What is an estimator?

最新推荐文章于 2021-03-29 08:46:46 发布

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本文介绍了统计学中的参数估计概念，包括估计量及其性质，并通过实例解释了如何使用样本均值来估计总体均值。

An “estimator” or “point estimate” is a statistic (that is, a function of the data) and a rule that is used to infer the value of an unknown parameter in a statistical model.
Any statistic whose values are used to estimate is defined to be an estimator of $θ\theta$ . If a parameter is estimated by an estimator, we usually write is as $θ^\hat{\theta}$ , where the hat indicates that we are dealing with an estimator of $θ\theta$ .
Estimators are random variables with a fixed (mean) and a random component (disturbance)
The formula or rule to calculate the mean/ variance (characteristic) from a sample is called estimator, the value is called estimate.
An estimator is a statistic that estimates some fact about the population. You can also think of an estimator as the rule that creates an estimate.

Example: the sample mean(x̄) is an estimator for the population mean, μ:

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The quantity that is being estimated (i.e. the one you want to know) is called the estimand（如果放在回归中，可以认为就是因变量）. For example, let’s say you wanted to know the average weight of students in a university with a population of 1000 students. You take a sample of 30 students, and find the mean weight is 56 kg. This is your sample mean, we call it the estimator . You can use the value of the estimator to as the population mean (your estimand), namely, about 56 inches. Sometimes the words “estimator” and “estimate” are used interchangeably.

值得一提的是，regressor 就是指回归中的自变量，还有其他叫法，如：explanatory variable, or independent variable。