A two-stage minimax procedure with screening for selecting the largest normal mean (ii): an improved pcs lower bound and associated tables

This paper is a follow-up to an earlier article by the authors in which they proposed a two-stage procedure with screening to select the normal population with the largest population mean when the populations have a common known variance. The two-stage procedure has the highly desirable property that the expected total number of observations required by the procedure is always less than the total number of observations required by the corresponding single-stage procedure of Bechhofer (1954), regardless of the configuration of the population means. The present paper contains new results which make possible the more efficient implementation of the two-stage procedure. Tables for this purpose are given, and the improvements achieved (which are substantial) are assessed.     

On the mean past lifetime of the components of a parallel system

In the study of reliability of the technical systems and subsystems, parallel systems play a very important role. In the present paper, we consider a parallel system consisting of n identical components with independent lifetimes having a common distribution function F. It is assumed that at time t the system has failed. Under these conditions, we obtain the mean past lifetime (MPL) of the components of the system. Some properties of MPL are studied. It is shown that the underlying distribution function F can be recovered from the proposed MPL. Also, a comparison between two parallel systems are made based on their MPLs in the case where the components of the system are ordered in terms of reversed hazard rate. Finally a characterization of the uniform distribution is given based on MPL.     

Kullback-leibler information approach to the optimum measurement point for bayesian estimation

When an appropriate parametric model and a prior distribution of its parameters are given to describe clinical time courses of a dynamic biological process, Bayesian approaches allow us to estimate the entire profiles from a few or even a single observation per subject. The goodness of the estimation depends on the measurement points at which the observations were made. The number of measurement points per subject is generally limited to one or two. The limited measurement points have to be selected carefully. This paper proposes an approach to the selection of the optimum measurement point for Bayesian estimations of clinical time courses. The selection is made among given candidates, based on the goodness of estimation evaluated by the Kullback-Leibler information. This information measures the discrepancy of an estimated time course from the true one specified by a given appropriate model. The proposed approach is applied to a pharmacokinetic analysis, which is a typical clinical example where the selection is required. The results of the present study strongly suggest that the proposed approach is applicable to pharmacokinetic data and has a wide range of clinical applications.     

Reliabilities of a single-unit system with multi-phased missions

ABSTRACT

Phased-mission systems (PMS) can be widely found in a lot of practical application areas. Reliability evaluations and analysis for this kind of systems become important issues. The reliability of PMS is typically defined as the probability that the system successfully accomplishes the missions of all phases. However, the k-out-of-n system success criterion for PMS has not been investigated. In this paper, according to this criterion, we develop two new models, which are static and dynamic, respectively. The assumptions for these two models are described in detail as well. The system reliabilities for both models are presented for the first time by employing finite Markov chain imbedding approach (FMCIA). In terms of FMCIA, we define different state spaces for the two models, and transition probability matrices are obtained. Then some numerical examples are given to illustrate the application of FMCIA. Finally, some discussions are made and conclusions are summarized.     

Maximum correlation for the generalized Sarmanov bivariate distributions

In order to improve the correlation of the traditional Sarmanov distribution, a ‘generalized’ version was introduced earlier by Bairamov et al. (2001). The extent of the improvement in correlation, however, was never investigated in the literature. In this note we compare the two Sarmanov models regarding their maximum correlation. Several examples are given. It is shown that unlike the traditional Sarmanov, the generalized one always has a correlation approaching one regardless of the marginals, as long as the marginals are of the same type. When they are not of the same type, however, the correlation has an upper bound strictly less than one. We find conditions under which the upper bound is attained. Finally, we investigate the rates of convergence to the maximum correlation for the generalized Sarmanov bivariate distributions.     

Perturbed robust linear estimating equations for confidentiality protection in remote analysis

National statistical agencies and other data custodians collect and hold a vast amount of survey and census data, containing information vital for research and policy analysis. However, the problem of allowing analysis of these data, while protecting respondent confidentiality, has proved challenging to address. In this paper we will focus on the remote analysis approach, under which a confidential dataset is held in a secure environment under the direct control of the data custodian agency. A computer system within the secure environment accepts a query from an analyst, runs it on the data, then returns the results to the analyst. In particular, the analyst does not have direct access to the data at all, and cannot view any microdata records. We further focus on the fitting of linear regression models to confidential data in the presence of outliers and influential points, such as are often present in business data. We propose a new method for protecting confidentiality in linear regression via a remote analysis system, that provides additional confidentiality protection for outliers and influential points in the data. The method we describe in this paper was designed for the prototype DataAnalyser system developed by the Australian Bureau of Statistics, however the method would be suitable for similar remote analysis systems.     

A Simple Diagnostic Plot Connecting Robust Estimation, Outlier Detection, and False Discovery Rates

Robust estimation of parameters, and identification of specific data points that are discordant with an assumed model, are often treated as different statistical problems. The two aims are, however, closely inter-related and in many cases the two analyses are required simultaneously. We present a simple diagnostic plot that connects existing robust estimators with simultaneous outlier detection, and uses the concept of false discovery rates to allow for the multiple comparisons induced by considering each point as a potential outlier. It is straightforward to implement, and applicable in any situation for which robust estimation procedures exist. Several examples are given.     

Some properties of hazard rate functions of systems with two components

In this paper we compare the hazard rate functions of two parallel systems, each of which consists of two independent components with exponential distribution functions. The paper gives various conditions under which there exists a hazard rate ordering between the two parallel systems. It is also shown that some of these conditions are both sufficient and necessary. In particular, it is proven that if the vector consisting of the two hazard rates of the two exponential components in one parallel system weakly supmajorizes the counterpart of the other parallel system, then the first parallel system is greater than the second parallel system in the hazard rate ordering. This paper further compares the hazard rate functions of two parallel systems when both systems have components following a certain bivariate exponential distribution.     

Calibration and refinement for classification trees

The calibration of forecasts for a sequence of events has an extensive literature. Since calibration does not ensure ‘good’ forecasts, the notion of refinement was introduced to provide a structure into which methods for comparing well-calibrated forecasters could be embedded.In this paper we apply these two concepts, calibration and refinement, to tree-structured statistical probability prediction systems by viewing predictions in terms of the expected value of a response variable given the values of a set of explanatory variables. When all of the variables are categorical, we show that, under suitable conditions, branching at the terminal node of a tree by adding another explanatory variable yields a tree with more refined predictions.     

Nonparametric conditional mean imputation

Imputation is a much used method for handling missing data. It is appealing as it separates the missing data part of the analysis, which is handled by imputation, and the estimation part, which is handled by complete data methods. Most imputation methods, however, either rely on strict parametric assumptions or are rather ad hoc in which case they often only work approximately under even stricter assumptions. In this paper a non-parametric imputation method is proposed. Since it is non-parametric it works under quite general assumptions. In particular, a model for the complete data is not required in the imputation step, and the complete data method used after the imputation may be a general estimating equation for estimating a finite-dimensional parameter. Large sample results for the resulting estimator are given.     

Estimation of the transition behaviour of term structures of interest rates

The current prices and interest rate sensitivities of interest rate derivatives depend on the stochastic behaviour of future term structures of interest rates. In this paper we present an arbitrage-free trinomial model to characterize possible changes of interest rates. This model is used to estimate the transition behaviour of term structures of interest rates in the German bond market. Research support from the Deutsche Forschungsgemeinschaft under the project Bu 671-2 within the Schwerpunktprogramm “Empirische Kapitalmarktforschung” is gratefully acknowledged. Comments by the editor, G. Bamberg, on an earlier version of this paper are very much appreciated.     

A micro analysis of the macro differences in refusal risk among metropolitan areas. The case of the Italian multipurpose survey

Although still modest, non response rates in multipurpose household surveys have recently increased, especially in some metropolitan areas. Previous analyses have shown that refusal risk depends on the interviewers' characteristics. The aim of this paper is to explain the difference in refusal risk among metropolitan areas by analysing the strategies adopted in the recruitment of interviewers through a multilevel approach. The Annual Survey on Living conditions is a PAPI survey of the "Multipurpose" integrated system of social surveys and it represents our data base. For non responding household, data on non response by reason, municipality and characteristics of the interviewer are available. The results highlight that those cities recruiting interviewers mainly among young students have a higher refusal risk. These results are particularly important as they indicate that recruitment strategies may have a substantial impact on non sampling errors. Acknowledgements An earlier version of this article was presented at the International Conference on Improving Survey, University of Copenhagen, Denmark, August 25-28, 2002. We would like to thank the participants to the presentation for their useful comments and suggestions. Opinions expressed are those of the authors and do not necessarily represent the official position of any of the institutions they work for.     

On the use of surrogate end points in randomized trials

In a recent paper Day and Duffy proposed a strategy for designing a randomized trial of different breast cancer screening schedules. Their strategy was based on the use of predictors of mortality determined by patients' factors at diagnosis as surrogates for true mortality. On the basis of the Prentice criterion for validity of a surrogate end point, and data from earlier studies of breast cancer case survival, they showed that, not only would the trial require a much shorter follow-up, but also that the information (i.e. inverse variance) for evaluating a treatment effect on mortality would be greater by a factor of nearly 3 if the predictors of mortality were used, compared with a trial in which mortality was actually observed. Although these results are technically correct, we believe that the conceptual strategy on which they are based is flawed, and that the fundamental problem is the Prentice criterion itself. In this paper the technical issues are discussed in detail, and an alternative structure for evaluating the validity of surrogate end points is proposed.     

Sequential Series Systems and Their Risk Assessments

System reliability models are critical in both theory and engineering. Although there are many system reliability models, they still cannot cover some practical situations. In this article, three sequential series systems are introduced in terms of some real backgrounds. An order profile for the system working is also introduced, because it can be used to describe the working component contribution for the system clearly. As the systems become more and more complicated and important, the safety issue is a hot topic. Risk analysis is one of the important ways for safety studies and implements. The formulae for some risk measures for the sequential systems are presented from a safety point of view. A numerical example is given to illustrate the details of the procedure and formulae.     

Covariates and Random Effects in a Gamma Process Model with Application to Degradation and Failure

The gamma process is a natural model for degradation processes in which deterioration is supposed to take place gradually over time in a sequence of tiny increments. When units or individuals are observed over time it is often apparent that they degrade at different rates, even though no differences in treatment or environment are present. Thus, in applying gamma-process models to such data, it is necessary to allow for such unexplained differences. In the present paper this is accomplished by constructing a tractable gamma-process model incorporating a random effect. The model is fitted to some data on crack growth and corresponding goodness-of-fit tests are carried out. Prediction calculations for failure times defined in terms of degradation level passages are developed and illustrated.     

On the Bayesian analysis of the mixture of power function distribution using the complete and the censored sample

The power function distribution is often used to study the electrical component reliability. In this paper, we model a heterogeneous population using the two-component mixture of the power function distribution. A comprehensive simulation scheme including a large number of parameter points is followed to highlight the properties and behavior of the estimates in terms of sample size, censoring rate, parameters size and the proportion of the components of the mixture. The parameters of the power function mixture are estimated and compared using the Bayes estimates. A simulated mixture data with censored observations is generated by probabilistic mixing for the computational purposes. Elegant closed form expressions for the Bayes estimators and their variances are derived for the censored sample as well as for the complete sample. Some interesting comparison and properties of the estimates are observed and presented. The system of three non-linear equations, required to be solved iteratively for the computations of maximum likelihood (ML) estimates, is derived. The complete sample expressions for the ML estimates and for their variances are also given. The components of the information matrix are constructed as well. Uninformative as well as informative priors are assumed for the derivation of the Bayes estimators. A real-life mixture data example has also been discussed. The posterior predictive distribution with the informative Gamma prior is derived, and the equations required to find the lower and upper limits of the predictive intervals are constructed. The Bayes estimates are evaluated under the squared error loss function.     

Estimation of tobit-type models with individual specific effects

The aim of this paper is two-fold. First, we review recent estimators for censored regression and sample selection panel data models with unobservable individual specific effects, and show how the idea behind these estimators can be used to construct estimators for a variety of other Tobit-type models. The estimators presented in this paper are semiparametric, in the sense that they do not require the parametrization of the distribution of the unobservables. The second aim of the paper is to introduce a new class of estimators for the censored regression model. The advantage of the new estimators is that they can be applied under a stationarity assumption on the transitory error terms, which is weaker than the exchangeability assumption that is usually made in this literature. A similar generalization does not seem feasible for the estimators of the other models that are considered.     

Estimation of tobit-type models with individual specific effects

The aim of this paper is two-fold. First, we review recent estimators for censored regression and sample selection panel data models with unobservable individual specific effects, and show how the idea behind these estimators can be used to construct estimators for a variety of other Tobit-type models. The estimators presented in this paper are semiparametric, in the sense that they do not require the parametrization of the distribution of the unobservables. The second aim of the paper is to introduce a new class of estimators for the censored regression model. The advantage of the new estimators is that they can be applied under a stationarity assumption on the transitory error terms, which is weaker than the exchangeability assumption that is usually made in this literature. A similar generalization does not seem feasible for the estimators of the other models that are considered.     

Multivariate multi-sample tests for location based on data depth

A notion of data depth is used to measure centrality or outlyingness of a data point in a given data cloud. In the context of data depth, the point (or points) having maximum depth is called as deepest point (or points). In the present work, we propose three multi-sample tests for testing equality of location parameters of multivariate populations by using the deepest point (or points). These tests can be considered as extensions of two-sample tests based on the deepest point (or points). The proposed tests are implemented through the idea of Fisher's permutation test. Performance of earlier tests is studied by simulation. Illustration with two real datasets is also provided.     

Selection of the best with a preliminary test for two-parameter exponential distributions

This paper deals with the problem of selecting the best population from among k(≥ 2) two-parameter exponential populations. New selection procedures are proposed for selecting the unique best. The procedures include preliminary tests which allow the xperimenter to have an option to not select if the statistical evidence is not significant. Two probabilities, the probability to make a selection and the probability of a correct selection, are controlled by these selection procedures. Comparisons between the proposed selection procedures and certain earlier existing procedures are also made. The results show the superiority of the proposed selection procedures in terms of the required sample size.