vickie
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？
JaneQ
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.
