Confidence Intervals for Current Status Data

Abstract.  The likelihood ratio statistic for testing pointwise hypotheses about the survival time distribution in the current status model can be inverted to yield confidence intervals (CIs). One advantage of this procedure is that CIs can be formed without estimating the unknown parameters that figure in the asymptotic distribution of the maximum likelihood estimator (MLE) of the distribution function. We discuss the likelihood ratio-based CIs for the distribution function and the quantile function and compare these intervals to several different intervals based on the MLE. The quantiles of the limiting distribution of the MLE are estimated using various methods including parametric fitting, kernel smoothing and subsampling techniques. Comparisons are carried out both for simulated data and on a data set involving time to immunization against rubella. The comparisons indicate that the likelihood ratio-based intervals are preferable from several perspectives.     

Just-in-time purchasing: an empirical investigation

The just-in-time (JIT) literature suggests that, for JIT to be successful, a manufacturing firm has to make changes in its purchasing operations. However, empirical examination of the JIT purchasing related issues is limited. For example, a literature search identified 49 JIT purchasing articles. Of these, only 14 are empirical studies; two dealing with statistical testing of a few JIT purchasing issues. This comprehensive empirical study is undertaken to investigate (a) changes in the purchasing attributes since JIT implementation, (b) supplier evaluation cri-teria, and (c) problems with JIT purchasing implementation. Statistically significant changes are observed in 28 out of 32 attributes identified in the literature, suggesting that the manufacturing firms are successfully implementing JIT purchasing programmes. Of the 14 supplier evaluation criteria, the empirical investigation shows nine of them being important. Erratic demand for the product and customized product are found to be problematic (but not very problematic as suggested in the JIT literature( in JIT purchasing implementation.     

Likelihood Ratio Tests Under Local and Fixed Alternatives in Monotone Function Problems

Abstract.  We focus on a class of non-standard problems involving non-parametric estimation of a monotone function that is characterized by n ^1/3 rate of convergence of the maximum likelihood estimator, non-Gaussian limit distributions and the non-existence of     -regular estimators. We have shown elsewhere that under a null hypothesis of the type ψ ( z ₀) =  θ ₀ ( ψ being the monotone function of interest) in non-standard problems of the above kind, the likelihood ratio statistic has a 'universal' limit distribution that is free of the underlying parameters in the model. In this paper, we illustrate its limiting behaviour under local alternatives of the form ψ _n ( z ), where ψ _n (·) and ψ (·) vary in O ( n ^−1/3) neighbourhoods around z ₀ and ψ _n converges to ψ at rate n ^1/3 in an appropriate metric. Apart from local alternatives, we also consider the behaviour of the likelihood ratio statistic under fixed alternatives and establish the convergence in probability of an appropriately scaled version of the same to a constant involving a Kullback–Leibler distance.     

Inference on Polychotomous Responses in Finite Populations

Abstract. A model‐based predictive estimator is proposed for the population proportions of a polychotomous response variable, based on a sample from the population and on auxiliary variables, whose values are known for the entire population. The responses for the non‐sample units are predicted using a multinomial logit model, which is a parametric function of the auxiliary variables. A bootstrap estimator is proposed for the variance of the predictive estimator, its consistency is proved and its small sample performance is compared with that of an analytical estimator. The proposed predictive estimator is compared with other available estimators, including model‐assisted ones, both in a simulation study involving different sampling designs and model mis‐specification, and using real data from an opinion survey. The results indicate that the prediction approach appears to use auxiliary information more efficiently than the model‐assisted approach.     

A multicriteria model for supporting setup reduction investment decisions

One critical manufacturing challenge of the 1990s is for firms to effectively apply new operations management techniques while embracing wider philosophies such as total quality management (TQM) and computer integrated manufacturing (CIM), etc. Setup cost and/or time reduction is one such technique capable of producing many benefits for manufacturing firms, including reduced inventory, better equipment utilization, and improved quality. It is thereby viewed as an important component of just-in-time (JIT) manufacturing practice. Existing problems with the setup reduction decision include the many factors that must be considered, as well of an absence of validated and usable models for estimating potential benefits from setup reduction investment made in different contexts. This paper discusses the attainment of gains from setup reduction mainly by improving existing equipment and work practices rather than purchasing new equipment or technology. The model proposed in this paper is based on the application of the analytic hierarchical process (AHP) on seven weighted factors to obtain a preliminary indication as to whether investment in setup reduction is desirable in a given manufacturing context, and the expected benefits of such investment. A flexible scaling system, thus obtained, allows the model to handle a wide range of managerial predispositions to setup reduction.     

Optimal investment in setup reduction for finite horizon periodic review inventory system under deterministic time varying demand

This paper examines the impact of setup reduction on a finite horizon, periodic review inventory system, under deterministic time varying demand. A total relevant cost function is developed for such systems. Using this, the impact of setup reduction is examined under various forms of setup reduction cost functions that have been suggested in the literature. The operating characteristics and optimization of the various scenarios are discussed. Our analysis shows that the effects of setup reduction in a periodic review system are similar to those in a reorder point system. Our results are likely to help practitioners who use similar periodic review systems towards decreasing total inventory related costs by investing in setup reduction.     

A Semiparametric Binary Regression Model Involving Monotonicity Constraints

Abstract.  We study a binary regression model using the complementary log–log link, where the response variable Δ is the indicator of an event of interest (for example, the incidence of cancer, or the detection of a tumour) and the set of covariates can be partitioned as ( X ,  Z ) where Z (real valued) is the primary covariate and X (vector valued) denotes a set of control variables. The conditional probability of the event of interest is assumed to be monotonic in Z , for every fixed X . A finite-dimensional (regression) parameter β describes the effect of X . We show that the baseline conditional probability function (corresponding to X  =  0 ) can be estimated by isotonic regression procedures and develop an asymptotically pivotal likelihood-ratio-based method for constructing (asymptotic) confidence sets for the regression function. We also show how likelihood-ratio-based confidence intervals for the regression parameter can be constructed using the chi-square distribution. An interesting connection to the Cox proportional hazards model under current status censoring emerges. We present simulation results to illustrate the theory and apply our results to a data set involving lung tumour incidence in mice.