能不能帮忙解释一下他们之间的关系？谢谢。
方差一致最小无偏估计（UMVUE)与极大似然估计(MLE)之间的关系
或者 方差最小无偏估计（MVUE）与MLE的关系。谢谢
test
说一下最小方差无偏估计与极大似然估计的关系吧。前者是根据估计量的性质来定义的，也就是说它是某一个参数的无偏估计中方差最小的那个估计；而后者是根据估计的方法来定义的，即使用极大似然法求得的估计量。在某些情况下，MLE就是MVUE，但有的情况不是；同样，MVUE也不一定通过MLE求得。总之两者是位于不同层面上的。
个别的UMVUE可以通过MLE来构造或者通过MLE能受到一些启发，而且我记得关于一个MLE的性质就是说如果MLE达到C-R下界，那么一定是有效估计…可以看看中科大的那本数理统计
7 天 后
In statistics, point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" for an unknown (fixed or random) population parameter.
以下是几种常用的
* maximum likelihood (ML)
* method of moments, generalized method of moments
* minimum mean squared error (MMSE)
* minimum variance unbiased estimator (MVUE)
* best linear unbiased estimator (BLUE)
在不同的情况下该如何选择呢？
以下是几种常用的
* maximum likelihood (ML)
* method of moments, generalized method of moments
* minimum mean squared error (MMSE)
* minimum variance unbiased estimator (MVUE)
* best linear unbiased estimator (BLUE)
在不同的情况下该如何选择呢？
MLE and MME are two principle methods to obtain a point estimate of a parameter. The properties for evaluate a point estimator are:
1. bias
2. variance
3. the form of the distribution
If a point estimator is unbiased and has minimum variance (MVUE), moreover the distribution is known, it will be ideal. However, it usually is not the case. Minimum Mean Squared Error (MSE) is a measure to tradeoff the bias and variance. People use MLE a lot as long as it can be obtained because it has nice properties. An MLE is not necessarily unbiased for a finite sample size, but it is consistent (asymptotically unbiased). It does not ncessarily has minimum variance, but asymptotically it does. Furthermore, it is asymptotically normally distributed. However, in some cases, it is too complicated or impossible to solve the equation(s) to get the MLE. In this case, we have to use some other methods, for example, MME.
1. bias
2. variance
3. the form of the distribution
If a point estimator is unbiased and has minimum variance (MVUE), moreover the distribution is known, it will be ideal. However, it usually is not the case. Minimum Mean Squared Error (MSE) is a measure to tradeoff the bias and variance. People use MLE a lot as long as it can be obtained because it has nice properties. An MLE is not necessarily unbiased for a finite sample size, but it is consistent (asymptotically unbiased). It does not ncessarily has minimum variance, but asymptotically it does. Furthermore, it is asymptotically normally distributed. However, in some cases, it is too complicated or impossible to solve the equation(s) to get the MLE. In this case, we have to use some other methods, for example, MME.