Asymptotics of Estimating Equations under Natural Conditions

In a variety of statistical problems one needs to solve an equation in order to get an estimator. We consider the large sample properties of such estimators generated from samples that are not necessarily identically distributed. Very general assumptions that lead to the existence, strong consistency, and asymptotic normality of the estimators are given. A number of results that are useful in verifying the general assumptions are given and an example illustrates their use. General applications to maximum likelihood, iteratively reweighted least squares, and robust estimation are discussed briefly.     

中立型时滞系统的时滞相关鲁棒控制

研究了一类具有时变时滞中立型系统的时滞相关鲁棒控制问题.利用Lyapunov-K rasovsk ii泛函方法,借助于积分不等式,得到了系统经无记忆状态反馈控制后可镇定的时滞相关条件.最后给出数值例子验证了所得结果的有效性.     

Testing several nonnested regressions simultaneously. A nonparametric approach

A test for the problem of choosing between several nonnested nonlinear regression models simultaneously is presented. The test does not require an explicit specification of a parametric family of distributions for the error term and has a closed form.     

Limit theorems for the median deviation

Summary In this paper, we obtain a strong law and central limit theorem for the median deviation under only very mild smoothness conditions on the underlying distribution. Under an additional condition implied by symmetry, we derive a weak Bahadur representation for the median deviation and establish the asymptotic equivalence of the median deviation and the semi-interquartile range.     

Robust inverse optimal control for flexible structures

An inverse optimal control problem is formulated to develop robust control laws for purely oscillatory systems. The optimal control solution requires output feedback with specified constraints, leading to robustness with respect to unmodeled modes and a large class of parameter variations. The robustness properties are proved directly from known properties of control laws resulting from quadratic performance indices. The control laws are useful for poorly damped flexible structures.This research was supported by the Office of Naval Research, Contract No. N00014-77-C-0247.     

Detection of multivariate outliers with location slippage or scale inflation in left orthogonally invariant or elliptically contoured distributions

This paper is concerned with two kinds of multiple outlier problems in multivariate regression. One is a multiple location-slippage problem and the other is a multiple scale-inflation problem. A multi-decision rule is proposed. Its optimality is shown for the first problem in a class of left orthogonally invariant distributions and is also shown for the second problem in a class of elliptically contoured distributions. Thus the decision rule is robust against departures from normality. Further the null robustness of the decision statistic which the rule is based on is pointed out in each problem.     

Convergence of a recursive robust algorithm with strongly regular observations

Robust estimation of parameters may be obtained via stochastic approximation algorithms. This paper deals with the properties of a recursive estimator of a location parameter in a stationary strongly regular process. Adaptive estimators of particular interest are also studied.     

Decentralized robust control for a class of uncertain large-scale interconnected nonlinear dynamical systems

The problem of the decentralized robust control for a class of large-scale interconnected nonlinear dynamical systems with input interconnection and external interconnection perturbations is considered. Based on the stabilizability of each nominal isolated subsystem (i.e., the isolated subsystem in the absence of interconnection perturbations), a class of decentralized local state feedback controllers is proposed, and some sufficient conditions are derived by making use of the Lyapunov stability criterion such that uncertain large-scale interconnected systems can be stabilized asymptotically by these decentralized state feedback controllers. For large-scale systems with only input interconnection perturbations, such decentralized controllers become a class of decentralized stabilizing state feedback controllers. That is, the decentralized stability of such large-scale systems can be guaranteed always by using the decentralized state feedback controllers proposed in the paper. Finally, a numerical example is given to demonstrate the validity of the results.     

Fitting a Normal Distribution When the Model is Wrong

The paper discusses a likelihood based method of estimation which allows for a small amount of misspecification in the assumption of normality. Asymptotic results suggest that the new method can give an estimated model which is closer to the true model. An application to hearing threshold data is discussed.     

Distributionally robust inference for extreme Value-at-Risk

Under general multivariate regular variation conditions, the extreme Value-at-Risk of a portfolio can be expressed as an integral of a known kernel with respect to a generally unknown spectral measure supported on the unit simplex. The estimation of the spectral measure is challenging in practice and virtually impossible in high dimensions. This motivates the problem studied in this work, which is to find universal lower and upper bounds of the extreme Value-at-Risk under practically estimable constraints. That is, we study the infimum and supremum of the extreme Value-at-Risk functional, over the infinite dimensional space of all possible spectral measures that meet a finite set of constraints. We focus on extremal coefficient constraints, which are popular and easy to interpret in practice. Our contributions are twofold. First, we show that optimization problems over an infinite dimensional space of spectral measures are in fact dual problems to linear semi-infinite programs (LSIPs) – linear optimization problems in Euclidean space with an uncountable set of linear constraints. This allows us to prove that the optimal solutions are in fact attained by discrete spectral measures supported on finitely many atoms. Second, in the case of balanced portfolia, we establish further structural results for the lower bounds as well as closed form solutions for both the lower- and upper-bounds of extreme Value-at-Risk in the special case of a single extremal coefficient constraint. The solutions unveil important connections to the Tawn–Molchanov max-stable models. The results are illustrated with two applications: a real data example and closed-form formulae in a market plus sectors framework.