Detecting fuzzy relationships in regression models: The case of insurer solvency surveillance in Germany

We develop a test for the fuzziness of regression coefficients based on the Tanaka et al. (1982) and He et al. (2007) possibilistic fuzzy regression models. We interpret the spread of the regression coefficients as a statistic measuring the fuzziness of the relationship between the corresponding independent variable and the dependent variable. We derive test distributions based on the null hypothesis that such spreads could have been obtained by estimating a possibilistic regression with data generated by a classical regression model with random errors. As an example, we show how our test detects a fuzzy regression coefficient in a solvency prediction model for German property-liability insurance companies.     

Reactions of 9-substituted guanines with bromomalondialdehyde in aqueous solution predominantly yield glyoxal-derived adducts

Reactions of 9-ethylguanine, 2'-deoxyguanosine and guanosine with bromomalondialdehyde in aqueous buffers over a wide pH-range were studied. The main products were isolated and characterized by (1)H and (13)C NMR and mass spectroscopy. The final products formed under acidic and basic conditions were different, but they shared the common feature of being derived from glyoxal. Among the 1 : 1 adducts, 1,N(2)-(trans-1,2-dihydroxyethano)guanine adduct (6) predominated at pH < 6 and N(2)-carboxymethylguanine adduct (10a,b) at pH > 7. In addition to these, an N(2)-(4,5-dihydroxy-1,3-dioxolan-2-yl)methylene adduct (11a,b) and an N(2)-carboxymethyl-1,N(2)-(trans-1,2-dihydroxyethano)guanine adduct (12) were obtained at pH 10. The results of kinetic experiments suggest that bromomalondialdehyde is significantly decomposed to formic acid and glycolaldehyde under the conditions required to obtain guanine adducts. Glycolaldehyde is oxidized to glyoxal, which then modifies the guanine base more readily than bromomalondialdehyde. Besides the glyoxal-derived adducts, 1,N(2)-ethenoguanine (5a-c) and N(2),3-ethenoguanine adducts (4a-c) were formed as minor products, and a transient accumulation of two unstable intermediates, tentatively identified as 1,N(2)-(1,2,2,3-tetrahydroxypropano)(8) and 1,N(2)-(2-formyl-1,2,3-trihydroxypropano)(9) adducts, was observed.