Asymptotically optimal estimation of smooth functionals for interval censoring, part 1

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. The asymptotic information lower bound for such functionals can be represented as an inner product of two functions. In case 1, i.e. one observation time per unobservable event time, both functions can be given explicitly. We mainly consider case 2, with two observation times for each unobservable event time, in the situation that the observation times can not become arbitrarily close to each other. For case 2, one of the functions in the inner product can only be given implicitly as solution to a Fredholm integral equation. We study properties of this solution and, in a sequel to this paper, prove that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

On sequential comparisons of means of first-order autoregressive models

The problem of estimating a linear combination,μ, of means ofp-independent, first-order autoregressive models is considered. Sequential procedures are derived (i) to estimateμ pointwise using the linear combination of sample means, subject to a loss function (squared error plus cost per observation), and (ii) to arrive at a fixed-width confidence interval forμ. It is observed that in the case of point estimation we do not require a sampling scheme, where as in the case of interval estimation we do require a sampling scheme and a scheme similar to the one given in Mukhopadhyay and Liberman (1989) is proposed. All the first order efficiency properties of the sequential procedures involved here are derived. This paper is an extension of results of Sriram (1987) involving one time series to multiple time series. Research supported by AFOSR Grant number 89-0225.     

Optimal stopping rules for multinomial observations

Many times sampling from a known or an unknown population results in observations that are integers and there is a payoff which depends on the observations. Thus, the experimenter is tempted to continue sampling in the hope of increasing his payoff. On the other hand, usually each observation costs a fixed amount and thus the experimenter also is reluctant to continue sampling because each additional sample increases the total sampling cost. The problem is to determine a place to stop making observations such that thenet payoff is a maximum. This paper considers stopping rules which will maximize the net payoff to the experimenter when the observations come from a multinomial population.     

Asymptotic linearity of minimax estimators

The celebrated local asymptotic minimax (LAM) theorem due to HÁjek (1972) also includes the statement that a LAM estimator Is necessarily asymptotically linear. A similar result. is true for semi-parametric models, but Hájek's result doesn't apply to this case as the efficient influence function is often not contained in the (proper) tangent space. This note gives a simple, elementary proof of both the LAM theorem and the necessity of asymptotic linearity of a LAM estimator sequence.     

Mixed-effects models for health care longitudinal data with an informative visiting process: A Monte Carlo simulation study

Electronic health records are being increasingly used in medical research to answer more relevant and detailed clinical questions; however, they pose new and significant methodological challenges. For instance, observation times are likely correlated with the underlying disease severity: Patients with worse conditions utilise health care more and may have worse biomarker values recorded. Traditional methods for analysing longitudinal data assume independence between observation times and disease severity; yet, with health care data, such assumptions unlikely hold. Through Monte Carlo simulation, we compare different analytical approaches proposed to account for an informative visiting process to assess whether they lead to unbiased results. Furthermore, we formalise a joint model for the observation process and the longitudinal outcome within an extended joint modelling framework. We illustrate our results using data from a pragmatic trial on enhanced care for individuals with chronic kidney disease, and we introduce user-friendly software that can be used to fit the joint model for the observation process and a longitudinal outcome.     

水位原始观测实现“三遍手”的方法

随着科学技术的发展,水位原始观测在不增加人力及很大投资的情况下可以实现真正意义上的"三遍手",保证水位观测成果的质量。     

Revealed preference theory on the choice of lotteries

The choice behavior of a decision-maker is said to be consistent with expected utility maximization if there exists a utility function defined on the set of prizes such that the decision-maker chooses lotteries with the highest expected utility. We present a revealed preference characterization of choice behavior that is consistent with expected utility maximization. A necessary and sufficient condition for expected utility maximization is that there does not exist a way to compound lotteries such that the probability distribution over the final prizes generated by the chosen lotteries of each observation is equal to that generated by the rejected lotteries of each observation. Our result is quite general and can be applied to any compact set of prizes and any choice correspondence.     

Efficiency of iterated WLS in the linear model with completely unknown heteroskedasticity

Iterated weighted least squares (IWLS) is investigated for estimating the regression coefficients in a linear model with symmetrically distributed errors. The variances of the errors are not specified; it is not assumed that they are unknown functions of the explanatory variables nor that they are given in some parametric way.
IWLS is carried out in a random number of steps, of which the first one is OLS. In each step the error variance at time t is estimated with a weighted sum of m squared residuals in the neighbourhood of t and the coefficients are estimated using WLS. Furthermore an estimate of the co-variance matrix is obtained. If this estimate is minimal in some way the iteration process is stopped.
Asymptotic properties of IWLS are derived for increasing sample size n . Some particular cases show that the asymptotic efficiency can be increased by allowing more than two steps. Even asymptotic efficiency with respect to WLS with the true error variances can be obtained if m is not fixed but tends to infinity with n and if the heteroskedasticity is smooth.     

Sequential estimation of a location parameter and powers of a scale parameter from delayed observations

The problem of sequentially estimating a location parameter and powers of a scale parameter is considered in the case when the observations become available at random times. Certain classes of sequential estimation procedures are derived under an invariant balanced loss function and with the observation cost determined by a convex function of the stopping time and the number of observations up to that time.     

On the convergence of moments of geometric and harmonic means

The moments of the geometric mean of n independent and identically distributed random variables are shown to converge as n→∞. Rates of convergence are determined for the first moment and the variance. The results relate to recent work on long term investment returns when yearly rates of return are randomly varying. Application is made to moments of the harmonic mean.     

Modelling of repairable systems with various degrees of repair

The availability of a stochastic repairable system depends on the failure behaviour and on repair strategies. In this paper, we deal with a general repair model for a system using auxiliary counting processes and corresponding intensities which include various degrees of repair (between minimal repair and perfect repair). For determining the model parameters we need estimators depending on failure times and repair times: maximum likelihood (ML) estimator and Bayes estimators are considered. Special results are obtained by the use of Weibull-type intensities and random observation times.     

电子水准仪和Excel在+255沉降观测中的应用

电子水准仪提高了水准测量的外业速度,同时也提高了测量数据的精度、效率;减轻了测量外业人员的劳动强度。在内业处理时,使用Excel做处理,快速准确的计算出各个观测点在不同观测日期时的高程值,并且通过Excel计算出各个观测的沉降值。根据各个观测点高程值、累计沉降值通过Excel做出各个点的沉降与时间关系图,无需人工作图。根据做出的沉降时间关系图,对沉降做出分析。     

Effective observation of random processes using derivatives

Metrika - What are optimal observation times of a random process to obtain good prediction or good estimation of the (parametric) trend? In the presented paper we discuss especially the following...     

医学论文资料的获取之管见

目的:针对医学生撰写医学论文中普遍感到资料匮乏这一现状,探寻并指导医学论文资料积累的方法,为撰写医学论文做前期准备。方法:通过细致观察,对科研工作进行真实记录,获取直接资料;通过查阅古今中外文献,获取间接资料。结果:在日常工作和学习中学会积累,获取大量的医学资料,确保医学论文的真实、准确、科学。结论:为医学生提供积累医学资料方法,养成在日常工作学习中累积材料的习惯,提高撰写医学论文的水平。     

Scheduling of re-entrant flow shops

We propose and develop a scheduling system for a very special type of flow shop. This flow shop processes a variety of jobs that are identical from a processing point of view. All jobs have the same routing over the facilities of the shop and require the same amount of processing time at each facility. Individual jobs, though, may differ since they may have different tasks performed upon them at a particular facility. Examples of such shops are flexible machining systems and integrated circuit fabrication processes. In a flexible machining system, all jobs may have the same routing over the facilities, but the actual tasks performed may differ; for instance, a drilling operation may vary in the placement or size of the holes. Similarly, for integrated circuit manufacturing, although all jobs may follow the same routing, the jobs will be differentiated at the photolithographic operations. The photolitho-graphic process establishes patterns upon the silicon wafers where the patterns differ according to the mask that is used.The flow shop that we consider has another important feature, namely the job routing is such that a job may return one or more times to any facility. We say that when a job returns to a facility it reenters the flow at that facility, and consequently we call the shop a re-entrant flow shop. In integrated circuit manufacturing, a particular integrated circuit will return several times to the photolithographic process in order to place several layers of patterns on the wafer. Similarly, in a flexible machining system, a job may have to return to a particular station several times for additional metal-cutting operations.These re-entrant flow shops are usually operated and scheduled as general job shops, ignoring the inherent structure of the shop flow. Viewing such shops as job shops means using myopic scheduling rules to sequence jobs at each facility and usually requires large queues of work-in-process inventory in order to maintain high facility utilization, but at the expense of long throughput times.In this paper we develop a cyclic scheduling method that takes advantage of the flow character of the process. The cycle period is the inverse of the desired production rate (jobs per day). The cyclic schedule is predicated upon the requirement that during each cycle the shop should perform all of the tasks required to complete a job, although possibly on different jobs. In other words, during a cycle period we require each facility to do each task assigned to it exactly once. With this requirement, a cyclic schedule is just the sequencing and timing on each facility of all of the tasks that that facility must perform during each cycle period. This cyclic schedule is to be repeated by each facility each cycle period. The determination of the best cyclic schedule is a very difficult combinatorial optimization problem that we cannot solve optimally for actual operations. Rather, we present a computerized heuristic procedure that seems very effective at producing good schedules. We have found that the throughput time of these schedules is much less than that achievable with myopic sequencing rules as used in a job shop. We are attempting to implement the scheduling system at an integrated circuit fabrication facility.     

Asymptotic non-deficiency of the Bayes sequential estimation in a family of transformed Chi-square distributions

Bayes sequential estimation in a family of transformed Chi-square distributions using a linex loss function and a cost c > 0 for each observation is considered in this paper. It is shown that an asymptotic pointwise optimal rule (A.P.O.) is asymptotically non-deficient, i.e., the difference between the Bayes risk of the A.P.O. rule and the Bayes risk of the optimal procedure is of smaller order of magnitude than c, the cost of single observation, as c → 0.     

The advantage of avoiding the Armington assumption in multi-region models

Most computable general equilibrium models that describe interactions between multiple regions employ the so-called Armington assumption that goods that are produced in different regions are imperfect substitutes for each other. The paper describes an alternative algorithm based on the assumption of perfect substitutability that accommodates the observation that each region produces all traded goods. For models with many regions and less-that-perfectly mobile factors, the alternative algorithm greatly reduces convergence time. The algorithm is illustrated by comparing two static multi-region models of the 50 U.S. states and the District of Columbia, with and without the Armington assumption. The model without the Armington assumption is then extended to a dynamic 51-region model with agents that have perfect foresight over 6 periods.     

析东方管理之治国理政观

中国传统文化源远流长，博大精深。经历千百年来的荡涤和演进，逐步形成群体本位、家庭中心、伦理倾向、重情重义等基本特征。与这些文化特征相适应，演化和编织出亲缘、地缘、商缘、文缘和神缘的“五缘”文化网络结构，在国家治理与社会管理中发挥着协调局部、统筹整体的功能。东方管理治国理政观正是立足于、脱胎于和超越于这一文化传统的现代政府管理理论。东方管理理论与西方管理理论互为补充、相辅相成，必将为世界管理的发展作出贡献。     

Parcel distribution timetabling problem

In this paper we propose a model to generate an effective timetable for time definite parcel distribution companies operating a hierarchical hub-and-spoke network. The model, referred to as parcel distribution timetabling problem, provides the departure times from each serviced city and each servicing facility in order to minimize the travel times of all shipments from their origin cities to their destination cities. Although the problem is faced by every parcel distribution company, it is rarely addressed in the literature. There is no evidence that parcel distribution companies, including the international ones, are developing operational research models in generating their timetables. The application of the model to a real-world case led to a decrease of more than 11% in the average travel time of the shipments. The company was even more delighted by the rapidity of the model in generating the timetable; this task that used to take weeks is decreased to just minutes.