An efficiency comparison of dual ratio and product estimatiors

The present paper investigates the efficiency of the dual ratio estimator under the super population model with uncorrelated errors and a gamma-distributed auxiliary variabble. It is found that the dual ratio estimator is more efficient than the product estimator when the auxiliary variable has a gamma distribution with parameter greater than or equal to one, in the case when the regression is through the origin or when the product of intercept and slope is positive.     

Efficiencies of six almost unbiased ratio estimators under a particular model

Efficiencies of six almost unbiased estimators for the ratio of population means of two characters, are compared under a linear regression model.     

Randomized nomination sampling for finite populations

We propose a randomized minima–maxima nomination (RMMN) sampling design for use in finite populations. We derive the first- and second-order inclusion probabilities for both with and without replacement variations of the design. The inclusion probabilities for the without replacement variation are derived using a non-homogeneous Markov process. The design is simple to implement and results in simple and easy to calculate estimators and variances. It generalizes maxima nomination sampling for use in finite populations and includes some other sampling designs as special cases. We provide some optimality results and show that, in the context of finite population sampling, maxima nomination sampling is not generally the optimum design to follow. We also show, through numerical examples and a case study, that the proposed design can result in significant improvements in efficiency compared to simple random sampling without replacement designs for a wide choice of population types. Finally, we describe a bootstrap method for choosing values of the design parameters.     

A regression estimator for finite population mean of a sensitive variable using an optional randomized response model

Kalucha et al. (Kalucha G., Gupta S., Dass B. K. (accepted). Ratio estimation of finite population mean using optional randomized response models. Journal of Statistical Theory and Practice) introduced an additive ratio estimator for finite population mean of a sensitive variable in simple random sampling without replacement and showed that this estimator performs better than the ordinary mean estimator based on an optional randomized response technique (RRT). In this paper, we introduce a regression estimator that performs better than the ratio estimator even for the modest correlation between the study and the auxiliary variables. A comparison of the proposed estimator with the corresponding ratio estimator and the ordinary RRT mean estimator is carried out theoretically, and is also illustrated with a simulation study.     

Bootstrap mean squared error of a small-area EBLUP

Concerning the estimation of linear parameters in small areas, a nested-error regression model is assumed for the values of the target variable in the units of a finite population. Then, a bootstrap procedure is proposed for estimating the mean squared error (MSE) of the EBLUP under the finite population setup. The consistency of the bootstrap procedure is studied, and a simulation experiment is carried out in order to compare the performance of two different bootstrap estimators with the approximation given by Prasad and Rao [Prasad, N.G.N. and Rao, J.N.K., 1990, The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association, 85, 163–171.]. In the numerical results, one of the bootstrap estimators shows a better bias behavior than the Prasad–Rao approximation for some of the small areas and not much worse in any case. Further, it shows less MSE in situations of moderate heteroscedasticity and under mispecification of the error distribution as normal when the true distribution is logistic or Gumbel. The proposed bootstrap method can be applied to more general types of parameters (linear of not) and predictors.     

Change-Point Detection in Two-Phase Regression with Inequality Constraints on the Regression Parameters

Two-phase regression models with inequality constraints on the regression coefficients and with a small number of measurements is considered. A new test based on the likelihood ratio in linear model with inequality constraints for the presence of a change-point is proposed. Numerical approximations to the powers against various alternatives are given and compared with the powers of the likelihood ratio test in the two-phase regression models without inequality constraints, the backwards CUSUM test, and the k-linear-r-ahead recursive residuals tests. Performance of related likelihood based estimators of the change-point is briefly studied in a Monte Carlo experiment.     

MODEL‐BASED DIRECT ESTIMATION OF SMALL‐AREA DISTRIBUTIONS

Much of the small‐area estimation literature focuses on population totals and means. However, users of survey data are often interested in the finite‐population distribution of a survey variable and in the measures (e.g. medians, quartiles, percentiles) that characterize the shape of this distribution at the small‐area level. In this paper we propose a model‐based direct estimator (MBDE, Chandra and Chambers) of the small‐area distribution function. The MBDE is defined as a weighted sum of sample data from the area of interest, with weights derived from the calibrated spline‐based estimate of the finite‐population distribution function introduced by Harms and Duchesne, under an appropriately specified regression model with random area effects. We also discuss the mean squared error estimation of the MBDE. Monte Carlo simulations based on both simulated and real data sets show that the proposed MBDE and its associated mean squared error estimator perform well when compared with alternative estimators of the area‐specific finite‐population distribution function.     

A study of ratio and product estimators under a super population model

In this paper ratio and product estimators are studied under a super population model considered by Durbin (1959. Biometrika) where a regression model of y (the characteristic variablel on x(the auxiliary variable) is assumed. The comparison of the ratio and the product estimators have been made in the literature (see Chaubey, Dwivedi and Singh (1984), Commun. Statist. - Theor. Meth.) When the auxiliary variable has a gamma distribution. In this paper similar analysis has been carried out when the auxiliary variable has an inverse Gaussian distribution.     

Confidence intervals for the closed population size under inverse sampling without replacement

Inverse sampling is an appropriate design for the second phase of capture-recapture experiments which provides an exactly unbiased estimator of the population size. However, the sampling distribution of the resulting estimator tends to be highly right skewed for small recapture samples, so, the traditional Wald-type confidence intervals appear to be inappropriate. The objective of this paper is to study the performance of interval estimators for the population size under inverse recapture sampling without replacement. To this aim, we consider the Wald-type, the logarithmic transformation-based, the Wilson score, the likelihood ratio and the exact methods. Also, we propose some bootstrap confidence intervals for the population size, including the with-replacement bootstrap (BWR), the without replacement bootstrap (BWO), and the Rao–Wu’s rescaling method. A Monte Carlo simulation is employed to evaluate the performance of suggested methods in terms of the coverage probability, error rates and standardized average length. Our results show that the likelihood ratio and exact confidence intervals are preferred to other competitors, having the coverage probabilities close to the desired nominal level for any sample size, with more balanced error rate for exact method and shorter length for likelihood ratio method. It is notable that the BWO and Rao–Wu’s rescaling methods also may provide good intervals for some situations, however, those coverage probabilities are not invariant with respect to the population arguments, so one must be careful to use them.     

Semi-empirical pseudo-likelihood for estimating equations in the presence of missing responses

Consider a semiparametric model which parameterizes only the conditional distribution of Y given X, f(y|x,β), and allows the marginal distribution of X to be completely arbitrary. Under the semiparametric model, we develop semi-empirical pseudo-likelihood inference with estimating equation in the presence of missing responses. We define semi-empirical likelihood pseudo-score estimates for both the model parameter and the parameter in the estimating equation simultaneously. Also, we develop semi-empirical pseudo-likelihood ratio inference for them, respectively. A simulation was conducted to evaluate the finite sample properties of the proposed estimators and semi-empirical pseudo-likelihood approach.     

Automated selection of post‐strata using a model‐assisted regression tree estimator

Despite having desirable properties, model‐assisted estimators are rarely used in anything but their simplest form to produce official statistics. This is due to the fact that the more complicated models are often ill suited to the available auxiliary data. Under a model‐assisted framework, we propose a regression tree estimator for a finite‐population total. Regression tree models are adept at handling the type of auxiliary data usually available in the sampling frame and provide a model that is easy to explain and justify. The estimator can be viewed as a post‐stratification estimator where the post‐strata are automatically selected by the recursive partitioning algorithm of the regression tree. We establish consistency of the regression tree estimator and a variance estimator, along with asymptotic normality of the regression tree estimator. We compare the performance of our estimator to other survey estimators using the United States Bureau of Labor Statistics Occupational Employment Statistics Survey data.     

Inference for Quantiles of a Finite Population: Asymptotic versus Resampling Results

The aim of the paper is to study the problem of estimating the quantile function of a finite population. Attention is first focused on point estimation, and asymptotic results are obtained. Confidence intervals are then constructed, based on both the following: (i) asymptotic results and (ii) a resampling technique based on rescaling the ‘usual’ bootstrap. A simulation study to compare asymptotic and resampling‐based results, as well as an application to a real population, is finally performed.     

Some improved ratio type estimators of population mean and ratio in finite population sample surveys

In this paper we present a class of ratio type estimators of the population mean and ratio in a finite population sample surveys with without replacement simple random sampling design, where information on an auxiliary variate x positively correlated with the main variate y is available. Large sample approximations to mean square errors (MSE) of these estimatorsare evaluated and their MSE's are compared with the MSE of the usual ratio estimator [ybar]_R of [ybar] the population mean of y. It is shown that under certain conditions these estimators are more efficient than [ybar]_R. When a prior knowledge of the value of thecoefficient of variation, c_y, of y is at hand, ratio type estimator, say [ybar]₁ of [ybar] is proposed. It is shown, under certain conditions, that [ybar]₁ is more efficient than [ybar]_R. When values of c_y, c_x and the population correlation coefficient ρ is at hand, then we have proposed another estimator, say [ybar]₂ of [ybar], which is always better than [ybar]_R as far as the efficiency is concerned. In fact, is [ybar] ₂ is shown to be even better than [ybar]₁. Finally estimators better than the usual ratio estimator [ybar]/[xbar] of [Ybar] are given.     

Conditional inference in finite population sampling under a calibration model

Several estimators, including the classical and the regression estimators of finite population mean, are compared, both theoretically and empirically, under a calibration model, where the dependent variable(y), and not the independent variable(x), can be observed for all units of the finite population. It is shown asymptotically that when conditioned on x, the bias of the classical estimator may be much smaller than that of the regression estimators; whereas when conditioned on y, the regression estimator may have much smaller conditional bias than the classical estimator. Since all the y's(not x's) can be observed, it seems appropriate to make comparison under the conditional distribution of each estimator with y fixed. In this case, the regression estimator has smaller variance, smaller conditional bias, and the conditional coverage probability closer to its nominal level     

A two-way classification of regression estimation strategies in probability sampling

This paper examines strategies for estimating the mean of a finite population in the following situation: A linear regression model is assumed to describe the population scatter. Various estimators β for the vector of regression parameters β are considered. Several ways of transforming each estimator β into a model-based estimator for the population mean are considered. Some estimators constructed in this way become sensitive to correctness of the assumed model. The estimators favoured in this paper are the ones in which the observations are weighted to reflect the sampling design, so that asymptotic design unbiasedness is achieved. For these estimators, the randomization distribution gives protection against model breakdown.     

On bootstrap testing inference in cure rate models

Survival models deal with the time until the occurrence of an event of interest. However, in some situations the event may not occur in part of the studied population. The fraction of the population that will never experience the event of interest is generally called cure rate. Models that consider this fact (cure rate models) have been extensively studied in the literature. Hypothesis testing on the parameters of these models can be performed based on likelihood ratio, gradient, score or Wald statistics. Critical values of these tests are obtained through approximations that are valid in large samples and may result in size distortion in small or moderate sample sizes. In this sense, this paper proposes bootstrap corrections to the four mentioned tests and bootstrap Bartlett correction for the likelihood ratio statistic in the Weibull promotion time model. Besides, we present an algorithm for bootstrap resampling when the data presents cure fraction and right censoring time (random and non-informative). Simulation studies are conducted to compare the finite sample performances of the corrected tests. The numerical evidence favours the corrected tests we propose. We also present an application in an actual data set.     

Minimax prediction in finite populations

In this paper, minimax predictors are considered for some population quantities of interest, under some specific superpopulation models. Minimax predictors are derived under a binomial superpopulation model. The well known ratio estimator is shown to be minimax under the usual simple regression normal model. Nonparametric minimax predictors are considered under some models. Some of the predictors considered also shown to be admis s ible.     

Testing for a finite mixture model with two components

Summary.  We consider a finite mixture model with k components and a kernel distribution from a general one-parameter family. The problem of testing the hypothesis k =2 versus k 3 is studied. There has been no general statistical testing procedure for this problem. We propose a modified likelihood ratio statistic where under the null and the alternative hypotheses the estimates of the parameters are obtained from a modified likelihood function. It is shown that estimators of the support points are consistent. The asymptotic null distribution of the modified likelihood ratio test proposed is derived and found to be relatively simple and easily applied. Simulation studies for the asymptotic modified likelihood ratio test based on finite mixture models with normal, binomial and Poisson kernels suggest that the test proposed performs well. Simulation studies are also conducted for a bootstrap method with normal kernels. An example involving foetal movement data from a medical study illustrates the testing procedure.     

Estimating the Size of a Subdomain: An Application in Auditing

This article suggests an alternative to the ratio estimator for estimating the total size of a subdomain of a population. The application that served as the genesis for this work is from auditing. The problem is to estimate the total of sales transactions that are not tax exempt from an audit sample of the population of nontaxed sales transactions. A superpopulation approach, which models the unit's probability of belonging to the subdomain as a function of its size, leads to a family of estimators. The simplest member of this famiiy is one in which that function is specified to be a constant. The optimal estimator for this model performs markedly better than the ratio estimator when the assumption is true and often performs better when it is not, though in that case it is biased. Stratification is shown to reduce this bias and at the same time make the ratio estimator more similar to the optimal estimator. A simulation experiment shows that the theoretical advantages hold in a real audit population.     

A Mixed Model-assisted Regression Estimator that Uses Variables Employed at the Design Stage

The Generalized regression estimator (GREG) of a finite population mean or total has been shown to be asymptotically optimal when the working linear regression model upon which it is based includes variables related to the sampling design. In this paper a regression estimator assisted by a linear mixed superpopulation model is proposed. It accounts for the extra information coming from the design in the random component of the model and saves degrees of freedom in finite sample estimation. This procedure combines the larger asymptotic efficiency of the optimal estimator and the greater finite sample stability of the GREG. Design based properties of the proposed estimator are discussed and a small simulation study is conducted to explore its finite sample performance.