Diagnostic checking for multivariate regression models

Diagnostic checking for multivariate parametric models is investigated in this article. A nonparametric Monte Carlo Test (NMCT) procedure is proposed. This Monte Carlo approximation is easy to implement and can automatically make any test procedure scale-invariant even when the test statistic is not scale-invariant. With it we do not need plug-in estimation of the asymptotic covariance matrix that is used to normalize test statistic and then the power performance can be enhanced. The consistency of NMCT approximation is proved. For comparison, we also extend the score type test to one-dimensional cases. NMCT can also be applied to diverse problems such as a classical problem for which we test whether or not certain covariables in linear model has significant impact for response. Although the Wilks lambda, a likelihood ratio test, is a proven powerful test, NMCT outperforms it especially in non-normal cases. Simulations are carried out and an application to a real data set is illustrated.     

Diagnostic checking for conditional heteroscedasticity models

We suggest the score type tests for goodness-of-fit of conditional heteroscedasticity models in both univariate and multivariate time series. The tests can detect the alternatives converging to the null at a parametric rate. Weight functions are involved in the construction of the tests, which provides us with the flexibility to choose scores, especially under directional alternatives, for enhancing power performance. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of alternatives. A possibility to construct score-based omnibus tests is discussed when the alternative is saturated. The power performance is also investigated. A simulation study is carried out and a real data is analyzed.     

Probability models for access security system architectures

This paper presents probability models of access control security system architectures. Access control is the process of screening objects; for example people, baggage, entering a secured area in order to detect and prevent entry by threats such as unauthorized personnel, firearms, explosives. A security system architecture consists of device technologies, as well as operational policies and procedures for utilizing the technologies. The probability models are developed based on Type I (a false alarm is given) and Type II (a threat is not detected) errors. The concept of controlled sampling, in which objects may take different paths through the system, is introduced. New architectures consisting of multiple devices and controlled sampling are proposed and analyzed. The results presented indicate that for specific threat levels, multiple-device systems can be identified which outperform single-device systems for certain error probability measures.     

Model checking for partially linear models with missing responses at random

In this paper, we investigate the model checking problem for a partial linear model while some responses are missing at random. By imputation and marginal inverse probability weighted methods, two completed data sets are constructed. Based on the two completed data sets, we build two empirical process-based tests for examining the adequacy of partial linearity of the model. The asymptotic distributions of the test statistics under the null hypothesis and local alternative hypotheses are obtained respectively. A re-sampling approach is applied to obtain the approximation to the null distributions of the test statistics. Simulation results show that the proposed tests work well and both proposed methods have better finite sample properties compared with the complete case (CC) analysis which discards all the subjects with missing data.     

A bootstrap approach to model checking for linear models under length-biased data

In this paper, we propose two bootstrap-based model checking tests for a parametric linear model when data are affected by length-bias. These tests are based on the measure of the discrepancy between nonparametric and parametric estimators for the regression function when the data are drawn under a length-biased mechanism. We consider two different discrepancy measures: the supremum and the integral of the quadratic difference between the parametric and nonparametric estimators.     

Efficient algorithms for checking the equivalence of programs in interrupt handling models

The problem of equivalence of interrupt handling programs in two algebraic models is studied. Program operators are divided into two classes, namely, the classes of basic operators and interrupt handling operators. The first model obeys the absorption law, i.e., each basic operator suppresses the result of application of any interrupt handling operator. This means that, if the interrupt handling is successfully finished and the control is passed to basic operators, then the result of interrupt handling has no influence on the program output. An algorithm that solves the problem of equivalence in the above model in O(n ²log n) operations is suggested. The other model obeys the absorption law and satisfies the commutative property for basic operators. For this model, we also propose an algorithm that checks the equivalence of programs in O(n ⁴log n) operations.     

Optimal control for supply network models: adjoint calculus

We consider a PDE based supply network model with controllable nodes for which we derive an optimal control problem and present an adjoint-based solution technique. The supply network has two basic building blocks: The dynamics in a supplier is governed by a PDE and the behavior inside a queue is described by an ODE. The network model provides a framework to couple these equations at nodes. We introduce controls at so-called dispersing nodes and discuss suitable cost functionals leading to optimal control problems which we solve by a projected gradient method. The gradient information can be obtained from adjoint equations which we derive in the context of our supply network model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

带有固定效应且n和T都很大的动态面板模型的诊断检验

研究了动态面板数据模型的诊断检验问题.对于带有固定个体效应且n和T都很大的的动态面板数据模型,通过残差的一阶差分构造了一个人工自回归模型,并基于该自回归模型系数的最小二乘估计构造了一个检验统计量检验模型的充分性.研究表明在一定的假设条件下,该检验渐近服从卡方分布,计算简单方便.模拟实验结果表明该检验表现很好.     

Independence issues in imprecise data models: A bayesian approach

A non-precise data problem is defined as a two-stage hierarchical model. The question considered in this Note is to explore some theoretical and practical problems involving independence and/or conditional independence relations among the parameters and the data. We present some results in this direction.     

Computational issues in parameter estimation for stationary hidden Markov models

The parameters of a hidden Markov model (HMM) can be estimated by numerical maximization of the log-likelihood function or, more popularly, using the expectation–maximization (EM) algorithm. In its standard implementation the latter is unsuitable for fitting stationary hidden Markov models (HMMs). We show how it can be modified to achieve this. We propose a hybrid algorithm that is designed to combine the advantageous features of the two algorithms and compare the performance of the three algorithms using simulated data from a designed experiment, and a real data set. The properties investigated are speed of convergence, stability, dependence on initial values, different parameterizations. We also describe the results of an experiment to assess the true coverage probability of bootstrap-based confidence intervals for the parameters.     

Equivalent models for finite-fuel stochastic control

A stochastic control problem with finite-fuel constraint, of the type studied by Bene?, Shepp and Witsenhausen (1980), is solved explicitly. It is shown to be reducible to “simpler” stochastic optimization problems, such as optimal stopping and singular control for Brownian motion with unlimited fuel.     

Simple models for control of epidemics

This study considers the problem of resource allocation between one or several epidemics by reference to a model involving both the stochastic and the geographical nature of the spread of the disease. In the simplest models each epidemic spreads amongst a single line of populations and is controlled to minimize the expected number infected. For these we find that the optimal policy is to treat the population which is immediately at risk, and that if there is more than one epidemic it is optimal to treat the fastest moving epidemics first. Some more realistic models are also briefly discussed.     

Optimal control for supply network models: Mixed integer programming

The aim of our investigations is the optimization of a continuous model for a special class of supply networks. We focus on the underlying fundamentals and show the relation to mixed-integer programming. This is done by applying numerical discretization schemes to the dynamics of the continuous equations and by approximations to the cost functional. One benefit of the MIP model is the adaptivity to real-world situations by adding reasonable extensions such as bounded queues. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Monotonicity and bounds for convex stochastic control models

We consider a general convex stochastic control model. Our main interest concerns monotonicity results and bounds for the value functions and for optimal policies. In particular, we show how the value functions depend on the transition kernels and we present conditions for a lower bound of an optimal policy. Our approach is based on convex stochastic orderings of probability measures. We derive several interesting sufficient conditions of these ordering concepts, where we make also use of the Blackwell ordering. The structural results are illustrated by partially observed control models and Bayesian information models.     

Nonlinear and bilinear models for chemical reactor control

The dynamic behavior of a continuously stirred tank reactor (CSTR) with an exothermic reversible reaction is studied. The balance equations of the reaction lead to a set of highly nonlinear differential equations. For system analysis and control synthesis the dynamic equation are rewritten as state space model. From this nonlinear model a bilinear model is derived. Then, two optimization problems are solved: The time optimal problem for the nonlinear model and the quadratic problem for the bilinear model. In case of the finite time bilinear-quadratic problem a modified Riccati approximation algorithm for a stabilizing feedback controller is presented.     

Mathematical models and control for systems with segregation

We consider mathematical models and optimal control problems for systems that consist of a large number of uncontrolled aggregates and an environment interacting with them. The evolution of each aggregate is described by an ordinary differential equation with a random parameter; the evolution of the environment is defined by the averaged interaction with aggregates and the values of control parameters. We obtain optimality conditions and develop an approach to the calculation of the distribution densities of the residence time of aggregates in the system.     

Hopf bifurcation control in the XCP for the Internet congestion control system

In this paper, we investigated the Hopf bifurcation of the eXplicit Control Protocol (XCP) for the Internet congestion control system. These bifurcation behaviors may cause heavy oscillation of average queue length and induce network instability. A time-delayed feedback control method was proposed for controlling Hopf bifurcation in the XCP system. Numerical simulation results are presented to show that the time-delayed feedback controller is efficient in controlling Hopf bifurcation.     

Multi-stage stochastic fluid models for congestion control

We consider multi-stage stochastic fluid models (SFMs), driven by applications in telecommunications and manufacturing in which control of the behavior of the system during congestion may be required. In a two-stage SFM, the process starts from Stage 1 in level 0, and moves to Stage 2 when reaching threshold _b2$b_2$ from below. Stage 1 starts again when reaching threshold _b1<_b2$b_1<b_2$ from above. While in a particular stage, the process evolves according to a traditional SFM with a unique set of phases, generator and fluid rates. We first consider a two-stage SFM with general, real fluid change rates. Next, we analyze a two-stage SFM with an upper boundary B>_b2$B>b_2$. Finally, we discuss a generalization to multi-stage SFMs. We use matrix-analytic methods and derive efficient methodology for the analysis of this class of models.     

Structural results for partially observed control models

A general partially observed control model with discrete time parameter is investigated. Our main interest concerns monotonicity results and bounds for the value functions and for optimal policies. In particular, we show how the value functions depend on the observation kernels and we present conditions for a lower bound of an optimal policy. Our approach is based on two multivariate stochastic orderings: theTP ₂ ordering and the Blackwell ordering.Dedicated to Prof. Dr. K. Hinderer on the occassion of his 60^th birthday     

Optimal greedy policies for stochastic control models

We introduce the notion of a greedy policy for general stochastic control models. Sufficient conditions for the optimality of the greedy policy for finite and infinite horizon are given. Moreover, we derive error bounds if the greedy policy is not optimal. The main results are illustrated by Bayesian information models, discounted Bayesian search problems, stochastic scheduling problems, single-server queueing networks and deterministic dynamic programs.