B******e
发帖数: 378 | 1 if flat fading,u can model channel as y_k = a_k*x_k + n_k
a is the fading coefficient.
the covariance function of flat fading process decides
T_coh, the channel coherent time. If T_coh > T_s (symbol period)
it's a slow fading process, otherwise, fast fading.
Usually, T_coh/4/T_s is the frame length if u model
slow fading channel as a block fading model.
T_coh also equals to 1/f_d, f_d is the doppler frequency. |
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J*******g
发帖数: 267 | 2 Since Y_1 and Y_2 are joint Gaussian, you only need their covariance matrix
to compute the joint entropy. No need for the joint density |
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t**********g
发帖数: 30 | 3 谢谢 那 C_(Y_1Y_2) 怎么用equation表示出来呢 现在我需要详细的数学推导 其实我
没有实际的Y_1 Y_2 可以直接算 convariance matrix. 我需要equation 来表示。 不
知道那个joint Gaussian 的 covariance 可不可以用
C_x 和 N1 N2 表示出来？ |
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a****l
发帖数: 8211 | 4 做power spectral density的测量的时候,各种估计的方法到底有什么不同?比如Welch,
Yule-Walker,Burg,covariance,eigenvector,他们在使用上的区别是什么?也就是说,
什么情况该用什么方法,有什么讲究?
谢谢! |
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i********n
发帖数: 53 | 5 是啊，每个用户都用symbol extension的话。但是super symbol 对应的是每个symbol
必须经历independent fading，暗含的假设就是需要code across n diversity
branch。
不知道是否有其他解释，因为印象中Jafar 在distributed interference alignment里
谈到了接收端只需知道interfernce covariance matrix 即可用algorithm找到
precoding matrix, 并且不需要n =\infty即可实现d.o.f.=1/2 per user, 不知道这个
理解是否正确。 |
|
s****e
发帖数: 1180 | 6 【 以下文字转载自 Statistics 讨论区 】
发信人: sheide (shei), 信区: Statistics
标 题: 诚心请教大data set到底该怎么分析？
发信站: BBS 未名空间站 (Wed Jun 22 18:39:19 2011, 美东)
诚心请教大data set到底该怎么分析？今天面试的一个问题，说是有一个data set要分
析，有100 million个observations，200 thousand个covariates，公司不用SAS，只用
R和Python，但这么大的data set R 完全handle不了，问我该怎么办？用C？我会C。好
象版上以前有讨论过大data set，但好象一般学校的phd program 都没这方面的
project（whatever,我胡说的，反正我们学校是这样，不知道其他学校怎么样？），今
天终于让我碰上了。大家知道这方面一般都怎么办？有什么常规方法？或是有什么实用
的参考书吗？还有如果用C的话，我一般就用 dev c++ IDE，或是用linux gcc，请问这
两种C平台能分析了这么大的data se... 阅读全帖 |
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j***y
发帖数: 1069 | 7 直观感觉只需计算cross correlation/covariance function(CCF)
如果CCF在某个lag比较大
说明两信号直接比较相似 但是有delay
或者如果你大致知道信号的模型(ARMA, harmonics, polynomial, linear..)
那直接用数据估计模型参数
然后再比较 |
|
i********e
发帖数: 31 | 8 There are several ways to define the distance measure between
two n by n SPD matrices.
(1) Easiest: just treat them as n by n symmetric matrices
and use the inner product on the space of n by n symmetric
matrices which is a vector space of dimension n*(n+1)/2
(2) From statistics point of view, think about the distance/
divergence between two normal distributions with same
mean but different covariance matrices.
keywords: Rao's distance, Fisher information matrix,
KL divergence, J-div |
|
h****f
发帖数: 24 | 9 Consider the hypotheses
H0: q=0 H1: q =/= 0
and the observations
zi=q+wi i=1,...,n
with wi zero-mean jointly Gaussian but not independent.
denoting w=[w1,...,wn]'
one has the covariance matrix (assumed given)
E[ww']=P
For the above
1. specify the optimal hypothesis test for false alarm
probability a
2. solve explicitly for n=2,
P=[1 0.5] (this is a matrix)
[0.5 1 ]
and a=1%
Thanks! |
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m*********s
发帖数: 6 | 10
you have not defined function yet, or you have not explained the difference
between f and f_hat
yes since the latter is just a constant. |
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r****y
发帖数: 1437 | 11 why? Just solve the eigenvalues and eigenvectors for
covariance matrix iteratively. There is numerical routine ready for this,
the first one is always 1st PC, etc.
In matlab, they have built-in PCA command, try princomp. |
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O**M
发帖数: 29 | 12 Let h be circularly complex Gaussian distributed with zero mean and identity
covariance matrix.
Let A be an unitary matrix.
Given h'Ah>0, what is the conditional pdf of h
pdf(h|h'Ah>0)?
thanks a lot. |
|
a****a
发帖数: 98 | 13
I think maybe he means the space of 1-dim random variables? this is not a
probability space itself. but it is a hilbert space if you define the inner
product to be covariance, and every hilbert space is a banach space (but
not the other way around) |
|
|
|
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D*******a
发帖数: 3688 | 17 use error covariance
你这个感觉像kalman filter |
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k*******l
发帖数: 69 | 18 可以不独立啊，quadratic covariation不为0就行了
rho(1, 2)未必一定是常数 |
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k*******l
发帖数: 69 | 19 ft
the quadratic covariation of two BMs is not necessarily rho*t
this is just model assumption, since time-dependent or stochastic
instantaneous correlation (the rho above) is too hard to estimate/calibrate
rate |
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p*****e
发帖数: 15 | 20 We treat the 0 variance/covariance case as normal.
X is a random vector with n components.
Then X is multivariate normal if and only if
LX is univariate normal, for every 1 x n vector L.
See any general multivariate statistics textbook.
Therefore, the sum of two normals (indep. or not) is still normal if
we choose L=(1, 1). |
|
q*******n
发帖数: 1334 | 21 Assume X = [X1, X2]^t is bivariate normal distributed with mean vector m = [
m1, m2]^t and covariance matrix C = [c1, r; r, c2].
1. Define s = [s1, s2]^t as the dumb variable vector for MGF, then the MGF
of the vector X is
M_X(s) = E[exp(s^t * X)] = exp(m^t s + 1/2*s^t*C*s). (eqn. 1)
2. Set s1 = s2 = u in (eqn. 2), then we can get the MGF of X1+X2
M_{X1+X2}(u) = E[exp( (X1+X2)u ) = exp((m1+m2)u + 1/2*(c1+c2+2r)*u^2) (eqn.
2)
3. Eqn. 2 is in the form of the MGF for Normal RV. Therefore, X1+X2 is |
|
j********9
发帖数: 162 | 22 I have some questions here:
Does the copula of M.R.V. LogNormal Distribution follow M.R.V. Normal
Distribution?
If yes, what is the covariance matrix of the copula distribution, is that
the normalized characteristic matrix of LogNormal Distribution?
What happen to the copula for T distribution (except Cauchy distribution) or
any elliptical distribution?
Can anyone recommend me some reference, online or book. I really want to
make it clear. Thank you so much. |
|
H****h
发帖数: 1037 | 23 If you have iid rv X_1,...,X_n ~N(0,1), and a matrix A.
Let Y=(Y_1,...,Y_n)^t=AX, where X=(X_1,...,X_n)^t.
Then the covariance matrix for Y is A^tA. |
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m****y
发帖数: 74 | 24 they are jointly gaussian. try to find its mean vector and covariance matrix
, then done. |
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t******y
发帖数: 147 | 25 三个零均值的高斯向量A,B,C组成一个Markov Chain，那么它们的covariance matrix有
什么关系？
请问从哪儿可以找到相关的定理？ |
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l*****n
发帖数: 18 | 26 我需要求下面这个目标函数关于矩阵W的微分：
Tr( (W'*inv(W*W')*W-I) * C * (W'*inv(W*W')*W-I)' )
这里面W是个M by N的矩阵，M
by N，semi-positive definite matrix；Tr是trace operator。
已经想了半天了，完全没有头绪。大家帮帮忙！ |
|
c*******d
发帖数: 353 | 27 In the book 'differential geometry' by Kreyszig, a result is frequently used
about the principal curvature k1, k2. For example, we know that gaussian
curvature K=k1*k2.
When lines of curvature (curves with principal curvature as tangents)
coincide with coordinate curves, it can be shown k1 = b_1^1, the first
element of a mixed tensor with degree 2 and 1 covariance indice. (p.131)
The author then equate k1 = b_11/g_11, k2=b_22/g_22. And this result is used
in several places. Here is what I am hav |
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w**a
发帖数: 1024 | 28 在tensor 里面，为什么这么叫啊，co- 和 contra-是什么意思，多谢 |
|
d*********0
发帖数: 222 | 29 CO-叫协变
CONTRA-叫反变
这个体现了在坐标变换下的张量变化规律。
和范畴里面的协变函子和反变函子类似。 |
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F********E
发帖数: 1025 | 30 有什么数值可以评价吗？（看到教科书上有covariance，但感觉不像）
最好有什么类似relative standard deviation的不依赖于原始数据大小的标准吗？
比如：如果是perfect的拟合，为0；如果是一塌糊涂的拟合，为1. |
|
g****t
发帖数: 31659 | 31 没有。
nonlinear是个太空泛的东西，你给的信息太少。
不能做统一评价。
有什么数值可以评价吗？（看到教科书上有covariance，但感觉不像）
最好有什么类似relative standard deviation的不依赖于原始数据大小的标准吗？
比如：如果是perfect的拟合，为0；如果是一塌糊涂的拟合，为1. |
|
d****y
发帖数: 53 | 32 in that case one would write down the covariant derivatives using
connections
(easily found in any general relativity / differential geometry books) |
|
b*********h
发帖数: 46 | 33 【 以下文字转载自 Statistics 讨论区 】
发信人: breakthough (吾将上下而求索), 信区: Statistics
标 题: 外行问个基本的统计问题
发信站: BBS 未名空间站 (Tue Aug 17 17:15:40 2010, 美东)
最近遇到的，应该是个很标准的estimation的问题，想来内行人很容易回答
一个线性模型， y=Ax+e, x是未知随机输入，A是已知的非随机模型，y是
观测到的输出，e是观测的随机误差。任务是根据y估计x。
给出的解是最小化(Ax－y)'*inv(Cy)*(Ax－y)'+x'*inv(Cx)*x, Cy和Cx是y和
x的covariance matrix，我的问题是，这种解法的数学解释是什么。
我不懂统计的术语，但是知道概率，分布，随机变量和随机过
程什么的。举个例子，你说“regression”我就听不懂。希望明白人给个解释，
如果有简单明了的tutorial，可以一看就懂是最好了。多谢了。 |
|
x*******3
发帖数: 396 | 34 Proof:
Suppose Z is the standard normal distribution with mean zero, co-variance
matrix I.
Then X=u+S^(1/2)*Z, and WX=Wu+W*S^(1/2)*Z
E(WX)= Wu,
Var(WX)=E(W*S^(1/2)*Z*Z'*S^(1/2)'*W)=W*S^(1/2)*E(Z*Z')*S^(1/2)'*W'=WSW'
关键点:任何多元高斯都是一个标准高斯(mean 为 0 covariance matrix 为 I)的
linear transformation. |
|
o*******w
发帖数: 349 | 35 这是我做的一些笔记的例子. 我自己是造不出这些, 我想表达的, 句子的. 笨人如我，
就得花些笨功夫
(JOEL A. TROPP "USER-FRIENDLY TAIL BOUNDS FOR SUMS OF RANDOM MATRICES")
... There is another contemporary line of research that uses ...
... In a significant article [Rud99], Rudelson obtains an optimal
estimate for the sample
complexity of approximating the covariance matrix of a general isotropic
distribution.
... By now, there is a substantial literature on other nc moment
inequalities.
... The argument in his paper, which is due to Pis... 阅读全帖 |
|
x******i
发帖数: 172 | 36 我有事情请教，就是关于做MANOVA
我用PCA找到componet 1 和component 2里面的成分
接下来我要把component 1 和 component 2作为dependent variables，手术前与手术
后作为independent variable，BMI作为covariance
我在网上查了下在SPSS里做MANOVA的步骤，大致知道做MANOVA的步骤，但是不知道把
component 1 和 component 2的什么值copy到MANOVA的column里，麻烦问下你们有谁做
过类似的分析么？谢谢！ |
|
x******i
发帖数: 172 | 37 我有事情请教，就是关于做MANOVA
我用PCA找到componet 1 和component 2里面的成分
接下来我要把component 1 和 component 2作为dependent variables，手术前与手术
后作为independent variable，BMI作为covariance
我在网上查了下在SPSS里做MANOVA的步骤，大致知道做MANOVA的步骤，但是不知道把
component 1 和 component 2的什么值copy到MANOVA的column里，麻烦问下你们有谁做
过类似的分析么？谢谢！ |
|
i***0
发帖数: 55 | 38 1. Show that if a discrete time Markov chain satis es detailed balance and
C(t) is the time t lag auto-covariance function in equilibrium, then C(2t)
>=for all t.
2 Suppose f(x), g(x), and h(x) are three probability densities with
f(x)
g(x) c ; and g(x)
h(x) c ;
for all x. Suppose we have an h sampler and want an f sampler based on
rejection from h. Consider the following two methods:
Direct method: Generate h samples and accept with probability pro-
portional to f(x)=h(x).
Indirect method |
|
Q******g
发帖数: 607 | 39 that's right. Coulomb gauge in QED is physical. of course, it's
mathematically harder and uglier to quantize it in this
non-covariant gauge. but it is doable. In fact, one can even do it
for QCD. It is much more uglier and complicated. One reference
for such kind of treatment is TD Lee's QFT book.
part
exis
the
sho
th
and
physi
spin |
|
r**a
发帖数: 536 | 40 what r u talking about? See your last eq.(eq.4), first you'd better not
raise $\mu$ to $\rho$ at this moment and leave $g^{\mu\rho}$ there. And
notice that $\mu, \nu$ are aniti-symmetric. Then change the partial
derivative to the covariant derivative. And then... |
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r******s
发帖数: 2155 | 41 Great! Another expert. I like your point 1 in particular because I'm into
Covariance Structure Modeling a lot.
Can you explain more about the difference between factor analysis and IRT?
summary
to
worked
easier
more
it
tests.
CTT.
test
while
be
IRT |
|
a****y
发帖数: 4 | 42 I guess:
(1) calculate covariance matrix of Xt(assume column vector), R=E{Xt*Xt'}, if
the eigenvalues of R are the same or very close (depends on the length of
Xt), then we may say r.v. in Xt are normally distributed; std = sqrt(
eigenvalue) |
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r*****t
发帖数: 286 | 43 ☆─────────────────────────────────────☆
theta (delta, gamma and vega) 于 (Tue May 1 22:59:25 2007) 提到:
(x1,x2,x3)--multiNorm(u,sigma), and we know u and sigma.
then condition on x3=x, what is the covariance matrix of muitinorm distr
ibution (x1,x2)?
anyone can shed light on this?
☆─────────────────────────────────────☆
quantler (quant) 于 (Tue May 1 23:03:41 2007) 提到:
熬了一个通宵后 我的神智已经不是很清醒了
不能帮您了：）
☆─────────────────────────────────────☆
theta (delta, gamma and vega) 于 (Tue May 1 2 |
|
B*********h
发帖数: 800 | 44 ☆─────────────────────────────────────☆
iambear (iambear) 于 (Mon Jun 18 14:55:45 2007) 提到:
不知道大家用哪个软件.我用UCSD garch toolbox中那个 dcc_mvgarch得出系数后如何
做一步或多步预测? 但这个function是假设arma(0,0)的.也有用SPLUS的,似乎更加方便
点,能够直接把cov(et+1,et+1|Ft)算出来,但我现在没splus.
☆─────────────────────────────────────☆
jasonma (大耳兔) 于 (Mon Jun 18 20:14:56 2007) 提到:
这个crappy得模型居然还有人用。。。
anyways, SPLUS+Finmetrics应该可以，SPLUS有学生版，发信向他们要。
另外，matlab也有GARCH toolbox...
☆─────────────────────────────────────☆
longtian (施主，小僧已经很久不烧香了) |
|
s******e
发帖数: 696 | 45 I want to learn about multi-factor models and covariance matrix
tracking error, etc..
is this a good book?
i use barra, and i heard the author worked at barra |
|
i*****r
发帖数: 1302 | 46 portfolio的标准差是: sqrt(weight*covariance*weight')
那每个资产的component volatility如何计算? 他们加起来要等于portfolio的
volatility |
|
s**m
发帖数: 25 | 47 It is a convention I think.
Recall the break-even point in a delta-hedged position. |
|
w*********r
发帖数: 488 | 48 我不太理解，如果mean不是zero，可以center一下的吧，每个数据都减去sample
average，mean就是0了。 |
|
f*******y
发帖数: 988 | 49 semivariance就是计算对于给定m的variance，m不一定要是mean
通常m为0，就是想知道赔钱或者赚钱时候的波动，这是很普通的做法，一些常见的c++
的库都有这些函数的 |
|
J****x
发帖数: 37 | 50 3. It is not possible, since the covariance matrix is not semi-positive-
definite (one eigenvalue -0.0487 is negatvie). |
|
