w****p
发帖数: 167 | 1 想要用bootstrap方法估计一个初始样本的参数A.方法如下：
Bootstrap抽样1000次后，从每个bootstrap样本中得到参数b_i（计算方法与A一致）。然后取b_1到b_1000的平均数得到B。最后用公式（2A-B）得到对A的bootstrap点估计。
这样做（尤其是最后的公式）对不对？为什么？谢谢。 |
w*******9
发帖数: 1433 | 2 B-A estimates the bias of the statistics, thus A-(B-A)=2A-B is kind of the
bias corrected estimator. |
w****p
发帖数: 167 | 3 So,can I understand your explanation like this?
A and B are two estimators of a parameter. A is biased but B is not.
Bootstrap can let us know the bias of A, so (A-bias) is unbiased estimate.
But why don't we just use B as the estimator?
【在 w*******9 的大作中提到】
: B-A estimates the bias of the statistics, thus A-(B-A)=2A-B is kind of the
: bias corrected estimator.
|
d*******y
发帖数: 1154 | 4 。。。
难道不是A-(A-B)=B才是无偏的估计？
【在 w*******9 的大作中提到】
: B-A estimates the bias of the statistics, thus A-(B-A)=2A-B is kind of the
: bias corrected estimator.
|
w*******9
发帖数: 1433 | 5 I am not an expert of bootstrap but I guess generally B is not guaranteed to
be unbiased. Let p be the population and a the true parameter. Let S1 be a
bootstrap sample, hopefully The gap between S1 and the original sample S is
similar to the gap between S and p, so it's reasonable to guess B-A is
similar to A-a. Equating them gives a=2A-B.
【在 w****p 的大作中提到】
: So,can I understand your explanation like this?
: A and B are two estimators of a parameter. A is biased but B is not.
: Bootstrap can let us know the bias of A, so (A-bias) is unbiased estimate.
: But why don't we just use B as the estimator?
|
r***c
发帖数: 398 | 6 you are expert. that is main assumption made in bootstrap
to
a
is
【在 w*******9 的大作中提到】
: I am not an expert of bootstrap but I guess generally B is not guaranteed to
: be unbiased. Let p be the population and a the true parameter. Let S1 be a
: bootstrap sample, hopefully The gap between S1 and the original sample S is
: similar to the gap between S and p, so it's reasonable to guess B-A is
: similar to A-a. Equating them gives a=2A-B.
|
w****p
发帖数: 167 | 7 I see... Thank you so much!
to
a
is
【在 w*******9 的大作中提到】
: I am not an expert of bootstrap but I guess generally B is not guaranteed to
: be unbiased. Let p be the population and a the true parameter. Let S1 be a
: bootstrap sample, hopefully The gap between S1 and the original sample S is
: similar to the gap between S and p, so it's reasonable to guess B-A is
: similar to A-a. Equating them gives a=2A-B.
|
T*******I
发帖数: 5138 | 8 那个bias的方向也可能是反的，所以，最后的估计结果也可以是
A+(B-A)
我的意思是，下一组1000次的bootstrap可能会给你一个反向的bias.
【在 w*******9 的大作中提到】
: B-A estimates the bias of the statistics, thus A-(B-A)=2A-B is kind of the
: bias corrected estimator.
|
