Incorporating support constraints into nonparametric estimators of densities

Let f_n ^? (x) be the usual Parzen-Rosenblatt kernel estimator of the pdf f of a random variable X based on a sample X₁,…,X_n from X.In many practical applications,it is knownt hat X>c and/or X<d for given constants c and d.Additionally, one might know the values of(c)and/or f(d).“mirrorimage”and“tieddown”modifications of f_n ^?incorporate this additional information into an estimator f_n which has support [c,d].This estimatoris interpreted in a manner which allows one to use most of the known convergence properties of kernel estimates in studying the behavior of f_n.     

Attitudes toward lesbians, gay men, bisexual women, and bisexual men in Germany

Attitudes toward lesbians, gay men, bisexual women, and bisexual men were assessed in a national representative sample of 2,006 self-identified heterosexual women and men living in Germany. Replicating previous findings, younger people held more favorable attitudes than older people; women held more favorable attitudes than men; and men held more favorable attitudes toward female than male homosexuality, whereas women did not differentiate. However, women held more favorable attitudes toward homosexuals than toward bisexuals, whereas men did not differentiate. Knowing a homosexual person was an important predictor of attitudes, as was political party preference. Both same-sex and opposite-sex sexual attraction were substantially related with attitudes. Our findings support the notion that attitudes toward lesbians, gay men, bisexual women, and bisexual men are related but distinct constructs.     

Benchmarks derived from quantitative endpoints - an approach accounting for litter effects

The use of quantitative variables for risk assessment suffers from the lack of a clear-cut definition of risk. The proposals of Chen and Gaylor (1992) and of Kodell and West (1993) showed a way out of this dilemma. Additional risk is defined as the increase in probability of being in an abnormal state for an exposed individual. In this paper we show how this approach can be generalized to situations where an additional source of variability, often called litter effect, is present. This occurs often in studies on teratogenicity. The coverage of confidence bounds on the additional risk is shown to be sufficient using a small simulation study.