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Many well-known rank tests can be viewed as score tests under probabilistic index models (PIMs), that is, regression models for the conditional probability that the outcome of one randomly chosen subject exceeds the outcome of another independently chosen subject. PIMs provide a natural regression framework for nonparametric rank tests. In addition, PIMs supplement these tests with effect sizes and ease the development of more flexible tests, such as tests that allow for covariate adjustment. Inferences for PIMs are currently based on an estimator, referred to as the standard estimator, that is derived heuristically. By appealing to semiparametric theory and a Hoeffding decomposition, we rigorously derive the class of all consistent and asymptotically normal estimators for the parameters indexing a PIM. We identify the (locally) semiparametric efficient estimator in this class, and derive a second estimator with a smaller second-order finite-sample bias. The properties of the estimator ....
We have more on a major story tonight the white house refusing to cooperate with any part of the impeachment inquiry. laura coates is who are now. hosting a special hour tonight the white house in crisis: the impeachment inquiry. coming up after this show. so, that letter is pretty am biggous. telling congress, no. what s your take? tonight we ll break down the very letter. the white house sent it to the democrats. refusing to cooperate with the impeachment inquiry. saying it violates fundamental fairness and constitutionally mandated bu process and that s absurd. how can it be the constitution gives the congress the right to impeachment. if you pursue it it s unconstitutional. second they say congress is denying the president the right to cross examine witnesses which means he can t confront the whistleblower the way he wants to. and make his case the to the american people. ....