Multiplicative Least Squares weights (nij)

[Maitre_Absolut]

For the iterative formula for Xi

Felblum's article has the weight's squared on the numerator and denominator

CSM has the weight squared on the denominator only. (probably a typo)

All 10 has no squares on either weights.

Feldblum's formula assumes SSE = SS (NijRij - NijXiYj)^2

All 10's assumes SSE = SS Nij (Rij - XiYj)^2

Naturally i would trust the articles forumla (Felblums), but Q #1 1994 has All10's formula as the answer, with reference to Brown.

So i guess Brown used All 10's version of the SSE, and Feldblum has updated that formula in his article?

EDIT: i just read the Errata....ok for the Mult Least Squares, but now the X squared SSE formulas have the weight inside the square....why hasnt he corrected this formula?

[frank_exams]

The second formula has the right weights; the first is incorrect.
(Think of each exposure as an independent observation.)

[Maitre_Absolut]

The second formula has the right weights; the first is incorrect.
(Think of each exposure as an independent observation.)

So how come the same logic isnt applied with the X squared bias function?

[frank_exams]

So how come the same logic isnt applied with the X squared bias function?

In fact, it is: The weight for each element in the sum is wij. Look on p.35, there's a typo listed in the errata for the formula on that page. There should be a wij^2 on the top and a wij on the bottom. These cancel and the weight given to each "error" is wij.

Frank

[LouisTheCat]

I have a different question about the Nij. Let's say you're given incurred losses, earned premiums, and current relativities (a la #45, 2002). We know the correct weights are based on the earned premiums, but should these be adjusted for current relativities or not? I notice the CAS accepted both approaches, but it seems to me that only one of these should be considered correct (or, to be precise, optimal, since this is really a question of credibility weights). Thoughts?

[3tac]

Yes, you should adjust for the current relativities. If not, you are neglecting to reflect them in your loss costs or loss ratios and therefore not getting the complete picture.