Complete Statistics
Вставка
- Опубліковано 21 вер 2024
- Here we provide the definition of a complete statistic and go over 2 examples.
Error: XIAO WEI pointed out the following, the notation in the parenthesis should be (x^2+mu^2) instead of (x^2-mu^2). Many thanks.
###############
If you'd like to donate to the success of my channel, please feel free to use the following PayPal link. $15, $10, $5 or other is fine! Many thanks in advance. Matthew
P.S. You may need to copy and paste into your browser.
paypal.me/statisticsmatt Help this channel to remain great! Donating to Patreon or Paypal can do this!
/ statisticsmatt
paypal.me/stat...
You're a hero my dude.
Thanks for kind words. Much appreciated. Many thanks for watching. Don't forget to subscribe and let others know about this channel.
ty 4 this king
Many thanks for watching! Don't forget to subscribe and let others know about this channel.
Can you please try for normal (0, ksigma^2) is complete statistic.
As a reminder, any distribution in the exponential family is complete, which normal(0,ksigma^2) is a part of. Many thanks for watching. Don't forget to subscribe and let others know about this channel.
@@statisticsmattthank you so much
Many thanks for watching!
hello. I heavily utilized your videos for my mathematical statistics course so first I wanted to thank you. for the first example I think you used the leibniz's rule for integration but since lower bound is zero we get the initial function. if there were theta in the lower boundary aswell would we get another function ? this might cause confusion for audience. (atleast it did for me).
You're words are spot on. Much appreciated. Many thanks for watching. Don't forget to subscribe and let others know about this channel.
thank you for a very helpful video. should the notation in the parenthesis be (x^2+mu^2) instead of (x^2-mu^2)
yes, you are correct. Many thanks for pointing this out. Much appreciated. Don't forget to subscribe and let others know about this channel. I've added your name in the description for finding this error.
Is the first example correct? At most you can say g is zero almost everywhere with respect to the Lebesgue measure on (0,inf). I think you need more to conclude that g(X_{(n)}) is almost surely zero
In regards to your question, here is a math stack exchange that helps answer your question. math.stackexchange.com/questions/2185822/if-integral-is-zero-then-function-is-zero-almost-everywhere
Many thanks for watching. Don't forget to subscribe and let others know about this channel.
Hi Matt, i dont get the part of bilateral transform since the previous step there is also a term exp{mu*x/(sigma^2)}
by the way, is there suggested resources to learn laplace transform and two-side laplace transform? i was introduced in my intro signal processing course but did not go in depth but i did use it to solve some improper integrals conveniently
Think of f(x)= exp{mu*x/(sigma^2) when using the definition of the Laplace transform. Here is link to a math.stackexchange.com page that may be helpful to you.
Many thanks for watching. Don't forget to subscribe and let others know about this channel.
is there suggested resources to learn laplace transform and two-side laplace transform? @@statisticsmatt
may I ask what is the intuitive interpretation of a complete statistic?
I have read many interpretations of a complete statistic and all fall short of being intuitive to me. However, some explanations are better than others. Keep trying to find the best explanation for you. Here are a few on "stat-exchange". stats.stackexchange.com/questions/53107/meaning-of-completeness-of-a-statistic stats.stackexchange.com/questions/196601/what-is-the-intuition-behind-defining-completeness-in-a-statistic-as-being-impos
A sufficient statistic T for some parameter t is said to be complete if it is the only function of T that estimates t unbiasedly. Also, those functions in consideration need to be measurable (to avoid functions varying discontinuously in single points).
An unbiased estimator of 0 is 0 itself
How to prove that x(n)(max xi) is complete for discrete uniform distribution?
Did your professor give you any hints?
No, no hints. I spend some time on it. Turned out that I was using the 'pdf' for order statistic (continous).I realized later that pmf for x(n) has to be used and then I was able to come about it. It proved to be a complete statistic using induction. Thank You for responding though.🙂
@@sirjankaur7594 so glad that you were able to solve the problem. Many thanks for watching and don't forget to subscribe.
Do you have any videos where you show a statistic is not complete?
Here's a pdf that has examples where the statistic is not complete. ani.stat.fsu.edu/~debdeep/complete.pdf I hope that this helps.
@@statisticsmatt that was very helpful, thank you!
Do you have any videos that could help me if I have a X1,X2,...Xn random variables from N(\theta,1), How can I prove that, \bar{x} is complete, but it's not suficient for this family?
First, x(bar) is sufficient theta. Use the Neyman-Fisher factorization theorem to show it.
@@statisticsmatt there’s a question, more precisely on Shao’s book chapter 2, number 45, that ask me to prove that xbar is complete but not sufficient. I already use the factorization theorem, but I can’t see this affirmation of shao’s book. I always prove that xbar is complete and suficiente.
Interesting. Unfortunately I don't have access to Shao's book to see the problem at hand.
Is this the book you are referring to? www.mim.ac.mw/books/Mathematical%20statistics%202nd%20edition.pdf
@@statisticsmatt it’s this one! On page 148, exercise 45.
Hi I am supposed to write a term paper on complete statistics for theory of estimation
Is this what I should write ?
Yes, this is the theory of complete statistics. Many thanks for watching. Don't forget to subscribe and let others know about this channel.
When you finish your term paper, please link it to this comment. I'd love to read it.
Hi, your content is amazing but the quality of the videos can somewhat improve. Thanks!
Thanks for your kinds words. Much appreciated. Your comment about the quality of the videos is my number one complaint. At some point I'll switch to a digital format. Just don't know when. Many thanks for watching. Don't forget to subscribe and let others know about this channel.