbiased estimator variance
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When the sample size tends to infinity, biased estimator and unbiased estimator are equivalent.
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The formula for unbiased estimation of variance proves
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the popular understanding of why the denominator is n-1.
The degree of freedom, in layman's terms, is the number of unconstrained variables.
Because μ is known, x1,...xn, n variables only need to know n-1 to know the last one, so the degree of freedom is n-1.

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Origin blog.csdn.net/Trance95/article/details/116457616