Local central limit theorems, the high-order correlations of rejective sampling and logistic likelihood asymptotics

Let I_1,...,I_n be independent but not necessarily identically distributed Bernoulli random variables, and let X_n=\sum_{j=1}^nI_j. For \nu in a bounded region, a local central limit theorem expansion of P(X_n=EX_n+\nu) is developed to any given degree. By conditioning, this expansion provides information on the high-order correlation structure of dependent, weighted sampling schemes of a population E (a special case of which is simple random sampling), where a set d\subset E is sampled with probability proportional to \prod_{A\in d}x_A, where x_A are positive weights associated with individuals A\in E. These results are used to determine the asymptotic information, and demonstrate the consistency and asymptotic normality of the conditional and unconditional logistic likelihood estimator for unmatched case-control study designs in which sets of controls of the same size are sampled with equal probability.Comment: Published at http://dx.doi.org/10.1214/009053604000000706 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Negotiate or Litigate? Effects of WTO Judicial Delegation on U.S. Trade Politics

Goldstein and Steinberg argue that the World Trade Organization Appellate Body has been able to use its authority to engage in judicial lawmaking to reduce trade barriers in ways that would not otherwise have been possible through negotiation. This lawmaking authority was not the result of a purposeful delegation; rather, it was an unintended byproduct of the creation of an underspecified set of rules and procedures. There is nevertheless a high rate of compliance with Appellate Body decisions because decentralized enforcement can induce domestic importers to lobby for trade liberalization. In the US, this judicial lawmaking may also allow the President to achieve trade policies that are more liberal than those desired by Congress, if compliance can be achieved by a regulatory change or by sole Executive action