Derivation of a Class of Frequency Distributions Via Bayes’s Theorem

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/146824/1/rssb01496.pd

Domain estimators calibrated on information from another survey

We examine calibration estimation in a setting where two surveys are conducted on the same finite population. Some variables of study are common to the two surveys, but the second one requires greater detail in the statistics produced than the already published first one. More specifically, we require estimates for sub-populations, called domains, that are identified only in the second survey to add up consistently to known or estimated totals published for the common variables in the first survey. We outline and study several options for deriving calibration estimators for the domains identified in the second survey. We obtain explicit expressions showing how the calibration weights are related in the different approaches. The concluding section presents the results of a simulation study, comparing the precisions attained in the different options

Should adjustment for covariates be used in prevalence estimations?

Background Adjustment for covariates (also called auxiliary variables in survey sampling literature) is commonly applied in health surveys to reduce the variances of the prevalence estimators. In theory, adjusted prevalence estimators are more accurate when variance components are known. In practice, variance components needed to achieve the adjustment are unknown and their sample estimators are used instead. The uncertainty introduced by estimating variance components may overshadow the reduction in the variance of the prevalence estimators due to adjustment. We present empirical guidelines indicating when adjusted prevalence estimators should be considered, using gender adjusted and unadjusted smoking prevalence as an illustration. Methods We compare the accuracy of adjusted and unadjusted prevalence estimators via simulation. We simulate simple random samples from hypothetical populations with the proportion of males ranging from 30% to 70%, the smoking prevalence ranging from 15% to 35%, and the ratio of male to female smoking prevalence ranging from 1 to 4. The ranges of gender proportions and smoking prevalences reflect the conditions in 1999–2003 Behavioral Risk Factors Surveillance System (BRFSS) data for Massachusetts. From each population, 10,000 samples are selected and the ratios of the variance of the adjusted prevalence estimators to the variance of the unadjusted (crude) ones are computed and plotted against the proportion of males by population prevalence, as well as by population and sample sizes. The prevalence ratio thresholds, above which adjusted prevalence estimators have smaller variances, are determined graphically. Results In many practical settings, gender adjustment results in less accuracy. Whether or not there is better accuracy with adjustment depends on sample sizes, gender proportions and ratios between male and female prevalences. In populations with equal number of males and females and smoking prevalence of 20%, the adjusted prevalence estimators are more accurate when the ratios of male to female prevalences are above 2.4, 1.8, 1.6, 1.4 and 1.3 for sample sizes of 25, 50, 100, 150 and 200, respectively. Conclusion Adjustment for covariates will not result in more accurate prevalence estimator when ratio of male to female prevalences is close to one, sample size is small and risk factor prevalence is low. For example, when reporting smoking prevalence based on simple random sampling, gender adjustment is recommended only when sample size is greater than 200

Estimation of Non-Linear Parameters with Data Collected Using Respondent-Driven Sampling

Respondent-driven sampling (RDS) is a snowball-type sampling method used to survey hidden populations, that is, those that lack a sampling frame. In this work, we consider the problem of regression modeling and association for continuous RDS data. We propose a new sample weight method for estimating non-linear parameters such as the covariance and the correlation coefficient. We also estimate the variances of the proposed estimators. As an illustration, we performed a simulation study and an application to an ethnic example. The proposed estimators are consistent and asymptotically unbiased. We discuss the applicability of the method as well as future research.Ministerio de Economia, Industria y Competitividad, Spain MTM2015-63609-

Variance estimation for a low-income proportion

Proportions below a given fraction of a quantile of an income distribution are often estimated from survey data in poverty comparisons. We consider the estimation of the variance of such a proportion, estimated from Family Expenditure Survey data. We show how a linearization method of variance estimation may be applied to this proportion, allowing for the effects of both a complex sampling design and weighting by a raking method to population controls. We show that, for 1998-99 data, the estimated variances are always increased when allowance is made for the design and raking weights, the principal effect arising from the design. We also study the properties of a simplified variance estimator and discuss extensions to a wider class of poverty measures

A simple variance estimator of change for rotating repeated surveys: an application to the EU-SILC household surveys

A common problem is to compare two cross-sectional estimates for the same study variable taken on two different waves or occasions, and to judge whether the change observed is statistically significant. This involves the estimation of the sampling variance of the estimator of change. The estimation of this variance would be relatively straightforward if cross-sectional estimates were based on the same sample. Unfortunately, samples are not completely overlapping, because of rotations used in repeated surveys. We propose a simple approach based on a multivariate (general) linear regression model. The variance estimator proposed is not a model-based estimator. We show that the estimator proposed is design consistent when the sampling fractions are negligible. It can accommodate stratified and two-stage sampling designs. The main advantage of the approach proposed is its simplicity and flexibility. It can be applied to a wide class of sampling designs and can be implemented with standard statistical regression techniques. Because of its flexibility, the approach proposed is well suited for the estimation of variance for the European Union Statistics on Income and Living Conditions surveys. It allows us to use a common approach for variance estimation for the different types of design. The approach proposed is a useful tool, because it involves only modelling skills and requires limited knowledge of survey sampling theory

Properties of Design-Based Functional Principal Components Analysis

This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA is a dimension reduction tool which is the first step to develop model assisted approaches that can take auxiliary information into account. FPCA relies on the estimation of the eigenelements of the covariance operator which can be seen as nonlinear functionals. Adapting to our functional context the linearization technique based on the influence function developed by Deville (1999), we prove that these estimators are asymptotically design unbiased and consistent. Under mild assumptions, asymptotic variances are derived for the FPCA' estimators and consistent estimators of them are proposed. Our approach is illustrated with a simulation study and we check the good properties of the proposed estimators of the eigenelements as well as their variance estimators obtained with the linearization approach.Comment: Revised version for J. of Statistical Planning and Inference (January 2009