"... In PAGE 122: ... Then, the MMSE lter output effective SNR can be computed for each q with (158) so that Lk;q;a = k;q;a 1 k;q;a ; (227) where k;q;a = jzqj2 k 1 + jzqj2 k;q k ; (228) with the correct level energy weighting taken into account by zq = z1 q = 1 (229) z3 q = 2. (230) The de-mapper for the Gray-QPSK is equivalent the the BPSK de-mapper with an input down-scaling, and its output average mutual information can be computed by the func- tional approximation given by (161), so that the utilized approximation parameters are those of the QPSK modulation in Table6 . The result is then two computed level-wise... ..."

"... In PAGE 47: ... Second, one of the algorithms, spectral Galerkin, actually failed to achieve a solution for two of the parameterizations. Third, though it is not evident from Table6 , conventional PEA also fails to meet the accuracy test at least for model (7). Table 4 shows that conventional PEA with N = 3, M = 10,000 and N = 5, M = 50,000 violates our accuracy criterion.... ..."

"... In PAGE 17: ... Therefore the immigrant and nationality indicators are to be inter- preted relative to the native average. Table5 presents the estimation results of the immigrant model in the rst column. As always in the framework of Poisson regressions, the estimated co- e cients can be interpreted as semi-elasticities.... In PAGE 18: ...15 We are most interested in the set of variable immigrant coe cients which is depicted in Figure 2. The un-dotted bands represent the coe cient estimates corresponding to the PML column of the immigrant model in Table5 . Figure 2 contains three interpretable pieces of information: First, over the entire range of fertile years that are possibly spent in Germany the immigrant e ect is positive.... In PAGE 19: ... As described in the methodology section above we developed an estimator that provides correct estimates if the equidispersion assumption is violated. The results based on this penalized quasi-maximum-likelihood estimation (PQML) are presented in the second coe cient column in Table5 . A comparison of the coe cient estimates yields that they are basically not a ected.... In PAGE 19: ...The con dence bands of the PQML estimation are within those derived by the PML estimation. Finally, Table5 provides some information on starting values as well as the nal estimates of the hyperparameters and shows some characteristics of the algo- rithm. The variability parameter Q is estimated slightly higher using the PQML estimation which corresponds to a slightly steeper decline in the immigrant e ect in Figure 2.... In PAGE 19: ... In step two of our empirical analysis we generalize the immigrant model to allow for nation-speci c fertility adjustments. Given the limited e ect of the underdispersion control for the immigrant model, the estimation results presented in the last column of Table5 are derived using the PML estimation. The estimates 16The equidispersion hypotheses is rejected even at a level of 0.... In PAGE 20: ...spent in Germany, hardly di er from those presented in the rst two columns of Table5 . The magnitudes of the coe cient for age increases and those for female schooling degrees fall slightly.... ..."