Asymptotic expansions and higher order properties of semi-parametric estimators in a system of simultaneous equations

Asymptotic expansions are made for the distributions of the Maximum Empirical Likelihood (MEL) estimator and the Estimating Equation (EE) estimator (or the Generalized Method of Moments (GMM) in econometrics) for the coefficients of a single structural equation in a system of linear simultaneous equations, which corresponds to a reduced rank regression model. The expansions in terms of the sample size, when the non-centrality parameters increase proportionally, are carried out to O(n⁻¹). Comparisons of the distributions of the MEL and GMM estimators are made. Also, we relate the asymptotic expansions of the distributions of the MEL and GMM estimators to the corresponding expansions for the Limited Information Maximum Likelihood (LIML) and the Two-Stage Least Squares (TSLS) estimators. We give useful information on the higher order properties of alternative estimators including the semi-parametric inefficiency factor under the homoscedasticity assumption.     

Chelation‐Assisted Nickel‐Catalyzed Oxidative Annulation via Double C−H Activation/Alkyne Insertion Reaction

A nickel/NHC system for regioselective oxidative annulation by double C?H bond activation and concomitant alkyne insertion is described. The catalytic reaction requires a bidentate directing group, such as an 8‐aminoquinoline, embedded in the substrate. Various 5,6,7,8‐tetrasubstituted‐N‐(quinolin‐8‐yl)‐1‐naphthamides can be prepared as well as phenanthrene and benzo[h]quinoline amide derivatives. Diarylalkynes, dialkylalkynes, and arylalkylalkynes can be used in the system. A Ni⁰/Ni^II catalytic cycle is proposed as the main catalytic cycle. The alkyne plays a double role as a two‐component coupling partner and as a hydrogen acceptor.     

Boundedness of bilinear pseudo-differential operators with BS0,0m$BS^{m}_{0,0}$ symbols on Sobolev spaces

In this paper, bilinear pseudo-differential operators with symbols in the bilinear Hörmander class $B{S}_{0,0}^m$ are considered. In particular, the boundedness of these operators on Sobolev spaces is established. Our main result is proved by using symbolic calculus and the boundedness of those operators with certain S_{0, 0}-type symbols on Lebesgue spaces.