Mahler 1 - Credibility and Shifting Risk Parameters

Question 1

3 Criteria for evaluating credibility weighting

Answer 1

1. Lease square error
   - minimizes the squared error between observed and predicted results
   - the smaller MSE, the better
2. Small chance of large errors
   - minimizes the probability that observed results will be greater than k% different from predicted.
3. correlation
   - calculate correlation between
4. ratio of actual losing % to predicted losing % and
5. ratio of predicted losing % to grand mean
   - closer to 0, the better

Question 2

three methods for testing risk parameter shift

Answer 2

1. Binomial test
   - determine whether there is an inherent difference in losing % among the teams
   - if all teams results are from a random distribution, 95% of the teams would have an average losing % between 49% and 51%.
   - only 3 of 16 teams did
2. Chi-squared
   - Null: risk parameters do not shift over time
   - Chi statistic = Sum[(actual - expected) ^2/expected]
   - to test if there is a inherent difference in results over the years (i.e. are parameters shifting over time?)
   - if statistic > chi-squared value => reject null
3. Study of correlation pairs
4. group data by pairs based on time lag
5. compute correlation between actual and expected for each pair
6. calculate avg correlation by time lag
   c. Exam correlation by lag pattern.
   - if correlation decreases as the difference in time between the years increases => parameters are shifting over time.

Question 3

Effect of a delay in receiving data

Answer 3

1. as delay increases, the squared error increases significantly
2. as delay increases, optimal credibility decreases

Question 4

Contrasting Meyers/Dorweillers method vs LSE & small chance of large errors

Answer 4

1. both least square and small chance of large errors method seek to eliminate large errors
2. Meyers/Dorweiller method is more concerned with patterns of error.

Question 5

The estimate gets worse or better when more years of data are used when parameters shift over time.

Answer 5

worse