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.

Abtsrcat Estimating finite population distribution function (hereafter FPDF) is an important problem to the survey samplers since it summarizes almost all the relevant information of interest about the finite population. Chambers and Dunstan (1986) (henceforth CD) in their seminal paper propose a predictive estimator of FPDF incorporating the unit level auxiliary information available for the entire population. CD estimator assumes a linear regression model in the superpopulation. However, even for moderate deviation from linearity assumption, significant performance deterioration of CD estimator is observed. Here we propose a predictive estimator of FPDF based on a semiparametric regression model. For this we use recently developed penalized splines (P-splines) regression. The proposed estimator performs better than CD estimator if the linearity assumption fails. We find its asymptotic bias and variance. Finally, we compare the performance of the proposed estimator with other alternative estimators through simulation studies and illustrate its use with a real data set.

We propose a model-based predictive estimator of the finite population proportion of a misclassified binary response, when information on the auxiliary variable(s) is available for all units in the population. Asymptotic properties of the misclassification-adjusted predictive estimator are also explored. We propose a computationally efficient bootstrap variance estimator that exhibits better performance compared to usual analytical variance estimator. The performance of the proposed estimator is compared with other commonly used design-based estimators through extensive simulation studies. The results are supplemented by an empirical study based on literacy data.

In this paper, a new natural discrete version of the one parameter polynomial exponential family of distributions have been proposed and studied. The distribution is named as Natural Discrete One Parameter Polynomial Exponential (NDOPPE) distribution. Structural and reliability properties have been studied. Estimation procedure of the parameter of the distribution have been mentioned. Compound NDOPPE distribution in the context of collective risk model have been obtained in closed form. The new compound distribution has been compared with the classical compound Poisson, compound Negative binomial, compound discrete Lindley, compound xgamma-I and compound xgamma-II distributions regarding suitability of modelling extreme data with the help of some automobile claim.

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