Abstract This is a short survey about asymptotic properties of a supercritical branching process (Z_{n}) with immigration in a stationary and ergodic or independent and identically distributed random environment. We first present basic properties of the fundamental submartingale (W_{n}) , about...

Valid instrumental variables must be relevant and exogenous. However, in practice it is difficult to find instruments that are exogenous in that they satisfy the knife-edged orthogonality condition and at the same time are strongly correlated with the endogenous regressors. In this paper we show...

This paper shows how valid inferences can be made when an instrumental variable does not perfectly satisfy the orthogonality condition. When there is a mild violation of the orthogonality condition, the Anderson and Rubin (1949) test is oversized. In order to correct this problem, the...

In this paper, we obtain the optimal rate of convergence in the central limit theorem for m-dependent U-statistics under mild conditions, which is similar to that in the independent rv's.