A General Class of Ratio‐Type Estimators Under Super‐Population Model

The problem of constructing classes of estimators for population mean has been widely discussed by various authors under design approach in sample surveys. An attempt by Upadhyaya , Singh , and Vos (1985) has been made to combine the usual mean and ratio estimator with suitable weights in order to define a general class of estimators. This paper is an attempt to study properties of the same estimator under super‐population model. Optimum weights have also been proposed. Results have been supported with some numerical examples.     

On the Use of Jack‐Knife Techniques in Systematic Sampling

We have proposed two general classes of ratio and product type estimators to estimate an unknown population parameter of a response variable y under systematic sampling strategy. Jack‐Knife technique is employed to make the classes almost/exactly unbiased and sampling variance of the proposed estimators are derived to the first order of approximation. The merits of the proposed estimators over other estimators are discussed in this paper.     

A Class of Ratio-Cum-Product-Type Estimator

The problem of estimating the population mean using an auxiliary information has been dealt with in literature quite extensively. Ratio, product, linear regression and ratio-type estimators are well known. A class of ratio-cum-product-type estimator is proposed in this paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight ‘a’ and good range of α-values, it is found that the proposed estimator is superior than a set of estimators (i.e., sample mean, usual ratio and product estimators, SRIVASTAVA's (1967) estimator, CHAKRABARTY's (1979) estimator and a product-type estimator) which are, in fact, the particular cases of it. At optimum value of α, the proposed estimator is as efficient as linear regression estimator.     

An Improved Estimator of the Variance of the Regression Estimator

In this paper, the problem of estimation of variance of the general linear regression estimator has been considered. It has been shown that the first order calibration approach is a special case of the class of estimators proposed by Deng and Wu (1987). A second order calibration approach is suggested. Some new estimators are shown to be the special case of the proposed calibration approach. The efficiency of the proposed strategy is shown to improve on the original strategy. An idea to find a non-negative estimate of variance has been suggested.     

Simultaneously model-unbiased, design-unbiased estimation

This paper proposes a class of inferential procedures (incorporating both design and estimation elements) that yield estimates of means that are simultaneously model unbiased and design unbiased. Classical regression procedures yield conditionally unbiased estimators for the mean (conditioning on the model and choice of observation points). In contrast, design-based methods yield estimators that are unconditionally unbiased on matter what the form of the underlying model. Variance properties of the proposed class are examined, and applications to bioavailability, water quality from mine run-off, and finite population regression estimation are considered. The proposed procedures perform well, especially in the typical case where a model is only approximately correct.     

Upper bound estimators of the population size based on ordinal models for capture‐recapture experiments

Capture‐recapture studies have attracted a lot of attention over the past few decades, especially in applied disciplines where a direct estimate for the size of a population of interest is not available. Epidemiology, ecology, public health, and biodiversity are just a few examples. The estimation of the number of unseen units has been a challenge for theoretical statisticians, and considerable progress has been made in providing lower bound estimators for the population size. In fact, it is well known that consistent estimators for this cannot be provided in the very general case. Considering a case where capture‐recapture studies are summarized by a frequency of frequencies distribution, we derive a simple upper bound of the population size based on the cumulative distribution function. We introduce two estimators of this bound, without any specific parametric assumption on the distribution of the observed frequency counts. The behavior of the proposed estimators is investigated using several benchmark datasets and a large‐scale simulation experiment based on the scheme discussed by Pledger.     

Efficient Estimators for the verianoe of a Finite Population

For the estimation of finite population variance of a character, DAS and TRIPATHI (1978) proposed some efficient estimators when population mean of variance of some other character (associated with main character) is known. We propose here some estimators for population variance using same information and compare with those given by DAS and TRIPATHI (1978). Some examples are given for illustration.     

Population intervention models in causal inference

We propose a new causal parameter, which is a natural extension of existing approaches to causal inference such as marginal structural models. Modelling approaches are proposed for the difference between a treatment-specific counterfactual population distribution and the actual population distribution of an outcome in the target population of interest. Relevant parameters describe the effect of a hypothetical intervention on such a population and therefore we refer to these models as population intervention models. We focus on intervention models estimating the effect of an intervention in terms of a difference and ratio of means, called risk difference and relative risk if the outcome is binary. We provide a class of inverse-probability-of-treatment-weighted and doubly-robust estimators of the causal parameters in these models. The finite-sample performance of these new estimators is explored in a simulation study.     

An Improved Class of Estimators for Finite Population Mean in Sample Surveys

This paper proposes a class of estimators for estimating the finite population mean -Y of a study variate y using information on two auxiliary variates, one of which is positively and the other negatively correlated with the study variate y. An “asymptotically optimum estimator” (AOE) in the class is identified with its bias and mean square error formulae. It is observed that the proposed AOE is more efficient than Srivastava (1965), Srivastava (1974), Prasad (1989) and Gandge , Varghese , and Prabhu-Ajgaonkar (1993) estimators.     

A comparison of estimators of the population recombination rate

Three new estimators of the population recombination rate C = 4Nr are introduced. These estimators summarize the data using the number of distinct haplotypes and the estimated minimum number of recombination events, then calculate the value of C that maximizes the likelihood of obtaining the summarized data. They are compared with a number of previously proposed estimators of the recombination rate. One of the newly proposed estimators is generally better than the others for the parameter values considered here, while the three programs that calculate maximum-likelihood estimates give conflicting results.     

Estimating selective advantage of two alleles in discrete time

A class of estimators for the selective advantage, s, in a Wright-Fisher model with two alleles, variable population size, and genic selection is derived via martingale theory. Explicit expressions are given for these estimators which only involve simple computation. The optimal estimate among this class of estimators is obtained. Asymptotic results are readily established by an application of a martingale central limit theorem. The performance of this optimal estimator is compared to known estimators by means of a simulation study.     

A Generic Estimation of Population Subdivision Using Distances between Alleles with Special Reference for Microsatellite Loci

Several estimators of population differentiation have been proposed in the recent past to deal with various types of genetic markers (i.e., allozymes, nucleotide sequences, restriction fragment length polymorphisms, or microsatellites). We discuss the relationships among these estimators and show how a single analysis of variance framework can accomodate these qualitatively different data types.     

A Generalized Class of Synthetic Estimators with Application to Crop Acreage Estimation for Small Domains

This paper defines and discusses a generalized class of synthetic estimators for small domains, using auxiliary information, under simple random sampling and stratified random sampling schemes. The generalized class of synthetic estimators, among others, includes the simple, ratio and product synthetic estimators. The proposed class of synthetic estimators gives consistent estimators if the synthetic assumption holds. Further, it demonstrates the use of the generalized synthetic and ratio synthetic estimators for estimating crop acreage for small domains and also compare their relative performance with direct estimators, empirically, through a simulation study.     

Class of Estimators of Mean and Variance Using Auxiliary Information when Correlation Coefficient is also Known

For estimating the mean of a finite population using information on an auxiliary variable, a class of estimators which also uses the value of the correlation coefficient between the two variables which is assumed known, is defined. Expression for its asymptotic mean squared error and its minimum value is obtained. An expression by which the minimum mean squared error of this class is smaller than those which use only the sample mean and the sample variance of the auxiliary variable is obtained. A similar class of estimators is considered for the estimation of the population variance. The gain in efficiency is illustrated for six populations considered in literature.     

A unified likelihood-based approach for estimating population size in continuous-time capture-recapture experiments with frailty

A unified likelihood-based approach is proposed to estimate population size for a continuous-time closed capture-recapture experiment with frailty. The frailty model allows the capture intensity to vary with individual heterogeneity, time, and behavioral response. The individual heterogeneity effect is modeled as being gamma distributed. The first-capture and recapture intensities are assumed to be in constant proportion but may otherwise vary arbitrarily through time. The approach is also extended to capture-recapture experiments with possible random removals. Simulation studies are conducted to examine the performance of the proposed estimators. By asymptotic efficiency comparison and simulation studies, the proposed estimators have been shown to be superior to their discrete-time model counterparts in genuine continuous-time capture-recapture experiments.     

The Chain Ratio Estimator and Regression Estimator with Linear Combination of Two Auxiliary Variables

In sample surveys, it is usual to make use of auxiliary information to increase the precision of the estimators. We propose a new chain ratio estimator and regression estimator of a finite population mean using linear combination of two auxiliary variables and obtain the mean squared error (MSE) equations for the proposed estimators. We find theoretical conditions that make proposed estimators more efficient than the traditional multivariate ratio estimator and the regression estimator using information of two auxiliary variables.     

An Efficient Regression Type Estimator in Survey Sampling

For the estimation of population mean in simple random sampling, an efficient regression-type estimator is proposed which is more efficient than the conventional regression estimator and hence than mean per unit estimator, ratio and product estimators and many other estimators proposed by various authors. Some numerical examples are included for illustration.     

2SUR回归模型系数估计的优良性比较

对于2SUR回归模型的参数估计问题,给出了一些一般均方误差矩阵比较结果,据此提出了一类线性估计和一类基于离差阵广义非限定估计的非线性两步估计,并获得了该两步估计类的一些有限样本性质。     

Complex population dynamics and the coalescent under neutrality

Estimates of the coalescent effective population size N(e) can be poorly correlated with the true population size. The relationship between N(e) and the population size is sensitive to the way in which birth and death rates vary over time. The problem of inference is exacerbated when the mechanisms underlying population dynamics are complex and depend on many parameters. In instances where nonparametric estimators of N(e) such as the skyline struggle to reproduce the correct demographic history, model-based estimators that can draw on prior information about population size and growth rates may be more efficient. A coalescent model is developed for a large class of populations such that the demographic history is described by a deterministic nonlinear dynamical system of arbitrary dimension. This class of demographic model differs from those typically used in population genetics. Birth and death rates are not fixed, and no assumptions are made regarding the fraction of the population sampled. Furthermore, the population may be structured in such a way that gene copies reproduce both within and across demes. For this large class of models, it is shown how to derive the rate of coalescence, as well as the likelihood of a gene genealogy with heterochronous sampling and labeled taxa, and how to simulate a coalescent tree conditional on a complex demographic history. This theoretical framework encapsulates many of the models used by ecologists and epidemiologists and should facilitate the integration of population genetics with the study of mathematical population dynamics.     

A Combined Product Estimator in Sample Survey

For the estimation of the population mean in stratified random sampling a ‘Combined Product Estimator’ is proposed which is more efficient than the ‘Combined Ratio’ and ‘Separate Ratio’ estimators. Also, the proposed estimator have exact expressions for bias and mean square error. An empirical illustration is given to compare the efficiencies of different estimators.