# A.02.Mahler 1

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1. Credibility vs time shifting parameters
When there are shifting param over time, older years of data should be given substantially less cred than more recent years. There may be only a minimal gain in efficiency from using add'l yrs of data.
2. Testing for shifting parameters over time
• Chi-square: |actual - exp|2/exp, df = n - 1
• Interpretation: x% chance diff obs from same distribution
• Avg Correlation btwn pair of yrs
• Interpretation: look if evolves or not over time
3. Simple methods to derive new estimate
• all weight in mean (Z = 0)
• all weight in latest data (Z = 1)
• X = ZY1 + (1 - Z)Y2
• X = (Z/M)ΣYi + (1-Z)M
• Note: A simplification of a general method is equal or inferior
4. General methods to derive new estimate
• goal is to reflect the fact that most recent yrs have more value
• exponential smoothing: Xj+1 = ZYj + (1-Z)Yj-1 + Z(1-Z)2Yj-2 + ... + (1-Z)nX0
• fully general: Xi+1 = ΣZiXi + (1-Zi)M
• (+) subsumes all other methods
• (-) difficult to select optimal weights
5. Criterias to assess quality of Z
• least square error: smaller the better; max = 75% of prev
• small chance of large error: minimize prob
• Meyers/Dorweiler: correlation btwn (actual/exp) and (pred/avg) → look for evidence that there's no pattern suggesting that larger predictions lead to larger errors
• First 2 methods minimize large errors; 3rd concerned w pattern of error
6. Variance of Data
• between variance: var between risks
• within variace = process var excl shift param + due to s.p.
7. Mahler's approach: baseball vs insurance
• constant set of risks over the period
• data is accurate & final
• same amount of exposure
• grand mean is fixed
8. Credibility of delayed data
Mahler shows that using delayed data substantially increases the squared arror btwn pred & obs. In particular, incr btwn 1 & 2 yrs of separation is dramatic.
 Author: Exam8 ID: 160998 Card Set: A.02.Mahler 1 Updated: 2012-08-14 01:13:44 Tags: credibility least square meyers dorweiler shifting parameters Folders: Description: An example of credibility and shifting risk parameters Show Answers: