f***c
发帖数: 301 | 1 最简单的比如 Yi= a + bXi + ei
这样一个线性模型 如果假设 Xi 也是一个random variable,服从正态分布不知道mean
和variance, 怎么estimate a,b还有X的mean,variance，用ML可以么
找了找相关的文献 似乎有人把这个算作measurement error model可是又没有讲怎么
estimate,希望有人可以指点一下 谢谢 | D******n
发帖数: 2836 | 2 Usually the distribution of Xi's does not matter for estimate a and b.
http://en.wikipedia.org/wiki/Regression_dilution#The_case_of_a_ | f***c
发帖数: 301 | 3 十分谢谢回复！！
我也咨询了下econometrics的老师 实际X也是random term 但是我们能够观察到X的值
可不可以这样理解 在一般的假设中 如果观察到的x值和实际值有偏差 比如实际值是x+
error, 那么这个error已经被e考虑到了
【在 D******n 的大作中提到】
: Usually the distribution of Xi's does not matter for estimate a and b.
: http://en.wikipedia.org/wiki/Regression_dilution#The_case_of_a_
| D******n
发帖数: 2836 | 4 Ya, everything is random. We usually think X is accurate and error of y
comes from measurement error of Y or unaccounted factors. Of course
there
are always errors when measuring X. But as you say, error of measuring X
can
be thought to be transferred to e.
But actually if you think about how you are going to use this model, you
don
't need to bother to have concern on X. Yes there are measurement error
on X
but it is likely when you use this model , you will still have the
measurement error on X, you never know or obtain the true X to feed into
your model for prediction. So under your model, u can say X is actually
accurate, and let everything unaccounted go to e. As long as e is still
normal.
last, usually we say something is random factor when we dont care about
its
effect. To me, X is not random term, but fixed term with measurement
error.
值
x+
【在 f***c 的大作中提到】
: 十分谢谢回复！！
: 我也咨询了下econometrics的老师 实际X也是random term 但是我们能够观察到X的值
: 可不可以这样理解 在一般的假设中 如果观察到的x值和实际值有偏差 比如实际值是x+
: error, 那么这个error已经被e考虑到了
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