Focused information criterion and model averaging for generalized additive partial linear models

We study model selection and model averaging in generalized additive partial linear models (GAPLMs). Polynomial spline is used to approximate nonparametric functions. The corresponding estimators of the linear parameters are shown to be asymptotically normal. We then develop a focused information criterion (FIC) and a frequentist model average (FMA) estimator on the basis of the quasi-likelihood principle and examine theoretical properties of the FIC and FMA. The major advantages of the proposed procedures over the existing ones are their computational expediency and theoretical reliability. Simulation experiments have provided evidence of the superiority of the proposed procedures. The approach is further applied to a real-world data example.Comment: Published in at http://dx.doi.org/10.1214/10-AOS832 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Partial Information Differential Games for Mean-Field SDEs

This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum principle for Nash equilibrium points. Subsequently, under additional assumptions, verification theorem for Nash equilibrium points is also derived. Finally, as an application, a linear quadratic example is discussed. The unique Nash equilibrium point is represented in a feedback form of not only the optimal filtering but also expected value of the system state, throughout the solutions of the Riccati equations.Comment: 7 page

On Weak Topology for Optimal Control of Switched Nonlinear Systems

Optimal control of switched systems is challenging due to the discrete nature of the switching control input. The embedding-based approach addresses this challenge by solving a corresponding relaxed optimal control problem with only continuous inputs, and then projecting the relaxed solution back to obtain the optimal switching solution of the original problem. This paper presents a novel idea that views the embedding-based approach as a change of topology over the optimization space, resulting in a general procedure to construct a switched optimal control algorithm with guaranteed convergence to a local optimizer. Our result provides a unified topology based framework for the analysis and design of various embedding-based algorithms in solving the switched optimal control problem and includes many existing methods as special cases

Research of the active reflector antenna using laser angle metrology system

Active reflector is one of the key technologies for constructing large telescopes, especially for the millimeter/sub-millimeter radio telescopes. This article introduces a new efficient laser angle metrology system for the active reflector antenna of the large radio telescopes, with a plenty of active reflector experiments mainly about the detecting precisions and the maintaining of the surface shape in real time, on the 65-meter radio telescope prototype constructed by Nanjing Institute of Astronomical Optics and Technology (NIAOT). The test results indicate that the accuracy of the surface shape segmenting and maintaining is up to micron dimension, and the time-response can be of the order of minutes. Therefore, it is proved to be workable for the sub-millimeter radio telescopes.Comment: 10 pages, 15 figure