Estimation procedures for grouped data – a comparative study

Interval-censored data are very common in the reliability and lifetime data analysis. This paper investigates the performance of different estimation procedures for a special type of interval-censored data, i.e. grouped data, from three widely used lifetime distributions. The approaches considered here include the maximum likelihood estimation, the minimum distance estimation based on chi-square criterion, the moment estimation based on imputation (IM) method and an ad hoc estimation procedure. Although IM-based techniques are extensively used recently, we show that this method is not always effective. It is found that the ad hoc estimation procedure is equivalent to the minimum distance estimation with another distance metric and more effective in the simulation. The procedures of different approaches are presented and their performances are investigated by Monte Carlo simulation for various combinations of sample sizes and parameter settings. The numerical results provide guidelines to analyse grouped data for practitioners when they need to choose a good estimation approach.     

Cross-over Designs in the Presence of Higher Order Carry-overs

In cross-over experiments, where different treatments are applied successively to the same experimental unit over a number of time periods, it is often expected that a treatment has a carry-over effect in one or more periods following its period of application. The effect of interaction between the treatments in the successive periods may also affect the response. However, it seems that all systematic studies of the optimality properties of cross-over designs have been done under models where carry-over effects are assumed to persist for only one subsequent period. This paper proposes a model which allows for the possible presence of carry-over effects up to k subsequent periods, together with all the interactions between treatments applied at k + 1 successive periods. This model allows the practitioner to choose k for any experiment according to the requirements of that particular experiment. Under this model, the cross-over designs are studied and the class of optimal designs is obtained. A method of constructing these optimal designs is also given.     

Estimation op parameters in finite mixtures of exponential families from censored data

A general successive substitutions' scheme is developed to estimate parameters in a finite mixture of distributions from the exponential family, based on censored data. It is assumed that the data can be grouped in the first class and the number of observations in each of the remaining classes are known Examples from Poisson Exponential and Normal distributions are given A small simulation exercise has also been carried out for the mixture of two one parameter exponential population.     

Estimation of Traffic Intensity Based on Queue Length in a Single M/M/1 Queue

In this article, maximum likelihood estimator (MLE) as well as Bayes estimator of traffic intensity (ρ) in an M/M/1/∞ queueing model in equilibrium based on number of customers present in the queue at successive departure epochs have been worked out. Estimates of some functions of ρ which provide measures of effectiveness of the queue have also been derived. A comprehensive simulation study starting with the transition probability matrix has been carried out in the last section.     

Measurement of occupational mobility using semi-markov models

As proposed by Bartholomew (1967), occupational mobility should better be represented by semi-Markov processes. In the present paper attempts have been made to develop some new measures of occupational mobility in terms of serai-Markov processes and their values have been studied in the three extreme situations of interest.     

Pseudo‐likelihood estimation in ARCH models

The author presents asymptotic results for the class of pseudo‐likelihood estimators in the autoregressive conditional heteroscedastic models introduced by Engle (1982). Unlike what is required for the quasi‐likelihood estimator, some estimators in the class he considers do not require the finiteness of the fourth moment of the error density. Thus his method is applicable to heavy‐tailed error distributions for which moments higher than two may not exist.     

Reliability estimates of some survey data on family planning

Summary A follow-up study employing the panel design which aimed to evaluate the temporal stability of rural respondents' answers to KAP and fertility-related questions after a lapse of nearly five months revealed that reports by females on factual data dealing with socio-economic and demographic topics are as highly reliable as are those of males. The study based on 79 males and 81 females in Haryana further supports the hypothesis that re-test reliabilities of factual data such as respondent's age, religion, occupation, etc. are substantially higher than those of knowledge about contraceptives. Attitude items showed very low re-test reliabilities although the internal consistency reliabilities of the two attitude scales were found to vary within the range of 0.72 to 0.88. Both attitude scales were found to have a very high reproducibility coefficient, all higher than 0.95, for both the interview sessions. Re-test reliabilities of data on contraceptive use were also found to be moderately high. However, the rates of loop insertion and condom use as reported by female respondents are likely to show a substantial amount of gross error as is evident from their low re-test reliabilities. The findings of the present study cast serious doubt on the assumption that married males are not capable of accurately reporting the pregnancy histories of their wives. Several implications of the findings are discussed. From the methodological point of view they suggest a need to develop improved techniques for assessing attitudes toward family planning programmes and abortion as well as to knowledge of contraceptive methods and desired family size. The findings also justify the inclusion of eligible male respondents in KAP and fertility surveys.     

Adaptive two-treatment two-period crossover design for binary treatment responses incorporating carry-over effects

Adaptive designs are sometimes used in a phase III clinical trial with the goal of allocating a larger number of patients to the better treatment. In the present paper we use some adaptive designs in a two-treatment two-period crossover trial in the presence of possible carry-over effects, where the treatment responses are binary. We use some simple designs to choose between the possible treatment combinations AA, AB, BA or BB. The goal is to use the better treatment a larger proportion of times. We calculate the allocation proportions to the possible treatment combinations and their standard deviations. We also investigate related inferential problems, for which related asymptotics are derived. The proposed procedure is compared with a possible competitor. Finally we use real data sets to illustrate the applicability of our proposed design.     

The asymptotic behaviour of a class of L.-estimators under long-range dependence

This paper obtains asymptotic representations of a class of L-estimators in a linear regression model when the errors are a function of long-range-dependent Gaussian random variables. These representations are then used to address some of the efficiency robustness properties of L-estimators compared to the least-squares estimator. It is observed that under the Gaussian error distribution, each member of the class has the same asymptotic efficiency as that of the least-squares estimator. The results are obtained as a consequence of the asymptotic uniform linearity of some weighted empirical processes based on long-range-dependent random variables.