s**s
发帖数: 1 | 1 There is no best choice. Which one is better depends on your problem. MLE is a
consitent estimate, provided that your model is correct. Consitency means that
MLE will converge to real parameter in probability as sample size goes to
infinity. What is more, MLE is asymptotically efficient, which means as sample
size goes to infinity, the variance of MLE will achieve Cramer-Rao lower
bound. In this sense, no other estimators can beat MLE. However, if sample
size is small, other estimators can be be |
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F******n
发帖数: 160 | 2
You are right, MLE is not Bayesian. MLE is biased and "the bias --> 0, as n --> infinity" (asymptotically unbiased). However, I don't think my question is focused on any concern with "whether it is Bayesian or not", so I would put this point aside later. To clarify this, I can give a bit more words on this. The general question, as posted below, is:
Probability(P|D，M) = ?
according to the Bayesian theorem, it can be expressed as:
Probability(P|D，M)
= Probability(P, M) * Probabil |
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S*****T
发帖数: 400 | 3 嗯
偶就把偶知道的那几个说说
名字和人怎么对应，你自己去看好了
edward witten，现在这个领域的大牛，任职princeton的IAS(高等研究院einstein过去待的地方)
fieldz medal winner, m-theory的发现者
steven weinberg,另一大牛，ut austin(本来是harvard的，被austin重金挖去）
nobel laureate, 弱电理论中的标准模型的创始人
glashow，boston univ,
和weinberg一起获得nobel奖，也是因为标准模型，据说是他老板schwinger布置了的题目
导致了这发现
david gross， ucsb的，好像是witten的老板，还有个著名的学生wilczek
他们一起发现了qcd的asymptotic free,所谓渐近自由，（就是能量越高，
相互作用越弱，quark间的强作用就符合这性质）
polichinski, ucsb的，他在austin的时候发现了m-theory的soliton解，也就是大家说的
d-brane
joe lykken, fermilab的，也在 |
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h*******e
发帖数: 68 | 4 The asymptotic equivalence between MLE and Bayes estimates at one time seemed
very hopeful and optimistic for objective Bayesians. But later results showed
that the consistency of Bayes estimate was very dubious, especially in high
dimensional case such as nonparametric problem. The proof of consistency of
Bayes estimate is still far from close. Even in fixed dimension problem, an
arbitary choice on prior (even with proper prior) does not guanrantee
consistency. Special type of prior such as tai |
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f*******r
发帖数: 257 | 5 OLS estimator is consistent given E(Xe)=0. There is nothing about the
distribution of the error term. It is true that MLE estimator with normal
error term turns out to be the same as the OLS estimator, but that does not
mean the OLS estimator relies on normal error term. If you have normal
error term, that's better: small sample inference is valid. If not, and you
have a relatively large sample, then you are still fine: asymptotic
inference is still valid. The key assumption is E(Xe)=0; bas |
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k***o
发帖数: 55 | 6 I assume you are looking for a point-wise confidence interval, if so, you
can compute the estimated asymptotic variance from your data point-by-point
and use the standard confidence interval formula with t-distribution to
obtain your CI's.
If you are looking for a uniform CI for the whole KM curve, sorry I have no
idea how to do that. |
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p********6
发帖数: 1339 | 7 google Lyapunov's central limit theorem
如果满足 limit (sum(mu3_i)/sum(sigma_i^2)) -> 0 (这里mu3_i是每个Xi的三阶中心
矩，sigma_i^2是每个Xi的variance)
那么 sum(Xi) asymptotically belong to Normal(M, V), M=sum(mean_i), V=sum(
sigma_i^2)/n |
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n*****1
发帖数: 172 | 8 I guess you can treat X as random variables in OLS. In that case, there is
not much to talk about the finite sample properties of the betas. For
asymptotic properties, you need additional (stronger) assumptions about X
and e to derive consistency. And I don't think you need to transform the
data ONLY because it is skewed. But that also depends on what your
underlying economic model is. |
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z****e
发帖数: 2024 | 9 "the interval estimation" or say the "inference", based on the law of large
numbers, ie, asymptotic normality.
However, since GAMMA has none zero mean, i'm not sure, how to fit b1 and b3
using OLS because GAMMA has two parameters \theta and \k as well.
no
be |
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n*****1
发帖数: 172 | 10 strictly speaking, you don't need normal errors. As long as your sample size
is large and the product of Xe
satisfies some CLT conditions, you still get asymptotic normality.
if you have heteroskedasticity and if you do OLS, then your estimated
coefficients are still unbiased, generally
consistent, but it is not efficient. This means, in EXPECTATION, you get the
right coefficient, but if you want a
confidence interval, then your estimated "range" is not correct. |
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t******l
发帖数: 32 | 11 Yes, that is Wald test.
你也可以代入想测的的值，那样就是score test.
Under the null, the two tests are asymptotically equivalent. |
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j*****e
发帖数: 182 | 12 To Alexwater, your comment indicates your lack of understanding of the
problem. The number of success out of 6 tries follows a binomial
distribution with parameter p that you wish to estimate. If you have
1000 tries and p is not too close to 0 or 1, you can estimate p using
asymptotic results(just like what you learn from an intro-level stat course).
The problem here is that the number of tries is low and p is very close to 1
. So, traditional methods don't work.
Even though you observe 100% suc |
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l******r
发帖数: 18699 | 13 你明显歧视非数学类申请者
你不就本科学过数学吗，
有什么了不起，不也就会证个asymptotics吗，
还是给人当陪衬的 |
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A*******s
发帖数: 3942 | 14 这本来就应该是bootstrap的assumption么，只要这个方法是asymptotic成立的就行。
bootstrap背后的philosophy我不太了解，这些高屋建瓴的问题得请教陈立功教授，呵
呵。俺这种低级民工只关心技术层次 |
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s******u
发帖数: 21 | 15 在网上找了很久也没找到，图书馆也没有:
"On some asymptotic properties of maximum likelihood estimates and related
Bayes' estimates" by Le Cam
University of California publications in statistics, v. 1. no. 11, p277-330 |
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s*****b
发帖数: 106 | 16 Could you please tell why do you think so?
The details of asymptotic distribution is not that interesting, which is the
main contents of the dissertation. and besides that, I would not have much
thing to talk about.
Thanks! |
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j*****e
发帖数: 182 | 17 First, the square of a standard normal r.v. is chi-squared with df=1.
Second, in SAS, CI of relative risk is constructed based on the asymptotic
normality of log(estimated RR).
It is impossible to have a Wald CI without some sort of normality assumption
. This is a concept issue. |
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D******n
发帖数: 2836 | 18 fts.....
if u randomly sample data from a population, it asymptotically follow the di
stribution of that population.
with |
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w********o
发帖数: 1621 | 19 我自己就比较反感bayesian。你知道从frequentist的角度分析问题，一个模型要用多
少力气去推算asymptotic properties，才能develop estimate, confidence interval
，test statistic and p-value吗？有时候推不出来，就得用bootstrap啊之类的
empirical estimate,或者EM algorithm，总之要多麻烦有多麻烦。所以统计要出点成
绩，那得要深厚的理论基础。
自从有了bayesian，什么都不用，任何能想出来的model都可以用，根本无需证明，只
要有prior information就成。这prior information还是可以试着用的。变成什么理论
都不懂也照样写paper的局面。很多老教授，尤其是对理论很自负的，就会变得对
bayesian有点厌恶。
本来5年才能统计博士毕业，有了bayesian model后，大概3，4年就可以了。 |
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f***a
发帖数: 329 | 20 有时候asymptotic推得是让人吐血。。。
bayesian自从有了MCMC确实应用起来非常畅快,什么model都能算出点结果，不过真正能
把问题看清
楚的人就不多了。
interval |
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y****u
发帖数: 11 | 21 Hi TNEGIETNI,
I briefly went through your "paper": The Fundamentals of Statistics for
Rebuilding the Methodology of
Piecewise Regression Analysis Based on a Functionalized General Trichotomy.
First of all, I am not sure what
fullwise regression model means. Is that a term you created? If you want to
question the role of the tuning
parameter (or the smoothing parameter), please read "Asymptotic Optimality
of $C_L$ and Generalized
Cross-Validation in Ridge Regression with Application to Spline Smo |
|
|
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d********t
发帖数: 837 | 24 It's assuming asymptotic normal distribution, why do you need degree of
freedom? |
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I*****a
发帖数: 5425 | 25 I dont know. I was just guessing ...
Did the paper you mentioned say anything about sample size, or asymptotic re
sults on this ? |
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m*****O
发帖数: 3558 | 26 didnt get ur question. but logLR is always asymp chi squared ba |
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j*********1
发帖数: 15 | 27 对于chi-square,alternative hypothesis是得pi是MLE吧（Xi/N),但是这里是已经定了
pi（theta.b和time interval决定)。Hogg的书上有asymp MLE到normal的，不知道是不
是也适用于这里的LR |
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n*****n
发帖数: 3123 | 28 have X1,... Xk+1 (each follow the exponential distribution) at different
time interval t1,...tk (equal) and tk+1=infinite.
你这个是什么意思，没看明白 |
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j*********1
发帖数: 15 | 29 X1 is the # of items at time interval t0 to t1
Xi follow exponential dist |
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y****d
发帖数: 432 | 30 A Course in Probability Theory Kai Lai Chung
A Modern Approach To Regression With R
A Second Course in Stochastic Processes
A First Course in Bayesian Statistical Methods
Advanced Statistics
An Introduction to the Bootstrap
Analysis of Incomplete Multivariate Data
Asymptotic Statistics
Bayesian Computation with R
Bayesian Data Analysis
Categorical Data Analysis
Continuous univariate distributions1
Continuous univariate distributions2
Generalized Additive Models
Graphical Models
Introducing Monte... 阅读全帖 |
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r*****y
发帖数: 199 | 31 I took a course of bootstrap this semester, it seems the situation we
discussed a lot is for small sample. For large sample, you can always rely
on the asymptotic theory. |
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A*******s
发帖数: 3942 | 32 if u aim at testing the sample mean, why do u care so much on the population
distribution? as long as the standardized sample mean is normal t test
should be valid. In Goldmember's case, several hundred sample size is large
enough to assure an asymptotic normality. |
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T*******I
发帖数: 5138 | 33 你觉得我的上述分析是否有道理吗？而不是只拿现存的理论来阐述你的观点。
你可以take the asymptotic normality，但是对于我来说，一个总体是否服从正态分布是一个很难从样本确定的，即使一个样本的分布表现是一个正态的，它也可能来自一个非正态总体；反之亦然。而分布的正态性或非正态性在概率空间上作判断时是一个连续测度，需要一个cut-off。所以，我们无需继续在这种会将我们的思路和逻辑导向困境的概念系统上打转转。我们必须走出这样的思维模式。
所以我说统计学的新地平线真的出现了。我在1998年的4月初就依稀望见了它。现在它终于成形了。这就是自权重的成功定义。 |
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f******9
发帖数: 267 | 34 我刚看了下课程内容，包括：
Nonparametric estimators
Lower bounds on the minimax risk
Asymptotic efficiency and adaptation
principal component
subsampling bootstrap |
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d******e
发帖数: 7844 | 35 这种课的minimax和Asymptotics对找工作完全没用。
对research来说也有些太旧了，都是low-dimension的theory |
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d******e
发帖数: 7844 | 36 统计的Data Mining就是machine learning的马甲，说到底都是统计模型。
Theory上最火的目前是High dimension的Asymptotics。
Methodology上Finance，Biology，Medical Imaging之类的基于统计模型的数据分析，
这部分普遍不强调理论。
Application上就无所谓模型了，用Data Mining的工具，有好的结果才是第一位的。
虽然统计的Data Mining很多时候用R就行，但是也有越来越多的人开始强调编程能力的
重要性了，尤其是大规模数据分析，用R基本就是自杀。
CS的data ming一般都是数据库的人在搞，不强调理论，也不用多少数学，算法味道很
重，重视coding，编程不行肯定是没法混的。 |
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d******e
发帖数: 7844 | 37 统计的Data Mining就是machine learning的马甲，说到底都是统计模型。
Theory上最火的目前是High dimension的Asymptotics。
Methodology上Finance，Biology，Medical Imaging之类的基于统计模型的数据分析，
这部分普遍不强调理论。
Application上就无所谓模型了，用Data Mining的工具，有好的结果才是第一位的。
虽然统计的Data Mining很多时候用R就行，但是也有越来越多的人开始强调编程能力的
重要性了，尤其是大规模数据分析，用R基本就是自杀。
CS的data ming一般都是数据库的人在搞，不强调理论，也不用多少数学，算法味道很
重，重视coding，编程不行肯定是没法混的。 |
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l*********s
发帖数: 5409 | 38 1. expectation and variance estimates are unbiased and asymptotically
efficient, as promised by the weak law of large number, unless the
underlying distributions are of certain special cases, such as cauchy.
2. that being said, mles are derived from the density functions and the result is only valid for a correctly specified distribution family; otherwise, it is going to be garbage no matter how
accurate parameter estimates are. |
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h******3
发帖数: 190 | 39 TDT的chi-square statistic和传统的chi-square statistic for independence理论上
来说应该是equivalent的。因为它们都是测试transimission和allele是不是
independent.
怎么才能推出那两个chi-square statistics是相等的，或者asymptotically相等的。
我想不出来。求助。 |
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a****e
发帖数: 150 | 40 关键是你说的经典到底是哪本书了,要是van der vaart的"asymptotic statistics"初
学者看不懂正常,要是casella的statistical inference,那耐心点找用这个教材的课件
看看先. |
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A*******s
发帖数: 3942 | 41 晕，我刚买到手asymptotic stats。。。难道得先懂real analysis才能看这本？ |
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A*******s
发帖数: 3942 | 42 if u wanna do some decent research and propose something new in academy, yes
u r right, u need a very solid understanding of analysis, measure,
probability, math stats, linear models, asymptotics, decision theory, stat
learning theory...
but my point is how to digest new things efficiently. or put it simply, to
be able to read papers in top journals, to understand new skills in a week..
. then u don't have to start with analysis. if u look at some decent stat
PhD programs they don't even need an... 阅读全帖 |
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A*******s
发帖数: 3942 | 43 he doesn't even know basic prob theory... not to mention asymptotics |
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A*******s
发帖数: 3942 | 44 r u able to read these? i doubt that...
Bootstrap Methods: Another Look at the Jackknife
B. Efron
Bootstrap Methods for Standard Errors, Confidence Intervals, and Other
Measures of Statistical Accuracy
B. Efron and R. Tibshirani
Some Asymptotic Theory for the Bootstrap
PJ BIQKEL |
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k********g
发帖数: 56 | 45 围观一年了，插一句嘴。
大师您数学不行这已经是公认的了，我也不逼你写个证明。
George E. P. Box有句名言，
all models are essentially wrong, but some are useful.
bootstrap在asymptotics的角度上是正确的，但你不懂。
ok，现在我们假设你批评的对，假设它的理论基础是错误的（请注意，仅仅是假设）。
但问题是在很多很广泛的情况下，这个方法很有用。
所以，如果没有人能够提出一个更“好”的方法，并在实践中在真实数据和数值模拟中
证明这种新方法在更多更广泛的情况下都很有用。那对bootstrap的质疑是没有意义的。
你要是有新方法，也要在真实数据和数值模拟中得到好的结果才行，光是哲学描述没意
义。 |
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j*****e
发帖数: 182 | 46 Not all the asymptotics have been solved. This paper is just a proof for a
special case. What kind of bootstrap works is still on-going research. |
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r*****y
发帖数: 199 | 47 你这是n goes to infiniti吧，给你sample size 10，你怎么办～ 不是什么时候都可
以依靠asymptotic result的吧～
s |
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d******e
发帖数: 7844 | 48 一般的logistic regression是不带penalty的，没法通过regularization来调节bias和
variance。所以我认为你是在说带ridge penalty的logistic regression。
如果是这两个比的花，两个方法的loss function非常像，性能上区别很小，不管是
linear的还是non-linear的，所以一般来说，你很难指望一个能明显beat另一个。
SVM能稍微robust一些，因为有sample上的sparsity。但是SVM并非对条件概率建模，所
以没法直接输出概率，也没办法做inference。Logistic Regression在这点上要强一些
，不过也只能做asymptotical inference. |
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p********a
发帖数: 5352 | 49 ☆─────────────────────────────────────☆
tamuer (hoho) 于 (Fri Oct 21 20:41:07 2011, 美东) 提到:
前面有人问bootstrap能不能更逼近真理。我不是这方面的专家，但是发表一点自己的简
介，希望和大家交流一下吧。
总体而言， 我觉得使用bootstrap不能说是逼近真理。但是有的时候，确实比不做boot
strap比更好，或者比使用单一样本更接近真理。大家都觉得bootstrap没有真正用处的
原因是觉得所有bootstrap重复抽样的样本都是从一个样本里出来的，所以用bootstrap
的效果不会比使用原来的样本好多少。这一点我也同意。
但是从另外一个角度来说，一个样本里面包含的信息是很丰富的，我们是否已经完全利
用了现有样本里面的信息呢？最简单的例子来说，一个样本，很多时候我们用就用samp
le mean来summarize样本信息，但是使用sample mean的时候又忽视了多少样本中原来的
信息呢? 比如各种quantile的信息之类。 类似的，换一个角度来说，bootstrap是在... 阅读全帖 |
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w*******9
发帖数: 1433 | 50 Clt only concerns the asymptotic distribution of sample mean. It probably
does not apply to this case. If I am wrong, please correct me: there might
be one or several zeros in your data. Delete these and try again. |
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