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# SMAT - Linear Models Course

I have a problem with the 4th lecture, concerning the slide with the graph showing an important covariate left out. I didnt get if on this graph there is or not a linear relationship between x3 and the residuals ? So when should we have included a variable that we did not ? And about the residuals, are they computed with the model or with all the explanatories ? Thank you very much !
Posted by Morgane Ferrara at 16:49
Weighted Least squares for Robust/Resistant estimators

i have a question about the theory. In the WLS estimator (Robust/Resistant), M.Panaretos define

\beta=(X^TV^{-1}X)^{-1}X^TV^{-1}Y

but in the course, when we first define the WLS, we say

\beta=(X^TV^{1}X)^{-1}X^TV^{1}y

hence, why do we have two different definitions? If we define V=diag{w_1, .., w_n} i think the definition \beta=(X^TV^{-1}X)^{-1}X^TV^{-1}Y is not correct?!

Thank's
Posted by Mahé Fellay at 13:11
Some questions

Hi,

I have some problems understanding these parts of the course/exercises

1) In series 12, why is the density of y_j, g(y_j-x_j^T beta), where g() is the denstiy of epsilon_j, my guess would be that y_j-x_j^T beta = epsilon_j but then why do they have different density functions ? Or are they actually the same "modulo a shift" ?

2)On the slides about Robust/Resistent Regression: M-estimation as Weighted Regression : when taking the derivative with respect to gamma, why is there still x_i^T  in the sum with psi, since according to the chain rule we take the transpose of x_i^T ?

Posted by Jean-Claude Ton at 0:13
Fisher information

Hi,

I have a question about the exercise 1 of serie 12. I don't really understand why the variance is the inverse of the fisher information?

Thanks,

Posted by Jad Abou-Moussa at 20:41
Serie 9, Exercice 1

Hello,

I don't understand how to find "la valeur critique de ce test au niveaux 5%" which is 5.32 in the correction ?

And how do we find s^2, "estimateur de la variance pour le modèle complet" to calculate Cp ?

Thanks

Posted by David Jules Froelicher at 9:39

Hello,

In week6, slide 3 page3, when computing delta for the 3 different cases, I don't understand the calculation that results to the bias in the wrong model and to 0 (no bias) for the correct and true model.. What am I missing?

Jérémy

Posted by Jeremy Gotteland at 18:00
Ridge regression
Hi, I don't really understand how you compute the parameter gamma in the Ridge regression (set 7/8/9). I know that it's equivalent to solve the minimization problem, but how can you solve this problem? Thanks, Jad
Posted by Jad Abou-Moussa at 14:21
Anova

Hi,

I'm just wondering if for each step of the anova method we must have independant column to be able to compute the matrix H?

Thanks!

Posted by Jad Abou-Moussa at 21:22
Diagnosing Multicollinearity

Hello! I was checking the course notes and on the slide "More on diagnosing Multicollinearity", we consider the spectral decomposition of the matrix (X^TX), but this matrix isn't always symethric! I'm a bit confused. Thanks in advanced, best wishes,

Agustin

Posted by Agustín Iglesias Villacampa at 15:27
Exercice 1, série 11

Bonjour,

il me semble que lorsque j'utilise la fonction bisquare, ma regression robuste fonctionne. Cependant quand je veux plotter cette regression, je reçois le message d'erreur suivant:

rfit2 <- rlm(calls~year, phones, method="M", psi=psi.bisquare)

plot(rfit2)

Erreur dans lm.influence(x, do.coef = FALSE) :
non-NA residual length does not match cases used in fitting

je ne comprends pas...

Posted by Mahé Fellay at 11:05