Відео

Hi Matt, Suppose I have a sample of data that I believe are sampled from a Cauchy distribution. Let's suppose it's symmetrical about 0, so it's Cauchy (0, gamma). However, let's suppose my observations of the underlying Cauchy (0, gamma) are truncated to the relatively limited range (0,2) -- that is, positive values from 0 to 2. All other potential values are not captured in my case. Do you have a way of estimating gamma from this set of limited observations?

Hi can you please share the lecture notes here? In a link ? It will be really helpful

Disgusting

Hi. A question. In the Graybill(1976) book, chapter 6 is called General Linear Model while Chapter 10 is called Multiple Regression. Could you please clarify for me on the difference between general linear model and multiple regression?

Damn man. You're my hero. :')

*Summary* *Parameter Estimation with Backfitting (Part 1/2)* * *Goal:* Estimate parameters in multiple linear regression using only simple linear regression. * *Method:* Backfitting - an iterative process of estimating parameters one at a time while holding others fixed. * *Steps:* 1. *Data Generation (**0:00**):* Create 100 data points with two predictors (X1, X2) and one response variable (Y). 2. *Initialization (**3:00**):* Make an initial guess for one parameter (e.g., beta 1). 3. *Iteration (**3:00**):* * Use the fixed value of beta 1 to estimate beta 2 via simple linear regression. * Fix beta 2 at its new estimate and re-estimate beta 1. * Use both beta 1 and beta 2 to estimate the intercept (beta 0). * Store these estimates and repeat the process for a set number of iterations (e.g., 50). * *Convergence (**6:00**):* The estimates for beta 0, beta 1, and beta 2 converge to the least squares estimates from multiple linear regression after a few iterations. * *Visualization (**8:42**):* The convergence of parameter estimates across iterations can be visualized using a plot. * *Comparison (**9:30**):* The backfitting estimates are shown to be identical to those obtained from directly fitting a multiple linear regression model. *Key takeaway:* Backfitting provides a way to estimate parameters in situations where only simple linear regression tools are available. i used gemini 1.5 pro to summarize the transcript

really interesting, thanks for the video

Your videos are excellent and helped me a lot understanding mathematical statistics. How can I make a one-time donation to your channel?

Your classes were really helpful, Matt! Thanks!

Since the slope could be negative, why do we do a right-side test on the t-statistic? Unless specified shouldn't the two-sided test be the default?

Great video! My only question is what do the new derivations achieve precisely? While they make sense, I don't see how them on their own lead to the conclusion that b0, b1 is normally distributed (that is in a way we couldn't have inferred from them being linear operators?) Was it just a fun exercise, or am I missing something?

Math is not a spectator sport, but your videos is kind of like the closest you can get to that. I got a sheet of paper besides me when a step does not quite make sense, or I want to make sure I understood the rationale, but your explanations make so much sense that I could probably get away with just watching. I still try to derive the important results on my own after watching because it's always good to get that practice in. Thank you a billion.

Great video, limpid explanations!

❤

didn't you only prove in "Derivatives of a Normal Density: Useful Identities" that x^3f(x) from -inf to inf goes to zero for standard normal distributions? if so it wouldn't necessarily apply to non-standard normal distributions

You are my god, literally.

This is wonderful~ Thank you for explaining EM in terms of sufficient statistics!

I really love this series. I told myself to stop getting side tracked and I only came here to study the proof for the parameters of the multi variate gaussian. But oh boy, I never regretted watching these videos.

Please keep making videos of advanced stats! I learned so much from you. Sometime when I can't understand some concepts in my class I can always find some of your videos helpful. Thank you for making these videos and making them available to us.

I've been reading proofs about this chi-square test, and not one of them is written well. Your video is the easiest explanation I've seen so far. It seems to me that the biggest stumbling block is how to deal with the lack of independence in the multinomial distribution. I suppose that's why you created that diagonal matrix.

Thanks boss you are the best!

Hi Matt. A long time subscriber here. Hope you are fine. I have a question → Can we use Helmert transformation to derive chi-square pdf ?

Hi Matt, thank you very much for your videos! Sorry if that's a dumb question, but how is saying that the error terms are i.i.d according to N(0, sigma^2) different from saying E(e_i) = 0 and Var(e_i) = sigma^2?

hi,, in last min around 30:04, you did cancel both g'(ui), however in denumerator has g'(ui)^2 while numerator only g'(ui)...

Hi matt, can you explain why you have witten (n*lambda) to the power {sum xi} in ex1 around 1:31? Thank you for such helpful videos!!

Another thing I just realize: The F statistics should (acc. to you, cf. around 9:35) be identical for RCB with fixed and random treatment effects. However, in this video you wrote F = ((SS_trt)/(a-1))/((SS_E)/((a-1)(b-1)), while in the video #46 in the playlist it is F = (((SS_trt)/sigma²)/(a-1))/(((SS_E)/sigma²)/((a-1)(b-1)). PS: I can also stop writing these things along my way through your playlists.

At 17:30 you said "it becomes a central F distribution, but you've written a chi-square).

thanks alot man

Here is my missing peace i would like to share with thouse who are watyching 6:44 $-\mathbb{E}[\ell'^2]=-\text{Var}(\ell')$ why? We should take a look the Variance definitione. $\text{Var}(\ell')=\mathbb{E}[\ell'^2]-(\mathbb{E}[\ell'])^2$ Since the $(\mathbb{E}[\ell'])^2=(0)^2=0$ Then $\text{Var}(\ell')=\mathbb{E}[\ell'^2]$ I always forget about that property of the variance!

may i ask if on 11:24, in the "there pieace" - haven't we lost the square/second power?

@statisticsmatt sorry for practicine questions under your video. So when you say that MLE theta satisfies the log likelihood first derivative = 0. you mean that - the equation will be equal to 0 once we take first derivative of log likelihood and use the hat theta as argument?

I have a question, at the 8:40 when you talk about the new formula. You in the formulat we have now the $\hat\theta$, and it's now the $\theta^*$ is between $\hat\theta$ and $\theta_0$ My question is - how did we transitioned to the $\hat\theta$? is that connection throught the Note (2)? where the $\hat\theta_{MLE}$ satisfyies the $\ell'(\hat\theta)=0$?

Love your videos so much!! Perfect revision before exams <3

I just love it! manby thanks for sharing this. May I ask you about the the last black square on the page - what is that?. I notice them in other stats book. It's like The End? Thanks

Great video, thanks. Would like to ask please: if in calculating the externally studentized residual for the ith data point, the leverage hii is calculated from a model with all data points (not with ith data point removed)?

this is the best lecture i've ever seen that explains how the factors are mathematically calculated. but couldn't figure out how the lambda are calculated. not clear

Is there a textbook you can recommend that shows these proofs?

A general question in regards to alpha error inflation (maybe you talk about this later on, but I just made it up to here right now): It is usually said that once you perform multiple tests on the same data, you should either reduce the p value or increase the alpha levels. What I don't get is this: Whenever 1 test is performed, you have a chance drawing the correct conclusion (1 - alpha)^(k = 1). Thus, why should one only correct when using same data. Wouldn't it be more plausible to correct whenever a test is performed, This would of course mean that k has to increase with every test performed by a person, and thus a scientist would hardly find and significant results towards the end of her career. Is there a (mathematical) reason for why you only correct if you perform tests on the same data?

I had a assignment to submit explaining minimax test and comparing it with MP, UMP test. After spending weeks searching for a book/ pdf, a friend found your channel and suggested it to me. I am glad to tell you I watched not only the minimax lectures but even beyond my presentation topic. Your delivery was great and I got clarity on earlier topics as well. Thank you

Around 5:20 - 5:30 I think it should be 1/sigma² ~ MNV(1/sigma² hat beta, I). Multiplied by 1/sigma should give sigma I for the variance, or 1/sigma² as coefficients for hat Y and the MVN average, shouldn't it? Nevertheless, great video as always!

Really great job. Appreciate you. Your presentation. Clarity. Thank you.

Hey matt i really love your videos it really helps me a lot. I am currently watching your videos and following casella and berger but don't exactly know which playlists to follow from your channel. Could you please list down the playlists which would align with casella and berger (statistical inference book)

Hi, it was so useful! Thank you for the detailed explanation. Do you have videos related to Quantiles Tests?

I think there's a problem with the FTP site? it gave an error, then I went online and saw they had changed the URL, but that gave an error too. Your videos are very clear to follow along to though without the data. I'm just asking in case I'm doing something wrong.

The website didn't show probabilities (or it was hidden) on the multiplier. I was thinking, "none" is only 1 of 5 options?? Of course I want it multiplied! But yeah, if 2x is more probable than 1x, I guess that's still worth it right?

If someone don't understand the expectation(Alternative Formula) actually it is very easy 4:22 P + P(1-P) + P(1-P)^2 + P(1-P)^3...... The first summation term P(1-P) + P(1-P)^2 + P(1-P)^3...... The second summation term P(1-P)^2 + P(1-P)^3...... The third summation term It just same as x*p*(1-P)^(x-1) x = 1 (the right most first column) x*p*(1-P)^(x-1) x = 2 (the right most second column) if u continue and sum it up it just same as the expectation formula which x > 0

Really like it and could only repeat everything the others already commented ... Please continue!

nice work!

This is a great video Sir but i hardly understand this mapping when looking for the limit of integration. How are the lines drawn and how is the shading done?