Nonparametric estimation of time-to-event distribution based on recall data in observational studies

In a cross-sectional observational study, time-to-event distribution can be estimated from data on current status or from recalled data on the time of occurrence. In either case, one can treat the data as having been interval censored, and use the nonparametric maximum likelihood estimator proposed by Turnbull (J R Stat Soc Ser B 38:290–295, 1976). However, the chance of recall may depend on the time span between the occurrence of the event and the time of interview. In such a case, the underlying censoring would be informative, rendering the Turnbull estimator inappropriate. In this article, we provide a nonparametric maximum likelihood estimator of the distribution of interest, by using a model adapted to the special nature of the data at hand. We also provide a computationally simple approximation of this estimator, and establish the consistency of both the original and the approximate versions, under mild conditions. Monte Carlo simulations indicate that the proposed estimators have smaller bias than the Turnbull estimator based on incomplete recall data, smaller variance than the Turnbull estimator based on current status data, and smaller mean squared error than both of them. The method is applied to menarcheal data from a recent Anthropometric study of adolescent and young adult females in Kolkata, India.     

Determination of the optimal number of kanbans and kanban allocation in a FMS: A simulationbased study

A simulation-based study is presented to compare the performance of a set of kanban allocation rules in a flexible manufacturing system (FMS) operating in a pull mode. This paper also presents a simulation-based direct search approach to determine the optimal number of kanbans and their simultaneous allocation to different part types. This paper presents a realistic cost function that includes a penalty for failing to meet the demand on time, and a penalty for rescheduling delivery of materials from vendors. The model captures limited flexibility in the form of operational flexibility in a FMS. Future extensions to this study are discussed.     

Asymptotic confidence interval of power spectrum of a continuous time process through progressively faster sampling

If the power spectral density of a continuous time stationary stochastic process is not limited to a finite bandwidth, data sampled from that process at any uniform sampling rate leads to biased and inconsistent spectrum estimators, which are unsuitable for constructing confidence intervals. In this paper, we use the smoothed periodogram estimator to construct asymptotic confidence intervals shrinking to the true spectra, by allowing the sampling rate to go to infinity suitably fast as the sample size goes to infinity. The proposed method requires minimal computation, as it does not involve bootstrap or other resampling. The method is illustrated through a Monte-Carlo simulation study, and its performance is compared with that of the corresponding method based on uniform sampling at a fixed rate.     

Design of Flexible Multi‐Stage Processes

Faced with demand uncertainty across multiple product lines, many companies have recourse to flexible capacities which can process different products in order to better balance the trade‐off between capacity utilization and cost efficiency. Many studies demonstrated the potential benefit of using flexible capacity at the aggregate level by treating a whole plant or a whole process as a single stage. This paper extends these analyses by studying the benefits of flexible capacity while considering the multi‐stage structure of processes and consequently determining which stages should be flexible, which should be dedicated, and how much capacity to assign to each stage. We consider a two‐product firm which operates in a process‐to‐order environment and faces uncertain demand. Each stage of the process can be designed as dedicated or flexible. Dedicated resources are highly cost efficient but limited to the single product they are exclusively designed for, whereas flexible resources are versatile to handle several products but are more expensive. Using a general mathematical formulation our analysis shows that the optimal design may have some dedicated and some flexible stages along the process. Interestingly, this decision should be decoupled from the chronological order of the stages along the process.     

Minimum Risk Estimation of Scalar Means under Convex Combination of Loss Functions

We derive the minimum risk estimates of the scalar means for Normal, Exponential, and Gamma distributions, under the convex combination of SEL and LINEX loss functions. The functional forms of the proposed estimates for the three examples are general in nature, and for the boundary conditions provide us with the corresponding estimates under SEL and LINEX loss, respectively. We authenticate our proposed models using different iterative as well as meta-heuristic techniques, and through extensive simulation as well as application of live data sets, validate the efficacy of our proposed results.     

Estimation for the Multiple Regression Setup Using Balanced Loss Function

Consider the estimation problem for the multiple linear regression (MLR) setup, under the balanced loss function (BLF), where goodness of fit and precision of estimation are modeled using either squared error loss (SEL) or linear exponential (LINEX) loss functions. The authors derive the minimum risk estimates for two different variants of BLF and prove for both the cases the existence of the ubiquitous SEL and LINEX estimates at the boundary conditions. Conclusions draw from the exhaustive simulation runs prove the general nature of proposed theorems.     

A Classification Method for Directional Data with Application to the Human Skull

There are many well-known methods applied in classification problem for linear data with both known and unknown distribution. Here, we deal with classification involving data on torus and cylinder. A new method involving a generalized likelihood ratio test is developed for classifying in two populations using directional data. The approach assumes that one of the probabilities of misclassification is known. The procedure is constructed by applying Gibbs sampler on the conditionally specified distribution. A parametric bootstrap approach is also presented. An application to data involving linear and circular measurements on human skull from two tribal populations is given.     

Unbiased Estimation of the Distribution Function of a Two-Parameter Exponential Population Using Order Statistics

In this article, we consider the problem of unbiased estimation of the distribution function of a two-parameter exponential population using order statistics based on a random sample from the population. We give necessary and sufficient conditions for the existence of an unbiased estimator based on an arbitrary set of order statistics and suggest unbiased estimators in some situations where unbiased estimators exist. A few properties of the suggested estimators for some special cases have also been discussed.     

A condition for Nash-stability under binary and democratic group decision functions

A necessary and sufficient condition is established in terms of restrictions on individual preferences for a class of democratic systems to be Nash-stable: that there is no one in the society who can profitably misrepresent his preferences. It is shown that only a very strong similarity of preferences can eliminate the incentive for individuals to misreveal their preferences. Since individual preferences in actual practice are not likely to be so similar, the result in this paper shows that strategic misrevelation of preferences by individuals remains a disturbing possibility under this class of democratic rules.We are grateful to Professor Prasanta K. Pattanaik for many helpful suggestions.