Chapter 5 Testing the Assumptions of Age-to-Age Factors - G. Venter

Definitions and standards used for Venter

• \(n\), \(m\), \(p\)

  • \(\star\) The \(n\) excludes the first column

  • Important for implication 2 counting parameters for adj SSE

• \(\star\) Project incremental losses, \(q(w,d+1)\) here

  • Column parameter \(f(d)\) is LDF - 1

\(\star \star\) Goodness of fit measure:

• Adj SSE (5.1)

• AIC (5.2)

• BIC (5.3)

6 testable implications

1. Statistical significance of factors

   • Coefficient \(> 2 \sigma\) is significant

2. \(\star \star\) Is there a better estimate for \(q\) than \(f \times c\)

   • Number of parameters (Table 5.3)

   • Counting parameters

   • \(\star \star\) BF parameters (Table 5.4)

   • Iteration process

3. Check residuals against \(c(w,d-1)\)

4. Stability of \(f(d)\) down the column

5. \(\star \star\) No correlation among columns

   • Remember we are testing \(f(d)\) so LDF - 1

   • Pearson correlation calculation (5.4) and test statistics (5.5)

   • To test for all different pairs (not just adjacent pairs) (5.6)

   • Similar to Mack’s adjacent LDF test

6. No particularly high or low diagonals

   • Setting up regression with CY dummy variable (5.7)