为什么样本方差(sample variance)的分母是 n-1? (補充一句哦,題主問的方差 estimator 通常用 moments 方法估計。如果用的是 ML 方法,請不要多想不是你們想的那樣, 方差的 estimator 的期望一樣是有 bias 的,有興趣的同學可以自己用正態分佈算算看。) 本來,按照定義,方差的 estimator 應該是這個: 但,這個 es...
样本方差估计量的分母是n-1的主要原因是我们希望获得一个总体方差的无偏估计量（unbiased estimator），这...
无偏的估计(unbiased estimator)比有偏估计(biased estimator)更好是符合直觉的，尽管有的统计学家认为让mean square error即MSE最小才更有意义，这个问题我们不在这里探讨；不符合直觉的是，为什么分母必须得是n-1而不是n才能使得该估计无偏。我相信这是题主真正困惑的地方。要回答这个问题，偷懒的办法是让困惑的题...
since this makes the sample variance an unbiased estimator for the population variance. The distinction between and is a common source of confusion, and extreme care should be exercised when consulting the literature to determine which convention is in use, especially since the uninformative notation ...
1 Unbiased estimator for a parameter in a Poisson distribution 3 Why doesn't the sample variance become the population variance when the sample has the whole population Hot Network Questions Is integration semi-algebraic? What is the use of the variable `B%` in DONKEY.BAS ...
It is possible to prove (seeVariance estimation) that, if areindependent, then the adjusted sample variance is an unbiased estimator of . Bias-variance trade-off The degrees of freedom adjustment is not a free lunch: it eliminates the bias, but it usually increases the variance of the sample...
Given a number of observations, their sample variance measures how far they are spread apart. It is also an estimator of the variance of the population from which the observations have been drawn. FormulaeGiven observations having sample mean there are two main ways to compute the sample ...
How do you find the sample variance? To find the sample variance, first find the sample mean. Then subtract the mean from each measurement and square the difference. Add all of these values together and divide the result by the number of measurements minus one. How do we calculate variance...
为什么样本方差(sample variance)的分母是n-1? 完整的问题描述 如果已知随机变量X的期望为μ,那么可以如下计算方差σ^2: 上面的式子需要知道X的具体分布是什么(在现实应用中往往不知道准确分布),计算起来也比较复杂。 所以实践中常常采样之后,用下面这个S^2来近似σ^2:...
doi:10.1080/03610928108828110The present paper explores the structure of linear exponential families for which the sample variance is a uniformly minimum variance unbiased estimator.Ludwig Baringhaus & Detlef PlachkyUniversity of HannoverCommunications in Statistics - Theory and Methods...