Truncated selection procedures for the most probable event and the least probable event

This paper proposes two sequential procedures for selecting respectively the multinomial cell with the largest cell probability and the multinomial cell with the smallest cell probability. The stopping rule for both procedures uses truncation of the procedure studied by Ramey and Alam (1979, Biometrika, 66, 171–173). A property of the least favorable configuration of the proposed procedures is proved, which partially solves a conjecture given in Ramey and Alam (1979). The proposed procedures are compared with other procedures which have been considered in the literature and are found to be better in certain respects.     

Genetic algorithm-based subproblem solution procedures for a modified shifting bottleneck heuristic for complex job shops

In this paper, we consider a modified shifting bottleneck heuristic for complex job shops. The considered job shop environment contains parallel batching machines, machines with sequence-dependent setup times and reentrant process flows. Semiconductor wafer fabrication facilities (Wafer Fabs) are typical examples for manufacturing systems with these characteristics. Our primary performance measure is total weighted tardiness (TWT). The shifting bottleneck heuristic uses a disjunctive graph to decompose the overall scheduling into scheduling problems for single tool groups. The scheduling algorithms for these scheduling problems are called subproblem solution procedures (SSPs). In previous research, only subproblem solution procedures based on dispatching rules have been considered. In this paper, we are interested in how much we can gain in terms of TWT if we apply more sophisticated subproblem solution procedures like genetic algorithms for parallel machine scheduling. We conduct simulation experiments in a dynamic job shop environment in order to assess the performance of the suggested subproblem solution procedures. It turns out that using near to optimal subproblem solution procedures leads in many situations to improved results compared to dispatching-based subproblem solution procedures.     

On the additive splitting procedures and their computer realization

Two additive splitting procedures are defined and studied in this paper. It is shown that these splitting procedures have good stability properties. Some other splitting procedures, which are traditionally used in mathematical models used in many scientific and engineering fields, are sketched. All splitting procedures are tested by using six different numerical methods for solving differential equations. Many conclusions, which are related both to the comparison of the additive splitting procedures with the other splitting procedures and to the influence of the numerical methods for solving differential equations on the accuracy of the splitting procedures, are drawn.     

Efficient on-line estimation of autoregressive parameters

New procedures for estimating autoregressive parameters in AR(m) models are proposed. The proposed method allows for incorporation of auxiliary information into the estimation process and produces estimation procedures, which are consistent and asymptotically efficient under certain regularity conditions. Also, these procedures are naturally on-line and do not require storing all the data. Theoretical results are presented in the case when m = 1. Two important particular cases are considered in detail: linear procedures and likelihood procedures with the LS truncations. A specific example is also presented to briefly discuss some practical aspects of applications of the procedures of this type.     

Parallel Galerkin domain decomposition procedures for wave equation

Parallel Galerkin domain decomposition procedures for wave equation are given. These procedures use implicit method in the sub-domains and simple explicit flux calculation on the inter-boundaries of sub-domains by integral mean method or extrapolation method. Thus, the parallelism can be achieved by these procedures. The explicit nature of the flux prediction induces a time step constraint that is necessary to preserve the stability. L²-norm error estimates are derived for these procedures. Experimental results are presented to confirm the theoretical results.     

Simple linear approximations to the likelihood equation for combining evidence in multiple 2×2 tables: A critique of conventional procedures

Summary The conventional procedures for a common odds ratio in multiple 2×2 tables are explored and critiqued. Three types of linear approximation to the likelihood equations under some models of common measures of association are used to derive the popular conventional estimators and test statistics. Some of them are derived using the model of the common standardized difference which is an unacceptable measure. The derivation provides us with some characteristics of the procedures. The advantages of procedures based on the conditional and unconditional likelihoods are discussed. The Institute of Statistical Mathematics     

Sequential procedures for a class of distributions related to the uniform

Summary The main purpose of this paper is to examine some sequential inference procedures, mainly in the one-sided hypothesis testing situation, for the parameter of a class of distributions related to the Uniform distribution on (0, θ). The procedures are all based on the sequence of maxima of independent and identically distributed random variables and, for the case of a single (upper) boundary, procedures which are optimal in the sense of minimizing the average sample size are discussed. The impossibility of using two boundaries is demonstrated, thus leaving the best procedure with one boundary as the optimal procedure. The novelty of this procedure is that it uniformly minimizes the average sample size.     

Semiparametric statistical inference in global random search

The multivariate multiextremal optimization problem is considered. Various statistical procedures based on the use of the asymptotic theory of extreme order statistics are thoroughly described. These procedures are used to infer about the maximal value of a function by its values at random points. A class of global random search methods underlying the procedures is considered. These methods generalize the well-known branch and bound methods. The article is mainly of a survey nature. It also contains new results.     

Computational approaches to estimation in the principal component analysis of a stochastic process

After performing a review of the classical procedures for estimation in the principal component analysis (PCA) of a second order stochastic process, two alternative procedures have been developed to approach such estimates. The first is based on the orthogonal projection method and uses cubic interpolating splines when the data are discrete. The second is based on the trapezoidal method. The accuracy of both procedures is tested by simulating approximated sample-functions of the Brownian motion and the Brownian bridge. The real principal factors of these stochastic processes, which can be evaluated directly, are compared with those estimated by means of the two mentioned algorithms. An application for estimation in the PCA of tourism evolution in Spain from real data is also included.     

Characterization of limits of Bayes procedures

For the problem of estimating the natural parameter of a p-dimensional exponential family, a characterization of regular limits of Bayes procedures is obtained which generalizes results of Sacks [14], Brown [3], and Berger and Srinivasan [1]. The form is deduced under regularity conditions for the loss function which are more general than squared error. As a corollary it is then stated that the class of procedures with this form is a complete class. The parameter space may be open, and when it is closed, the limits of Bayes procedures are generalized Bayes.     

What one looks for in software for teaching mathematics

The purpose of this article is to delineate procedures for viewing education software intended for use in a mathematics classroom. These procedures are applicable at all levels.     

General communication schemes for multiobjective decision making

In this paper four general communication schemes for multiobjective decision making are presented. The procedures are completely general and make no presumptions about linearity or convexity. Nevertheless, improving bounds on the optimal value are available in each iterative step. Hereby, the procedures model the essential judgements to make and the necessary information to exchange between the decision maker and an analyst in order to make the communication progress. The procedures provide valuable theoretical insight. They also supply a framework for synthesizing known and developing new procedures.     

一类非线性算子的带误差的Ishikawa迭代程序及其稳定性

建立了任意实Banach空间中带误差的Ishikawa迭代程序逼近Lipschitz强伪压缩算子的不动点的一般性定理,指出已被广泛广泛研究的Ishikawa迭代序列的稳定性问题仅是带误差的Ishikawa迭代程序的特例,作为直接的应用,用不同于通常的方法证得任意实Banach空间中的Ishikawa迭代序列关于Lipschitz强伪压缩算子是稳定的,这些推广或发展了近期许多相应的结果。     

Approximation of the initial reserve for known ruin probabilities

An important problem in the study of actuarial risk theory is approximating the probability of ruin within finite time based on a specified initial reserve. In this paper we address the similar, but mathematically different, problem of how to approximate a desired initial reserve given a pre-specified probability of ruin. Although the procedures introduced here have desirable asymptotic properties such as consistency and asymptotic normality, they are computer-intensive and would not have been practicable before the wide spread availability of high-speed computers. The procedures rely on simulated realizations of a general risk process. Thus, they can be used in many of the models of risk processes that appear in the literature such as the Compound Poisson, ARMA and Stochastic Discounting models. Examples of several models are given to demonstrate the versatility of the procedures and to demonstrate that the procedures are computationally feasible.     

Inferences on Correlation Coefficients in Some Classes of Nonnormal Distributions

Correlation coefficients have many applications for studying the relationship among multivariate observations. Classical inferences on correlation coefficients are mainly based on the normality assumption. This assumption is hardly realistic in the real world, which implies that the procedures on correlation coefficients used in many statistical software packages may not be relevant to most data sets in practice. However, we show that the classical procedures, possibly after simple corrections, are also valid in classes of distributions with large skewnesses and heterogeneous marginal kurtoses. A useful class of nonnormal distributions is identified for each of several types of correlation coefficients. The marginals of these distributions may include a variety of univariate distributions with different shapes. The results generalize the classical procedures to much larger classes of distributions than previously known and give a better understanding of the historical controversy regarding the behavior of the sample correlation coefficient. An implication is that one need not be worried so much by the nonnormality of data sets when using these classical procedures, providing simple corrections are evaluated and possibly undertaken.     

计数调整型抽样标准在防毒面具验收中的应用

本文介绍了ＭＦ１１ １２防毒面具计数调整整型抽检方案的制订过程及其使用情况．通过对该方案与我厂防毒面具一直采用的百分比抽检方案的对比分析──抽查特性及平均出厂质量对比、平均样本量对比和方案实施情况对比分析等，阐述了采用调整方案的优越性．     

Economic design of inspection procedures using guard band when measurement errors are present

One of the most important aspects in designing production systems is implementing an adequate inspection procedure to ensure the product quality. Our literature study indicates that two important questions still remain unanswered. First, most of the previous studies on inspection procedures are mainly concerned with how to evaluate and analyze the adequacy of inspection procedures during a production stage. Although the issue of the adequacy of inspection procedures at this point is clearly important, many production processes may better benefit from designing enhanced inspection procedures during an early design stage. Second, the majority of previous studies do not incorporate possible economic impacts of measurement errors when inspection procedures need to be designed. More extensive efforts in designing inspection procedures need to be investigated based on economic considerations. Two approaches, the use of guard band and the selection of inspection precision level, are simultaneously examined for designing economic inspection procedures. By incorporating these two approaches, this paper proposes an optimization scheme for economic design of inspection procedures. A numerical example along with sensitivity analysis demonstrates the applicability of the proposed model.     

Affine-invariant aligned rank tests for the multivariate general linear model with VARMA errors

We develop optimal rank-based procedures for testing affine-invariant linear hypotheses on the parameters of a multivariate general linear model with elliptical VARMA errors. We propose a class of optimal procedures that are based either on residual (pseudo-)Mahalanobis signs and ranks, or on absolute interdirections and lift-interdirection ranks, i.e., on hyperplane-based signs and ranks. The Mahalanobis versions of these procedures are strictly affine-invariant, while the hyperplane-based ones are asymptotically affine-invariant. Both versions generalize the univariate signed rank procedures proposed by Hallin and Puri (J. Multivar. Anal. 50 (1994) 175), and are locally asymptotically most stringent under correctly specified radial densities. Their AREs with respect to Gaussian procedures are shown to be convex linear combinations of the AREs obtained in Hallin and Paindaveine (Ann. Statist. 30 (2002) 1103; Bernoulli 8 (2002) 787) for the pure location and purely serial models, respectively. The resulting test statistics are provided under closed form for several important particular cases, including multivariate Durbin-Watson tests, VARMA order identification tests, etc. The key technical result is a multivariate asymptotic linearity result proved in Hallin and Paindaveine (Asymptotic linearity of serial and nonserial multivariate signed rank statistics, submitted).     

THE FAO PRECAUTIONARY APPROACH AFTER ALMOST 10 YEARS: HAVE WE PROGRESSED TOWARDS IMPLEMENTING SIMULATION‐TESTED FEEDBACK‐CONTROL MANAGEMENT SYSTEMS FOR FISHERIES MANAGEMENT?

ABSTRACT. It is almost ten years since the FAO Technical Consultation on the Precautionary Approach to Capture Fisheries took place in Lysekil, Sweden. One outcome from this Technical Consultation was a set of guidelines on the precautionary approach to capture fisheries and species introductions. These guidelines include the need to incorporate harvest control rules in management plans. Harvest control rules should specify what action is to be taken when specified deviations from the operational targets and constraints are observed. The specification should include minimum data requirements for the types of assessment methods to be used for decision‐making. Combinations of harvest control rules, assessment methods and data collection schemes are referred to as management procedures. It is now well‐recognized that using management procedures is likely to lead to improved conservation of fishery resources, and that they should be evaluated to assess whether they are likely to achieve the goals for fishery management given the types of uncertainties that are likely to frustrate this venture. In general, evaluation of management procedures has been based on simulation modeling. This paper reviews the progress that has been made in various fisheries jurisdictions in terms of implementing management procedures, and why and where it has proved difficult or even impossible to implement management procedures.     

New labeling procedures for the basis graph in generalized networks

Labeling procedures for the basis graph of a generalized network are introduced which build on procedures designed for pure networks. Computational results are presented which show that a primal simplex code which uses these procedures is about 60 times faster than a general purpose linear programming code.