Estimation of population product in presence of non-response in successive sampling

The design of this paper is to examine the problem of estimation of finite population product in mail surveys for the current occasion in the context of sampling on two occasions is attempted when there is non-response on both the occasions. Estimators for the current occasion are derived as a particular case when there is non-response on first and second occasion only. The gain in efficiency of the proposed estimate over the direct estimate using no information gathered on the first occasion is computed. The proposed strategy has been compared with other estimators. An empirical study is carried out to study the performance of the proposed strategy.     

Filtering via approximate Bayesian computation

Approximate Bayesian computation (ABC) has become a popular technique to facilitate Bayesian inference from complex models. In this article we present an ABC approximation designed to perform biased filtering for a Hidden Markov Model when the likelihood function is intractable. We use a sequential Monte Carlo (SMC) algorithm to both fit and sample from our ABC approximation of the target probability density. This approach is shown to, empirically, be more accurate w.r.t.?the original filter than competing methods. The theoretical bias of our method is investigated; it is shown that the bias goes to zero at the expense of increased computational effort. Our approach is illustrated on a constrained sequential lasso for portfolio allocation to 15 constituents of the FTSE 100 share index.     

A note on the estimation methods of crop production at the block level

This paper presents a method of estimation of crop-production statistics at smaller geographical levels like a community development block (generally referred to as a block) to make area-specific plans for agricultural development programmes in India. Using available district-level data on crop yield from crop-cutting experiments and data on auxiliary variables from various administrative sources, a suitable regression model is fitted. The fitted model is then used to predict the crop production at the block level. Some scaled estimators are also developed using predicted estimates. An empirical study is also carried out to judge the merits of the proposed estimators.     

ON THE CHOICE OF ESTIMATOR IN SURVERY SAMPLING*

We re-examine the criteria of “hyper-admissibility” and “necessary bestness”, for the choice of estimator, from the point of view of their relevance to the design of actual surveys. Both these criteria give rise to a unique choice of estimator (viz. the Horvitz-Thompson estimator ?_HT) whatever be the character under investigation or sample design. However, we show here that the “principal hyper-surfaces” (or “domains”) of dimension one (which are practically uninteresting)play the key role in arriving at the unique choice. A variance estimator v₁(?_HT) (due to Horvitz-Thompson), which takes negative values “often”, is shown to be uniquely “hyperadmissible” in a wide class of unbiased estimators of the variance of ?_HT. Extensive empirical evidence on the superiority of the Sen-Yates-Grundy variance estimator v₂(?_HT) over v₁(?_HT) is presented.     

Balanced Confidence Regions Based on Tukey's Depth and the Bootstrap

We propose and study the bootstrap confidence regions for multivariate parameters based on Tukey's depth. The bootstrap is based on the normalized or Studentized statistic formed from an independent and identically distributed random sample obtained from some unknown distribution in R ^q . The bootstrap points are deleted on the basis of Tukey's depth until the desired confidence level is reached. The proposed confidence regions are shown to be second order balanced in the context discussed by Beran. We also study the asymptotic consistency of Tukey's depth-based bootstrap confidence regions. The applicability of the method proposed is demonstrated in a simulation study.     

ESTIMATION OF A DISTRIBUTION FUNCTION DOMINATING STOCHASTICALLY A KNOWN DISTRIBUTION FUNCTION

This paper considers the problem of estimating a cumulative distribution function (cdf), when it is known a priori to dominate a known cdf. The estimator considered is obtained by adjusting the empirical cdf using the prior information. This adjusted estimator is shown to be consistent, its limiting distribution is found, and its mean squared error (MSE) is shown to be smaller than the MSE of the empirical cdf. Its asymptotic efficiency (compared to the empirical cdf) is also found.     

Atmospheric Dispersion of Inflammable Substances for Estimating Vulnerable Zones in Hydrocarbon Industry

The present study utilizes an operational model as well as simple empirical relationships for estimating hazard zones due to fire, explosion, and toxic vapor cloud dispersion. The empirical relationships are based on giving appropriate weightage to each of the parameters on which the hazard in question (viz, fire, explosion, toxic vapour dispersion) is dependent. Results from these two approaches [i.e., an operational model FLAMCALC of U.K. Health and Safety Executive (HSE) and an empirical model named FIREX] have been compared with the data obtained from the Mexico City disaster in 1984. In general, results from the empirical approach and FLAMCALC are comparable to the observed effects.     

Estimation of Vulnerable Zones Due to Accidental Release of Toxic Materials Resulting in Dense Gas Clouds

Heavy gas dispersion models have been developed at IIT (hereinafter referred as IIT heavy gas models I and II) with a view to estimate vulnerable zones due to accidental (both instantaneous and continuous, respectively) release of dense toxic material in the atmosphere. The results obtained from IIT heavy gas models have been compared with those obtained from the DEGADIS model [Dense Gas Dispersion Model, developed by Havens and Spicer (1985) for the U.S. Coast Guard] as well as with the observed data collected during the Burro Series, Maplin Sands, and Thorney Island field trials. Both of these models include relevant features of dense gas dispersion, viz., gravity slumping, air entrainment, cloud heating, and transition to the passive phase, etc. The DEGADIS model has been considered for comparing the performance of IIT heavy gas models in this study because it incorporates most of the physical processes of dense gas dispersion in an elaborate manner, and has also been satisfactorily tested against field observations. The predictions from IIT heavy gas models indicate a fairly similar trend to the observed values from Thorney Island, Burro Series, and Maplin experiments with a tendency toward overprediction. There is a good agreement between the prediction of IIT Heavy Gas models I and II with those from DEGADIS, except for the simulations of IIT heavy gas model-I pertaining to very large release quantities under highly stable atmospheric conditions. In summary, the performance of IIT heavy gas models have been found to be reasonably good both with respect to the limited field data available and various simulations (selected on the basis of relevant storages in the industries and prevalent meteorological conditions performed with DEGADIS). However, there is a scope of improvement in the IIT heavy gas models (viz., better formulation for entrainment, modification of coefficients, transition criteria, etc.). Further, isotons (nomograms) have been prepared by using IIT heavy gas models for chlorine, which provide safe distance for various storage amounts for 24 meteorological scenarios prevalent in the entire year. These nomograms are prepared such that a nonspecialist can use them easily for control and management in case of an emergency requiring the evacuation of people in the affected region. These results can also be useful for siting and limiting the storage quantities.     

A non-normal class of distribution function for dose-binary response curve*

A non-normal class of distribution (Edgeworth Series distribution) function in three and four parameters has been considered for dose-binary response relationship. This class accounts for the non-normality (expressed in terms of skewness and kurtosis) present in the relationship in addition to the usual location and scale parameters (generally considered by two parameter models). We present the maximum likelihood method of estimation of the parameters and test of probit (normal distribution) hypothesis. Edgeworth Series distribution when fitted to the data of Milicer & Szczotka (1966) showed an excellent closeness to the observed values, significant improvement over probit and logit fit (Aranda-Ordaz, 1981), and better fit compared to Prentice (1976) model.     

Testing order restricted hypotheses with proportional hazards

Inferences for survival curves based on right censored continuous or grouped data are studied. Testing homogeneity with an ordered restricted alternative and testing the order restriction as the null hypothesis are considered. Under a proportional hazards model, the ordering on the survival curves corresponds to an ordering on the regression coefficients. Approximate likelihood methods are obtained by applying order restricted procedures to the estimates of the regression coefficients. Ordered analogues to the log rank test which are based on the score statistics are considered also. Chi-bar-squared distributions, which have been studied extensively, are shown to provide reasonable approximations to the null distributions of these tests statistics. Using Monte Carlo techniques, the powers of these two types of tests are compared with those that are available in the literature.