Rate of consistency of one sample tests of location

Let X₁,…,X_n be a sample from a population with continuous distribution function F(x?θ) such that F(x)+F(-x)=1 and 0<F(x)<1, x?R¹. It is shown that the power- function of a monotone test of H: θ=θ₀ against K: θ>θ₀ cannot tend to 1 as θ?θ₀ → ∞ more than n times faster than the tails of F tend to 0. Some standard as well as robust tests are considered with respect to this rate of convergence.     

Second order asymptotic relations of M-estimators and R-estimators in two-sample location model

Let T_M be an M-estimator (maximum likelihood type estimator) and T_R be an R-estimator (Hodges-Lehmann's estimator) of the shift parameter Δ in the two-sample location model. The asymptotic representation of √N(T_M-T_R) up to a term of the order O_p(N^{-$\text{1}\text{4}$}) is derived which is valid if the functions Ψ and ? generating T_M and T_R, respectively, decompose into an absolutely continuous and a step-function components; the order O_p(N^{-$\text{1}\text{4}$}) cannot be improved unless the discontinuous components vanish. As a consequence, the conditions under which √N(T_M-T_R)=O_p(N^{-$\text{1}\text{4}$}) are obtained. The main tool for obtaining the results is the second order asymptotic linearity of the pertaining linear rank statistics which is proved here under the assumption that the score-generating function ? has some jump-discontinuities.     

Who's Who in Networks. Wanted: The Key Player

Finite population noncooperative games with linear‐quadratic utilities, where each player decides how much action she exerts, can be interpreted as a network game with local payoff complementarities, together with a globally uniform payoff substitutability component and an own‐concavity effect. For these games, the Nash equilibrium action of each player is proportional to her Bonacich centrality in the network of local complementarities, thus establishing a bridge with the sociology literature on social networks. This Bonacich–Nash linkage implies that aggregate equilibrium increases with network size and density. We then analyze a policy that consists of targeting the key player, that is, the player who, once removed, leads to the optimal change in aggregate activity. We provide a geometric characterization of the key player identified with an intercentrality measure, which takes into account both a player's centrality and her contribution to the centrality of the others.     

Measuring policy entitlements at the micro-level: maternity and parental leave in Europe

Comparative social policy analysis has been shaped by the measurement of policy as a macro phenomenon. However, social policy theories have consistently asserted that policy entitlements vary across class, gender, ethnicity and the life-course. This paper synthesises a number of innovations to produce an approach which allows researchers to explore the policy heterogeneity within populations, across populations and over time. Using the example of maternity and parental leave, policy entitlements are identified through the calculation of financial support an individual would receive if they were to have a child, using a combination of legislative rules with representative survey sample. The results reveal far greater heterogeneity in policy entitlements than existing indicators suggest, with considerable implications for research on maternity and parental leave. This approach is not limited to maternity and parental leave benefits and demonstrates a way to explore comparative social policy in greater depth and detail.     

The impact of high-stakes school admission exams on study achievements: quasi-experimental evidence from Slovakia

We explore whether and to what extent the presence of high-stakes admission exams to selective schools affects student achievement, presumably through more intensive study effort. Our identification strategy exploits a quasi-experimental feature of a reform in Slovakia that shifted the school grade during which high-stakes exams are taken by 1 year. This reform enables us to compare students at the moment when they pass these exams with students in the same grade 1 year ahead of the exams. Using data from the low-stakes international TIMSS skills survey and employing difference-in-difference methodology, we find that the occurrence of high-stakes admission exams increased 10-year-old students’ math test scores by 0.2 standard deviations, on average. This effect additionally accrues by around 0.05 standard deviations among students with the highest probability of being admitted to selective schools. Although we find similar effects for both genders, there are indications that high-stakes exams in more competitive environments affect girls more than boys.