We consider the classic problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample. We look first at the Chao-Lee estimator: we initially show that such estimator can be obtained by reconciling two estimators of the unobserved probability, and then develop a sequence of improvements culminating in a Dirichlet prior Bayesian reinterpretation of the estimation problem. By means of this, we obtain simultaneous estimates of T, of the normalized interspecies variance $γ^2$ and of the parameter $λ$ of the prior. Several simulations show that our estimation method is more flexible than several known methods we used as comparison; the only limitation, apparently shared by all other methods, seems to be that it cannot deal with the rare cases in which $γ^2 >1$
We present an alternative approach to the Bayesian nonparametric analysis of conditional species richness under two-parameter Poisson Dirichlet priors. We rely on a known characterization by deletion of classes property and on results for Beta-Binomial distributions. Besides leading to simplified and much more direct proofs, our proposal provides a new scale mixture representation of the conditional asymptotic law.
In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown that they can also be exploited in species sampling problems: indeed they are natural tools for modeling the random proportions of species within a population thus allowing for inference on various quantities of statistical interest. For applications that involve large samples, the exact evaluation of the corresponding estimators becomes impracticable and, ther…
The number of species can be estimated by sampling individuals from a species assemblage. The problem of estimating generalized species accumulation curve is addressed in a nonparametric Poisson mixture model. A likelihood-based estimator is proposed and illustrated by real examples.
We obtain a limit of a hierarchical Bayes estimator of a finite population mean when the sample size is large. The limit is in the sense of ordinary calculus, where the sample observations are treated as fixed quantities. Our result suggests a simple way to correct the hierarchical Bayes estimator to achieve design-consistency, a well-known property in the traditional randomization approach to finite population sampling. We also suggest three different measures of uncertainty of our proposed estimator.
Consider two independent exponential populations having different unknown location parameters and a common unknown scale parameter. Call the population associated with the larger location parameter as the "best" population and the population associated with the smaller location parameter as the "worst" population. For the goal of selecting the best (worst) population a natural selection rule, that has many optimum properties, is the one which selects the population corresponding to the larger (smaller) minimal sufficient statistic. In this article, we consider the problem of estimating the loc…
In this paper we have proposed an almost unbiased estimator using known value of some population parameter(s) with known population proportion of an auxiliary variable. A class of estimators is defined which includes [1], [2] and [3] estimators. Under simple random sampling without replacement (SRSWOR) scheme the expressions for bias and mean square error (MSE) are derived. Numerical illustrations are given in support of the present study. Key words: Auxiliary information, proportion, bias, mean square error, unbiased estimator.
This article presents the problem of estimating the population mean using auxiliary information in the presence of measurement errors. A numerical study is made among the proposed estimator, the exponential ratio estimator, Singh and Solanki (2012) estimator and the mean per unit estimator in the presence of measurement errors. Key words: Population mean, Study variate, Auxiliary variates, Mean squared error, Measurement errors, Efficiency
Richness estimation of an interesting area is always a challenge statistical work due to small sample size or species identity error. In the literatures, most richness estimators were only proposed to tackle the underestimation of the size-limited sample. However, species identity error almost occurs in each species survey and seriously reduces the accuracy of observed, singleton, and doubleton richness in turns to influence the behavior of richness estimator. Therefore, to estimate the true richness, the biased collected data due to species identity error should be modified before processing …
In this paper, we consider capture-recapture experiments with heterogenous catchability. In the setting we consider, the widespread Huggins-Alho estimator is not very suitable and we introduce and study a new generalized Horvitz-Thompson estimator. Our motivation is Respondent Driven Sampling (RDS), a prime example for such a setting where the capture probability is dependent on both the unknown population size as well as on an observable covariate, the network degree of an individual, due to peer recruitment. After discussing the theoretical properties of the new estimator, with full details …
In the present study, we propose a new estimator for population mean of the study variable y in the case of stratified random sampling using the information based on auxiliary variable x. Expression for the mean squared error (MSE) of the proposed estimators is derived up to the first order of approximation. The theoretical conditions have also been verified by a numerical example. An empirical study is carried out to show the efficiency of the suggested estimator over sample mean estimator, usual separate ratio, separate product estimator and other proposed estimators.
In this paper, we suggest an estimator using two auxiliary variables in stratified random sampling. The propose estimator has an improvement over mean per unit estimator as well as some other considered estimators. Expressions for bias and MSE of the estimator are derived up to first degree of approximation. Moreover, these theoretical findings are supported by a numerical example with original data. Key words: Study variable, auxiliary variable, stratified random sampling, bias and mean squared error.
In this article we have suggested an improved estimator for estimating the population mean in simple random sampling using auxiliary information under the presence of measurement errors. The mean square error (MSE) of the proposed estimator has been derived under large sample approximation. Besides, considering the minimum case of the MSE equation, the efficient conditions between the proposed and existing estimators are obtained. These theoretical findings are supported by a numerical example.
In this paper we have proposed an almost unbiased estimator using known value of some population parameter(s). A class of estimators is defined which includes Singh and Solanki [1] and Sahai and Ray [2], Sisodia and Dwivedi [3], Singh et. al. [4], Upadhyaya and Singh [5], Singh and Tailor [6] estimators. Under simple random sampling without replacement (SRSWOR) scheme the expressions for bias and mean square error (MSE) are derived. Numerical illustrations are given in support of the present study. Key words: Auxiliary information, bias, mean square error, unbiased estimator.
In the present study, we propose estimators based on geometric and harmonic mean for estimating population mean using information on two auxiliary attributes in simple random sampling. We have shown that, when we have multi-auxiliary attributes, estimators based on geometric mean and harmonic mean are less biased than Olkin (1958), Naik and Gupta (1996) and Singh (1967) type- estimator under certain conditions. However, the MSE of Olkin(1958) estimator and geometric and harmonic estimators are same up to the first order of approximation.
The network scale-up method enables researchers to estimate the size of hidden populations, such as drug injectors and sex workers, using sampled social network data. The basic scale-up estimator offers advantages over other size estimation techniques, but it depends on problematic modeling assumptions. We propose a new generalized scale-up estimator that can be used in settings with non-random social mixing and imperfect awareness about membership in the hidden population. Further, the new estimator can be used when data are collected via complex sample designs and from incomplete sampling fr…
Advances in field techniques have lead to an increase in spatially-referenced capture-recapture data to estimate a species' population size as well as other demographic parameters and patterns of space usage. Statistical models for these data have assumed that the number of individuals in the population and their spatial locations follow a homogeneous Poisson point process model, which implies that the individuals are uniformly and independently distributed over the spatial domain of interest. In many applications there is reason to question independence, for example when species display terri…
Current methods for population mean estimation from data collected by Respondent Driven Sampling (RDS) are based on the Horvitz-Thompson estimator together with a set of assumptions on the sampling model under which the inclusion probabilities can be determined from the information contained in the data. In this paper, we argue that such set of assumptions are too simplistic to be realistic and that under realistic sampling models, the situation is far more complicated. Specifically, we study a realistic RDS sampling model that is motivated by a real world RDS dataset. We show that, for this m…
