Perturbation analysis of theGI/GI/1 queue

We examine a family ofGI/GI/1 queueing processes generated by a parametric family of service time distributions,F(x,), and we show that under suitable conditions the corresponding customer stationary expectation of the system time is twice continuously differentiable with respect to. Expressions for the derivatives are given which are suitable for single run derivative estimation. These results are extended to parameters of the interarrival time distribution and expressions for the corresponding second derivatives (as well as partial second derivatives involving both interarrivai and service time parameters) are also obtained. Finally, we present perturbation analysis algorithms based on these expressions along with simulation results demonstrating their performance.     

Estimation of Multinomial Probabilities under a Model Constraint

In this paper estimation of the probabilities of a multinomial distribution has been studied. The five estimators considered are: unrestricted estimator (UE), restricted estimator (RE) (under model ), preliminary test estimator (PTE) based on a test of the model , shrinkage estimator (SE) and the positive-rule shrinkage estimator (PRSE). Asymptotic distributions of these estimators are given under Pitman alternatives and the asymptotic risk under a quadratic loss has been evaluated. The relative performance of the five estimators is then studied with respect to their asymptotic distributional risks (ADR). It is seen that neither of the preliminary test and shrinkage estimators dominates the other, though each fares well relative to the other estimators. However, the positive rule estimator is recommended for use for dimension 3 or more while the PTE is recommended for dimension less than 3.     

Measurement scheduling for recursive team estimation

We consider a decentralized LQG measurement scheduling problem in which every measurement is costly, no communication between observers is permitted, and the observers' estimation errors are coupled quadratically. This setup, motivated by considerations from organization theory, models measurement scheduling problems in which cost, bandwidth, or security constraints necessitate that estimates be decentralized, although their errors are coupled. We show that, unlike the centralized case, in the decentralized case the problem of optimizing the time integral of the measurement cost and the quadratic estimation error is fundamentally stochastic, and we characterize the -optimal open-loop schedules as chattering solutions of a deterministic Lagrange optimal control problem. Using a numerical example, we describe also how this deterministic optimal control problem can be solved by nonlinear programming.This research was supported in part by ARPA Grant N00174-91-C-0116 and NSF Grant NCR-92-04419.     

A note on smoothed estimating functions

The kernel estimate of regression function in likelihood based models has been studied in Staniswalis (1989,J. Amer. Statist. Assoc.,84, 276–283). The notion of optimal estimation for the nonparametric kernel estimation of semimartingale intensity (t) is proposed. The goal is to arrive at a nonparametric estimate of ₀=(t ₀) for a fixed pointt ₀ [0, 1]. We consider the estimator that is a solution of the smoothed optimal estimating equation is the optimal estimating function as in Thavaneswaran and Thompson (1986,J. Appl. Probab.,23, 409–417).     

AnL 1 smoothing spline algorithm with cross validation

We propose an algorithm for the computation ofL ₁ (LAD) smoothing splines in the spacesW _M (D), with . We assume one is given data of the formy _i =(f(t _i ) + _i , i=1,...,N with {itt_i} _i=1 ^{N D} , the _i are errors withE( _i )=0, andf is assumed to be inW _M . The LAD smoothing spline, for fixed smoothing parameter0, is defined as the solution,s , of the optimization problem (1/N) _i=1 ^N ¦y _i –g(t _i ¦+J _M (g), whereJ _M (g) is the seminorm consisting of the sum of the squaredL ₂ norms of theMth partial derivatives ofg. Such an LAD smoothing spline,s , would be expected to give robust smoothed estimates off in situations where the _i are from a distribution with heavy tails. The solution to such a problem is a thin plate spline of known form. An algorithm for computings is given which is based on considering a sequence of quadratic programming problems whose structure is guided by the optimality conditions for the above convex minimization problem, and which are solved readily, if a good initial point is available. The data driven selection of the smoothing parameter is achieved by minimizing aCV() score of the form .The combined LAD-CV smoothing spline algorithm is a continuation scheme in 0 taken on the above SQPs parametrized in, with the optimal smoothing parameter taken to be that value of at which theCV() score first begins to increase. The feasibility of constructing the LAD-CV smoothing spline is illustrated by an application to a problem in environment data interpretation.     

New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.     

动力学体系中双组份的协同效应研究及其分析应用

用停流ＦＩＡ－分光光度法研究了铬（Ⅵ）－碘化钾动力学反应体系中铁(Ⅱ)和钒(Ⅳ)的协同诱导效应，以协同系数（Ｄ）表示二者相互作用程度的大小，在此基础上提出了一种新的动力学双组份同时测定的方法，本法可扩大前述方法的线性范围，并降低检测限，测定了模拟水样品中铁和钒的含量，结果满意。     

Self-strengthening and high temperature sintering in binder-free silicon nitride

A thermal strengthening process, which occurs during low-temperature heating of binder-free silicon nitride, has been investigated using simultaneous thermal analysis, dilatometry and FTIR and shown to occur in separate stages over clearly identifiable temperatures. Reactions which give the strengthening are the loss of physically and chemically combined water and the decomposition of ammonium carbonate and various hydrosilicates. Compacts have bend strengths of 8–10 MPa after strengthening at 500°C and 30–34 MPa after strengthening at 900°C. High-temperature dilatometry shows several stages of sintering. The maximum rate occurs at 1800°C with shrinkage commencing at 1450°C. Densities of 98.3% theoretical are obtained on heating to 1900°C.     

光度分析中协同系数补偿方法的研究──三次标准加入法同时测定钼、钨和钛

本文在两次标准加入法[1]的基础上，提出了三组份同时测定的三次标准加入法，并应用于钼、钨和钛的流动注射同时测定。测定条件：［水杨基荧光酮（SAF）］＝1．25　×10-4mol／L，［溴化＋六烷基三甲基铵（CTMAB）」＝2．5×10－3mol／L，pH1．35，25℃，采样、进样时间分别为10s和18s，进样频率128次／h。为消除组份间协同作用引起的吸光度加合性的偏离，定义了三组份协同系数。将其引入三组份同时测定方法，补偿了吸光度对线性的偏离。补偿后钼、钨和钛的测定范围分别为0．05～0．35，0．25～1．00，0．025～0．30mg／L。测定了钢样及模拟样品中钼、钨和钛含量，结果较好。     

The identification of tricyclic neuroleptics and sulphonamides by high-performance thin-layer chromatography

Circular high-performance thin-layer chromatography (HPTLC) has been used to differentiate a series of twelve tricyclic neuroleptics, using both normal phase and reverse phase procedures. The use of normal phase systems also allows the resolution of geometric isomers of chlorprothixene, clopenthixol and flupenthixol. Thirteen sulphonamides and Trirnethoprim may also be distinguished using HPTLC.