Using pseudometrics in kernel density estimation

Common kernel density estimators (KDE) are generalised, which involve that assumptions on the kernel of the distribution can be given. Instead of using metrics as input to the kernels, the new estimators use parameterisable pseudometrics. In general, the volumes of the balls in pseudometric spaces are dependent on both the radius and the location of the centre. To enable constant smoothing, the volumes of the balls need to be calculated and analytical expressions are preferred for computational reasons. Two suitable parametric families of pseudometrics are identified. One of them has common KDE as special cases. In a few experiments, the proposed estimators show increased statistical power when proper assumptions are made. As a consequence, this paper describes an approach, where partial knowledge about the distribution can be used effectively. Furthermore, it is suggested that the new estimators are adequate for statistical learning algorithms such as regression and classification.     

Public transfers and marital dissolution

In this paper, we analyze determinants of marital dissolution, focusing on the alleged influences from public transfers, child allowance, and child support awards. We use a Norwegian panel of 2,806 couples with information on public and private transfers in cases of divorce. The sample was observed over a 5-year period, with the purpose of registering marital dissolution. We find that the level of transfers has a significantly positive effect on divorce probability and that the distribution of transfers in favor of the wife increases this probability. Our findings are consistent with noncooperative family models allowing for inefficient outcomes.

Income effects of divorce in families with dependent children

The Norwegian post-divorce transfer scheme for families with children guarantees minimum maintenance payments from the non-custodial to the custodial parent. We studied the economic effects of divorce in such families. When the mother has custody, she falls behind before maintenance payments. After adding these, the outcomes at the median are very similar for both parents, contrasting studies from other countries, but the risk of a drop in equivalized income is large.