1,697 reputation
1820
bio website nicolasessisbreton.com
location Montreal, Canada
age 30
visits member for 3 years, 4 months
seen 8 hours ago

I'm a graduate math student at Concordia University, Montreal.


Jun
7
comment Inscribed circle: find distance to circumscribing circle
Also the tangent $T$ does not pass through the point $d$. And the distance $cd$ seems shorter than the distance $tT$ (at the tangencial contact point).
Jun
7
comment Inscribed circle: find distance to circumscribing circle
If I understand correctly, I draw the tangent $t$ at the point $c$. Then I draw a tangent $T$ of the great circle parallel to $t$. Let say $T$ is on the side of the point $d$. Then the distance between the tangencial contact points is the minimum distance from the point $c$ to the great circle. I don't see how this resolve the uniqueness of the length $cd$.
Jun
4
comment smaller circle into larger circle : find length of common arc
@YvesDaoust I made my question more precised. Does your assertion still hold with my precisions?
Feb
10
comment Is finding the maximum of a polynomial of degree one a linear programming problem?
Thank you, your answer really help.
Feb
9
comment Is finding the maximum of a polynomial of degree one a linear programming problem?
@MichaelC.Grant I see that my proposed equivalent is wrong. Can you indicate how to get, or if possible write as an answer, the equivalent problem using binary constraints? I tried to find my way with google, but I don't see how to do it.
Feb
9
comment Is finding the maximum of a polynomial of degree one a linear programming problem?
@MichaelC.Grant I think, the 'max' in the problem can be 'linearized' so that the problem becomes an LP (see edit). Is it true?
Oct
20
comment What is the error when approximating $L^2([0,1])$ by a finite dimensional space?
@PrahladVaidyanathan Yes, thank you. I forgot to say that $X$ contains only bounded function. I added it.
Oct
20
comment What is the error when approximating $L^2([0,1])$ by a finite dimensional space?
@PrahladVaidyanathan I see, I miswrite the max notation. I have corrected it, is it better now?
Oct
20
comment What is the error when approximating $L^2([0,1])$ by a finite dimensional space?
@PrahladVaidyanathan For my understanding, the error is in the orthogonal space. If I use your formula, the error will be too big: for any $f$, the closest $g \in X_n$ to $f$ is $\sum (f,v_i) v_i$, I think.
Oct
1
comment Is there a continuous bijection between an interval and a square: $[0,1] \mapsto [0,1] \times [0,1]$?
@copper.hat Your answer shows an other side of the die. Please let it live.
Oct
1
comment Is there a continuous bijection between an interval and a square: $[0,1] \mapsto [0,1] \times [0,1]$?
@BobPego The bijection requirement was a first instinct. You made me realized I can forgo it. Thank you for your insightfull comment.
Aug
31
comment Show that, for a random walk $X$ on $\mathbb Z_2$, $X_\infty$ is independent of the past $\left\{ X_t \right\}_{0\le t<\infty}$
By 'coincides', you mean in distribution: if $X$ is a random walk on $\mathbb Z_2$, as above, and $\left(Y_t\right)$ is an i.i.d sequence with uniform distribution on $\mathbb Z_2$. Then $X_t \buildrel{d}\over = Y_t, \forall t$. I don't see a proof for a stronger mode of convergence.
Aug
31
comment Show that, for a random walk $X$ on $\mathbb Z_2$, $X_\infty$ is independent of the past $\left\{ X_t \right\}_{0\le t<\infty}$
@Did I tagged too much. Thanks For letting me know.
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 $2n-n=n$.