Least sq additive

[ed999]

for that question, i simply set up the ESS formula

something like

[1000-200-X1-Y1]^2 + ... ... ... (three more terms)

anybody? I also stated the formula per Feldblum's paper

and partial derivatives need to be taken... to solve.

[GefilteFish144]

Was glad they didn't ask us to solve it all the way thru -- really screwed me on last year's exam.

[Avi]

Same. (200 + M + U - 1000)²… Then take partials w.r.t. each of the four variables, set equal to 0, four equations, four unknowns.

[Me3]

Um, maybe I am missing something, but isn't least squares additive recursive equation (from p. 53 after applying errata):

xi = sumj(nij*(rij-yj)) / sumj(nij) - B

which does not involve any terms that are squared? (This was the same minimum bias function in last year's 5.5 point question, #21.)

[Ullico]

you're all correct. setting up (OBS - base - x - y)^2 and taking partial derivatives gives you those recursive equations (least squares additive boils down to a weighted average with the exposures being the weights incidentally)

[Avi]

I made the decision not to memorize any of the recursion relations, and to approach everything from first principles. Prevents confusion and frees my brain up for other fascinating pieces of information like basic premium components. Or so my theory went

[KindGrind]

I memorize all formulas, including the "oh so horrible" X squared additive...

I wonder if I will get credit if I explained the whole process, and plugged directly the recursive formula...

[Avi]

Thankfully, they said not to solve

[Me3]

Originally Posted by Avi

I made the decision not to memorize any of the recursion relations, and to approach everything from first principles. Prevents confusion and frees my brain up for other fascinating pieces of information like basic premium components. Or so my theory went

I realize that the syllabus stated that we did not have to memorize formulas, but I also rememberd that they asked a question last year for which it would have been helpful to have memorized the formula. (How else do you ask a decent minimum bias question?) So I decided to memorize them. But I realized that although the reading presented them as 9 different, sometimes pretty complicated, formulas, they really boil down to 5, of which I only memorized 4: 3 easy and one semi-difficult.

(The one I refused to memorize was the chi-squared additive, because I had realized during studying that I did not know how to use it (meaning that I could not use it to duplicate the numbers in the table on p. 39).)

[The following order follows the reading: balance, least square, chi-square, MLE (NEP: Normal Exponential, Poisson)]:

The balance ones were the simplest to understand and memorize. They were basically the same except that the multiplicative effectively did x=r/y and the additive did x=r-y -- both with n as the weights.

Next, Least squares: The multiplicative was the same as the balance mult, with an extra y in the numerator and denominator. The additive was the same as the balance additive with an extra -B at the end.

Chi squareed Multiplicative: memorized using brute force. (Remember, for all of the recursive equations there is a reasonableness check you can do to check if you are missing a y or an r: if you remove the summation signs and ignore subscripts, the multiplicative ones boil down to x=r/y.)

MLE:
normal: mult. same as least squares; add. same as balance.

exponential:mult. memorize: simply straight average of the r/y's. (no additive)

poisson: mult. same as balance. (no additive)

So the 4 actual formulae to memorize were 3 easy ones (balance mult & add, and MLE exponential mult) and one semi-difficult one (chi-square mult). Just needed to remember the mappings of the others to these with very simple adjustments for the 2 least squares.

[Avi]

Originally Posted by Me3

I realize that the syllabus stated that we did not have to memorize formulas, but I also rememberd that they asked a question last year for which it would have been helpful to have memorized the formula. (How else do you ask a decent minimum bias question?) So I decided to memorize them. But I realized that although the reading presented them as 9 different, sometimes pretty complicated, formulas, they really boil down to 5, of which I only memorized 4: 3 easy and one semi-difficult.

…

So the 4 actual formulae to memorize were 3 easy ones (balance mult & add, and MLE exponential mult) and one semi-difficult one (chi-square mult). Just needed to remember the mappings of the others to these with very simple adjustments for the 2 least squares.

On the other hand, my reasoning went, if you memorized first principles, there was only ONE thing to know, and NO formulæ and that was how to set p the equations. The rest is just plug-and-chug. While one's chance of careless arithmetic error increases, one will never be confused as to the r's, n's, x's and such and which appears in the numerator and which in the denominator.

De gustibus non est disputatum.

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