In this paper we consider the problem of making inference on a structural parameter in instrumental variables regression when the instruments are only weakly correlated with the endogenous explanatory variables. Adopting a local-to-zero assumption as in Staiger and Stock (1994) on the coe cients of the instruments in the rst stage equation, the asymptotic distributions of various test statistic...

Principal component analysis (PCA) is commonly used to compute a bounding box of a point set in R. The popularity of this heuristic lies in its speed, easy implementation and in the fact that usually, PCA bounding boxes quite well approximate the minimumvolume bounding boxes. We present examples of discrete points sets in the plane, showing that the worst case ratio of the volume of the PCA bou...

A degree is saturated bounding if it can compute a saturated model for any complete, decidable theory whose types are all computable. All high and PA degrees are saturated bounding (following from results of Jockusch and MacIntyre-Marker.) We show that for every n, no lown c.e. degree is saturated bounding, extending the previous known result that 0 is not saturated bounding, by Millar.

Priority constructions are the trademark of theorems on the recursively enumerable Turing degrees. By their combinatorial patterns, they are naturally identified as finite injury, infinite injury, and so forth. Following Chong and Yang [4], [3], we analyze the complexity of infinite injury arguments and pinpoint exactly the position of their degree-theoretic applications within the hierarchy of...