meta user
network profile
| bio | website | neblink.wordpress.com |
|---|---|---|
| location | Montreal, Canada | |
| age | 29 | |
| visits | member for | 1 year, 9 months |
| seen | 3 hours ago | |
| stats | profile views | 533 |
I'm a graduate math student at Concordia University, Montreal.
|
May 20 |
comment |
Finding the range of a vector valued function What is then the conclusion, once $\det J_f=0$ on the line $y=x$? |
|
May 13 |
comment |
Maximum likelihood in exponential family: $\partial_{\theta,\theta} \ln L = -\mathrm{Var}(T)$, $T$ sufficient for $\theta$ @Caran-d'Ache I think you mean $$\mathrm{Var}(T) \ge (E(-\partial_{\theta,\theta} \ln L))^{-1},$$ the Cramer-Rao lower for the variance of $T$. From my calculation, this works, and it explains why they are inverse of each other. Thanks for your input, combine with Did comment, I better understand what is going on. |
|
Apr 29 |
comment |
$X_n \sim \text{Exponential}(\lambda_n)$, independent, $\sum 1/\lambda_n = \infty$, then, $\sum X_n=\infty$ a.s. Whoa! Of very great level. Thanks. |
|
Apr 22 |
comment |
Is it possible to construct a Loeb measure for $\{\epsilon: \epsilon\in[0,1], \epsilon \text{ infinitesimal}\}$? @user72694 How can I string finite numbers to get say $A=\{\frac{1}{\omega},\frac{2}{\omega}$\}? My thinking is $\mathrm{st}(A)=\{0,0\}$, so I don't see what to string. |
|
Apr 10 |
comment |
Harmonic mean: show $\max\{ax,by\} \ge \frac{1}{a+b}(x+y)$, $a,b>1$, $x,y\ge 0$ Great proof. I see my (a)-(c) ideas were wrongs. I made no typos though. Thanks. |
|
Mar 4 |
comment |
Likelihod ratio test: $f_0(x)=2x$ vs $f_1(x)=3x^2$ : $2n$ degree of freedom? Asked and answer on statSE. @passerby51 the trick is that $-ln X_i$ has an exponential distribution under $H_0$, that is a $\chi^2$ with $2$ degrees of freedom. |
|
Feb 27 |
comment |
Likelihod ratio test: $f_0(x)=2x$ vs $f_1(x)=3x^2$ : $2n$ degree of freedom? @passerby51 I think everything of the problem is here. I will try to find such a sequence $Y_n$. I tried to view the LRT as a goodness-of-fit test with $n$ cells in $H_0$ and $2n$ cells in $H_1$ ($max(f_0(X_i),f_1(X_i))$). Then the degree of freedom is $2n-n=n$. |
|
Feb 24 |
comment |
Likelihod ratio test: $f_0(x)=2x$ vs $f_1(x)=3x^2$ : $2n$ degree of freedom? @passerby51 Thanks, I meant asymptotically but didn't write clearly. I tried to copy a proof on the asymptotics of $\lambda$, but all the proof I know makes reference to the parameter space $\Theta_1$ and $\Theta_0$. |
|
Feb 23 |
comment |
$X_i \sim N(\theta,1), \theta \in \Bbb Z$: $T=\left\lfloor \bar X_n \right \rfloor$ not consistent for $\theta$ \begin{align} P\left( \left \lfloor \bar X_n \right \rfloor - \theta < -1/2 \right) &= P\left( \left \lfloor \bar X_n \right \rfloor < \theta -1/2 \right) P\left( \bar X_n < \theta \right) \\ &+P\left( \left \lfloor \bar X_n \right \rfloor < \theta -1/2 \right) P\left( \bar X_n \ge \theta \right) \\ &\ge 1 \cdot 1/2 + 0 \cdot 1/2 \\ &= 1/2. \end{align} Is it like that? |
|
Feb 22 |
comment |
efficencie implies unbiased and consistence? Asked and answered on statSE |
|
Feb 17 |
comment |
Show the $l^2$ ellipsoid is close : $\left\{(x_n) \in l^2 : \sum\frac{x_n^2}{a_n^2} \le 1\right\}, a_n \to 0$ I don't see the dominating function which permits application of the DCT. I see that $\sum_n \frac{\left(x_n^{(k)}\right)^2}{a_n^2} \le 1$, but $\sum_n 1 = \infty$. |
|
Feb 12 |
comment |
Levy process: reversed $\overset{d}{=}$ dual : $X_{t-s}-X_t \overset{d}{=} - X_s$ @StefanHansen You are right, I understand now. Thanks. |
|
Feb 11 |
comment |
$d\left(\left(x_1,x_2\right),\left(y_1,y_2\right)\right)=|x_1-x_2|+|x_1-y_1|+|y_1-y_2|$ : complete? @JonasMeyer From my university past comprehensive exam. |
|
Feb 9 |
comment |
Show with maximum principle: $|f|$ constant, f analytic, then $f$ constant in open domain $D$ @user45150 Very true, thanks. |
|
Feb 8 |
comment |
Circulant matrix : eigenvector @julien I had the wrong eigenvalue, with the right one I can show $Cv_j=w_jv_j$. I didn't know the VanderMonde determinant. Your comments are helpful, thank you. |
|
Feb 8 |
comment |
Circulant matrix : eigenvector @julien For linear independence, I didn't realized the eigenvalues were distinct, thanks. For the good old way, say the first row of $w_jv_j$, I don't see how to show: $c_0+\sum_{x=1}^{n-1}c_{n-x}w_j^x=w_j$. |
|
Feb 7 |
comment |
$A$ skew-symmetric, then $x^T A^2 x \le 0$ Is $B^T B \ge 0$ for any $B$ : $-\left( x^T A^T \right) \left(A x \right) = - \left(A x \right)^T \left(A x \right) $ |
|
Feb 5 |
comment |
Set of continuous function defined on some segment $[0,a]$: completeness @ABlumenthal I specified over which interval the sup is taken for $c$. Yes, I mean $a_f+a_g-2c_{fg}$. |
|
Feb 2 |
comment |
Pointwise limit of $f_n(0)=0$, $f_n(1/n)=n$, linear in between I did upvote your answer, right after reading it. |
|
Feb 2 |
comment |
Pointwise limit of $f_n(0)=0$, $f_n(1/n)=n$, linear in between I've been too hasty in asking julien to turn his comments into an answer. I guess you were typing your answer at that time. I will give him the point, but your answer confirm our thoughts. Thanks. |
