在电脑前打喷嚏对《统计推断》的笔记(3)

在电脑前打喷嚏
在电脑前打喷嚏 (我爸以为我分分钟都在努力读书~~)

在读 统计推断

统计推断
  • 书名: 统计推断
  • 作者: George Casella/Roger L. Berger
  • 页数: 660
  • 出版社: China Machine Press
  • 出版年: 2002
  • 第591页

    最开始看Logistic 回归的时候,蹭得一下,我就看到了一个logit变换,紧随其后的是一个线性模型。得来容易的东西背后往往空空荡荡。正统的教材里才有逻辑坎坷走过留下的背景——因变量是Random的(哪怕确定了自变量,它也不确定)、假设因变量是Beroulli的密度函数的形式稍加转变变成指数形式、在指数形式很重要的参数地方出现了一个logit、非常好对这个logit进行建模。然后就是参数的估计,MLE就出场了,而后可以惊喜地发现,在上述的假设&建模下,MLE求偏导为0时分外简洁。

    2017-05-02 11:49:38 回应
  • 第468页
    The probability definition deals with one probability structure, but the statistis definition deals with an entire family.

    .... 知道一个估计量在n趋于无穷时足够好还不够,还要考虑这个估计量的方差(估计量也是随机变量)。

    The property of consistency is concerned with the asymptotic accuracy of an estimator: Does it converge to the parameter that it is estimating? In this section we look at a related property, efficiency, which is concerned with the asymptotic variance of an estimator.

    ...Cramér-Rao Lower Bound.

    2017-05-02 12:29:15 回应
  • 第521页

    章节的最初有段话很漂亮:

    "I've wasted time enough," said Lestrade rising. "I believe in hard work and not in sitting by the fire spinning fine theories."

    出发点是为了比较不同总体之间的均值-analyzing variation in means,但是落脚点却是组间与组内方差的比较,所以叫做方差分析😉:

    ANOVA belies its name in that it is not concerned with analyzing variances but rather with analyzing variation in means.

    它所关注的不是如何观测才能得到最多的总体信息,而是如何根据数据进行推断。检验各组均值不全相等并不是它的目标,关键是——哪些组之间差异最大,于是就有了拆解的思想:

    The ANOVA null is the intersection of more easily understood univariate hypotheses. Most interesting inferences in an ANOVA can be expressed as contrasts or sets of contrasts.

    2017-05-09 13:37:35 回应