Asymptotic Tail Properties of Student's t-Distribution

We investigate the asymptotic behavior of the probability density function (pdf) and the cumulative distribution function (cdf) of Student's t-distribution with ν > 0 degrees of freedom (t _ν for short) for ν tending to infinity when the argument x = x _ν of the pdf (cdf) depends on ν and tends to ± ∞ (?∞). To this end, we consider the ratio of the pdf's (cdf's) of the t _ν- and the standard normal distribution. Depending on the choice of the argument x _ν, the pdf-ratio (cdf-ratio) tends to 1, a fixed value greater than 1, or to ∞. As a byproduct, we obtain a result for Mill' ratio when x _ν → ?∞.     

Produktrückgaben und Preise im Versandhandel: Ein internationaler Vergleich

E-Commerce sales have been constantly rising over the past years. Among the reasons for this trend are advantages such as reduced search costs and low transaction costs for the buyer. A disadvantage of online shopping is that customers cannot inspect the product they buy online. In Germany, customers are entitled to get full refund when withdrawing from any distance selling. Customers can withdraw from a contract within two weeks without any explanation. Many retailers in the USA do not refund the full price to the customer in case of product return and charge restocking fees. A reason for such a restrictive return policy is the reduction of opportunistic product returns. In this paper, the authors compare prices in online-shops for identical products in the USA and Germany. The comparison shows that the alleged consumer protection achieved by a legal prohibition of restocking fees leads to higher average prices for electronic products in Germany.     

Randomized p-values for multiple testing of composite null hypotheses

We are considered with the problem of m simultaneous statistical test problems with composite null hypotheses. Usually, marginal p-values are computed under least favorable parameter configurations (LFCs), thus being over-conservative under non-LFCs. Our proposed randomized p-value leads to a tighter exhaustion of the marginal (local) significance level. In turn, it is stochastically larger than the LFC-based p-value under alternatives. While these distributional properties are typically nonsensical for m  =1, the exhaustion of the local significance level is extremely helpful for cases with m>1$m>1$ in connection with data-adaptive multiple tests as we will demonstrate by considering multiple one-sided tests for Gaussian means.     

Soziale Ungleichheiten beim Schulstart

Although there is a regular age of school entry in Germany, some children start school later than usual and some children start ahead of schedule. While there has been some decrease in delayed school entries in the last years, the rate of premature school entry has increased substantially. Paradoxically, while the delayed entry is primarily because professionals rate a child as not ready for school, the premature entry is mainly based on parents’ choice. The first aim of the paper is to discover whether kindergarten attendance can reduce the risk of a delayed entry. The arguments and hypotheses are mainly based on the theory on the ecology of human development of Bronfenbrenner. The empirical analyses demonstrate that low educated families profit most by kindergarten attendance, but only if the child begins attending the care institution before reaching age four. The second aim concerns considerations in regard to the decision of prematurely entering school. Socio-economic conditions are not as important at this point as compared with a delay in school entry. However, there are some effects indicating that higher educated parents foster a premature entry to elementary schools. The analyses are based on over 1.400 children in the relevant age group and their parents taking part in the large nationwide German Socio-Economic Panel Study (SOEP).