Then, fourth, you need a collection of statistics on risks, and you need to evaluate the quality of those statistics.
Further, we find that our primary results obtain only in ABS deals with above-median risk layering in the underlying assets, for which pool-level summary statistics of credit risk metrics (e.g., pool-level average borrower FICO scores) are less informative, and with above-median complexity in the tranching of credit risk.
The test statistics of AR, Risk Difference (RD) and CK were calculated and summarised in accordance with methods described in the standard texts [ 24- 26].
To test for the significance of differences between AIC values, between weighted ROC curves, and between C statistics of different risk models, we used the rescaling bootstrap method of Cheng et al. (36) and Rao et al. (37) that takes into account the complex survey design by changing the sampling weights for each resample.
The following information was extracted from each included study: journal name, title of the article, date of publication, study design, source of funding, information about primary and secondary end points, method for assessment of significance (p values, CI or descriptive statistics), and assessment of risk of bias and risk of random error.
We apply exponential tilts to (i) the distribution of the natural sufficient statistics of the systematic risk factors and (ii) conditional default probabilities, given the simulated values of the systematic risk factors, and select parameter values by minimizing the Kullback Leibler divergence of the resulting parametric family from the ideal (zero-variance) importance density.
Two formulations of HL statistics exist, depending on whether the statistics are derived using fixed deciles of risk, Ĥ-statistics, or by partitioning observations into equal sized groups according to their predicted probabilities, Ĉ-statistics.
Even with about 2,000 guests a year now at the Wiegele resort, these statistics suggest a level of risk significantly higher than that of big North American ski resorts.
More basic has been the failure of risk statistics to remain constant over time.
