统计学中的一些概念

Standard Error is the Standard deviation of a statistic computed from a random sample. Any sample variable has an associated sampling distribution.

For example, \bar X is the sample mean, which is distributed with means \mu and variance \frac{1}{n} \sigma ^2. The standard deviation of \bar X, called its standard error, would be \sigma_{\bar X} = \frac{\sigma}{\sqrt{n}}.

In practice, the population variance will not be known, but it can be estimated from the sample. In such case, the quantity s_{\bar X}=\frac{(\frac{1}{n-1}\Sigma(X_i-\bar{X})^2)^{\frac{1}{2}}}{\sqrt{n}} would be called estimated standard error.

Mean squared error is defined as
MSE = E[(X-Y)^2]
if X_i and Y_i are sequences, then MSE = \frac{1}{n} \Sigma_{i=1}^{n}(X_i - Y_i)^2, which is a value computed from two different sequences. In contrast, variance is obtained from a single random variable or sequence.

MSE是两个序列值比较的结果,而方差是一个随机变量变动的情况。

RSS(residual sum of squares)和MSE类似。(待续)

©著作权归作者所有,转载或内容合作请联系作者
平台声明:文章内容(如有图片或视频亦包括在内)由作者上传并发布,文章内容仅代表作者本人观点,简书系信息发布平台,仅提供信息存储服务。

推荐阅读更多精彩内容