Horvitz-Thompson estimators for functional data: asymptotic confidence bands and optimal allocation for stratified sampling

Adapting a global stratified random sample for regional estimation of forest cover change derived from satellite imagery

Optimal spatial sampling techniques for ground truth data in microwave remote sensing of soil moisture

There are several reasons why robust regression techniques are useful tools in sampling design. First of all, when stratified samples are considered, one needs to deal with three main issues: the sample size, the strata bounds determination and the sample allocation in the strata. Since the target variable Y, the objective of the survey, is unknown, some auxiliary information X known for the entire population from which the sample is drawn, is used. Such information is helpful as it is typically strongly correlated with the target Y. However, some discrepancies between these variables may arise. The use of auxiliary information, combined with the choice of the appropriate statistical model to estimate the relationship between Y and X, is crucial for the determination of the strata bounds, the size of the sample and the sampling rates according to a chosen precision level for the estimates, as has been shown by Rivest (2002). Nevertheless, this regression-based approach is highly sensitive to the presence of contaminated data. Since the key tool for stratified sampling is the measure of scale of Y conditional on the knowledge of the auxiliary X, a robust approach based on the S-estimator of the regression is proposed in this paper. The aim is to allow for robust sample size and strata bounds determination, together with optimal sample allocation. Simulation results based on data from the Construction sector of a Structural Business Survey illustrate the advantages of the proposed method.

For surveys of sensitive issues in life sciences, statistical procedures can be used to reduce nonresponse and social desirability response bias. Both of these phenomena provoke nonsampling errors that are difficult to deal with and can seriously flaw the validity of the analyses. The item sum technique (IST) is a very recent indirect questioning method derived from the item count technique that seeks to procure more reliable responses on quantitative items than direct questioning while preserving respondents' anonymity. This article addresses two important questions concerning the IST: (i) its implementation when two or more sensitive variables are investigated and efficient estimates of their unknown population means are required; (ii) the determination of the optimal sample size to achieve minimum variance estimates. These aspects are of great relevance for survey practitioners engaged in sensitive research and, to the best of our knowledge, were not studied so far. In this article, theoretical results for multiple estimation and optimal allocation are obtained under a generic sampling design and then particularized to simple random sampling and stratified sampling designs. Theoretical considerations are integrated with a number of simulation studies based on data from two real surveys and conducted to ascertain the efficiency gain derived from optimal allocation in different situations. One of the surveys concerns cannabis consumption among university students. Our findings highlight some methodological advances that can be obtained in life sciences IST surveys when optimal allocation is achieved.

Estimation of contingency tables in complex survey sampling using probabilistic expert systems

In many real-world situations, systems frequently fail due to demanding operating conditions. In particular, when systems reach their lowest, highest, or both extremes operating conditions, they usually fail to accomplish their intended functions. This study considers estimating the stress–strength reliability, for a component with a strength (X) that is independent of the opposing lower bound stress (Y) and upper bound stress (Z). We assumed that the strength and stress random variables followed a generalized inverse exponential distribution with different shape parameters. Under ranked set sampling (RSS) and simple random sampling (SRS) designs, we obtained four reliability estimators using the maximum likelihood method. The first and second reliability estimators were deduced when the sample data of the strength and stress distributions used the sample design (RSS/SRS). The third reliability estimator was determined when the sample data for Y and Z were received from the RSS and the sample data for X were taken from the SRS. The fourth reliability estimator was derived when the sample data of Y and Z were selected from the SRS, while the sample data of X were taken from the RSS. The accuracy of the suggested estimators was compared using a comprehensive computer simulation. Lastly, three real data sets were used to determine the reliability.

In this study, comparison has been made for different sampling designs, using the HIES data of North West Frontier Province (NWFP) for 2001-02 and 1998-99 collected from the Federal Bureau of Statistics, Statistical Division, Government of Pakistan, Islamabad. The performance of the estimators has also been considered using bootstrap and Jacknife. A two-stage stratified random sample design is adopted by HIES. In the first stage, enumeration blocks and villages are treated as the first stage Primary Sampling Units (PSU). The sample PSU’s are selected with probability proportional to size. Secondary Sampling Units (SSU) i.e., households are selected by systematic sampling with a random start. They have used a single study variable. We have compared the HIES technique with some other designs, which are: Stratified Simple Random Sampling. Stratified Systematic Sampling. Stratified Ranked Set Sampling. Stratified Two Phase Sampling. Ratio and Regression methods were applied with two study variables, which are: Income (y) and Household sizes (x). Jacknife and Bootstrap are used for variance replication. Simple Random Sampling with sample size (462 to 561) gave moderate variances both by Jacknife and Bootstrap. By applying Systematic Sampling, we received moderate variance with sample size (467). In Jacknife with Systematic Sampling, we obtained variance of regression estimator greater than that of ratio estimator for a sample size (467 to 631). At a sample size (952) variance of ratio estimator gets greater than that of regression estimator. The most efficient design comes out to be Ranked set sampling compared with other designs. The Ranked set sampling with jackknife and bootstrap, gives minimum variance even with the smallest sample size (467). Two Phase sampling gave poor performance. Multi-stage sampling applied by HIES gave large variances especially if used with a single study variable.

There are two distinct types of domains, design- and cross-classes domains , with the former extensively studied under the topic of small-area estimation. In natural resource inventory, however, most classes listed in the condition tables of national inventory programs are characterized as cross-classes domains, such as vegetation type, productivity class, and age class. To date, challenges remain active for inventorying cross-classes domains because these domains are usually of unknown sampling frame and spatial distribution with the result that inference relies on population-level as opposed to domain-level sampling. Multiple challenges are noteworthy: (1) efficient sampling strategies are difficult to develop because of little priori information about the target domain; (2) domain inference relies on a sample designed for the population, so within-domain sample sizes could be too small to support a precise estimation; and (3) increasing sample size for the population does not ensure an increase to the domain, so actual sample size for a target domain remains highly uncertain, particularly for small domains. In this paper, we introduce a design-based generalized systematic adaptive cluster sampling (GSACS) for inventorying cross-classes domains. Design-unbiased Hansen-Hurwitz and Horvitz-Thompson estimators are derived for domain totals and compared within GSACS and with systematic sampling (SYS). Comprehensive Monte Carlo simulations show that (1) GSACS Hansen-Hurwitz and Horvitz-Thompson estimators are unbiased and equally efficient, whereas the latter outperforms the former for supporting a sample of size one; (2) SYS is a special case of GSACS while the latter outperforms the former in terms of increased efficiency and reduced intensity; (3) GSACS Horvitz-Thompson variance estimator is design-unbiased for a single SYS sample; and (4) rules-of-thumb summarized with respect to sampling design and spatial effect improve precision. Because inventorying a mini domain is analogous to inventorying a rare variable, alternative network sampling procedures are also readily available for inventorying cross-classes domains. ⁃ Generalized systematic adaptive cluster sampling devised for inventorying cross-classes domains ⁃ Unbiased Hansen-Hurwitz and Horvitz-Thompson estimators derived for domain estimation ⁃ Analytical and empirical comparisons made within GSACS and with systematic sampling ⁃ GSACS provides estimates identical to SS using observations fewer on the order of 20%–40% ⁃ Network sampling procedures including GSACS are efficient for inventorying small domains

The aim of this paper is to verify the validity of the model-based approach in sampling from finite populations. Standard sampling techniques are compared to model-based sampling with reference to stratified sampling. In particular, we compare the strategies of Dalenius and Hodges, which regard optimum and proportional allocation and the use of auxiliary variables, in contrast with the sampling strategies which use model-based stratification with a uniform allocation. These comparisons are made verifying the efficiency of the above mentioned estimators with respect to the lower bound variance of the Horvitz-Thompson estimator. We assume a linear model of superpopulation and a gamma distribution of the auxiliary variable.

Two Stage Sampling procedure has been found to be much more acceptable for demographic surveys owing to the lower cost involved and also due to the fact that it gives rise to a good representative sample. .As such, it has been found to be much acceptable for estimating total fertility rate (TFR), an important measure of fertility. The objective of this paper is to estimate the TFR in the slum pockets of Guwahati city in Assam under two stage sampling technique and to bring out a comparative analysis of the TFR calculated under the proposed sampling design and under the Simple Random Sampling (SRS) method.The study reveals that the overall fertility scenario in the slum areas of Guwahati, as far as TFR is concerned, when calculated under two stage sampling technique is above the replacement level. However, the TFR calculated by SRS method is found to be almost equal to the replacement level, implying under estimation of TFR when calculated by this method. Moreover, it has been seen that the adjusted TFRs derived after adjusting the biases marginally increases in case of SRS technique and decreases in case of two stage sampling technique. The MSE s are found to be higher in case of conventional technique, implying that the sampling error involved in the conventional method is more as compared to two stage sampling technique. We may thus consider two stage sampling method as a better technique for estimating TFR.

This chapter includes basic survey data analysis, such as estimating frequencies, means, and statistical models, using ‘survey instruments’ but not going into most complex cases. The purpose is to give instructions for survey analysis using general statistical software, such as SAS, SPSS, STATA, or R, but without details about them. Examples using PISA and ESS are the main part here, some being derived from ESS-related test data as well (see Sect. 6.1). The chapter is primarily based on these examples. They do not cover complex samples, but such can be rather straightforwardly calculated using one of the software packages. The SAS, SPSS, STATA, or R software work well with the following sampling designs in cross-sectional surveys: Simple or stratified random sampling Equidistance sampling, assuming that it corresponds to simple random sampling Unstratified or stratified two-stage cluster sampling

To look at the individual features of three different methods used to estimate simple parameters--means, totals, and percentages, as well as their standard errors--and of logistic regression models, and to describe how such methods can be used for analyzing data obtained from complex samples. Data from Cuba's Second National Survey of Risk Factors and Non-Communicable Chronic Ailments [Segunda Encuesta Nacional de Factores de Riesgo y Afecciones Crónicas No Transmisibles], which was conducted in 2001, were studied. A complex, stratified multi-stage cluster sampling design was used. Cuba's 14 provinces and the municipality of Isla de la Juventud served as the strata, while the clusters consisted of sampled geographic areas (SGA), blocks, and sectors. Samples were weighted in inverse proportion to their probability of being selected, and estimates were performed by sex and age group (15-34, 35-54, 55-74, and 75 or more years). Taylor approximations were used to estimate variances. Three statistical methods were compared: conventional analysis, which assumes all data were obtained through simple random sampling; weighted analysis, which only takes into account the weight of the samples when performing estimates; and adjusted analysis, which looks at all aspects of the sampling design (namely, the disparity in the probability of being included in the sample and the effect of clustering on the data). The point estimates obtained with the three different types of analytic methods were similar. Standard error (SE) estimates for the prevalence of overweight and of arterial hypertension that were obtained by conventional analysis were underestimated by 19.3% and by more than 11.5%, respectively, when such estimates were compared to those obtained with the other two analytic methods. On the other hand, weighted analysis generated SE values that were much smaller than those obtained with the other two types of analyses. The same pattern was noted when odds ratios were calculated using the different methods. Analytic methods that take into account the way the data are structured as well as the study design give a more realistic picture of the problem under study and provide more exact estimates of the study parameters and their SE than conventional analytic methods. Because data from epidemiologic and public health research are often obtained through complex sampling designs, the methods described in this paper and the statistical packages that utilize them should be used more widely.

Numerous optimization problems arise in survey designs. The problem of obtaining an optimal (or near optimal) sampling design can be formulated and solved as a mathematical programming problem. In multivariate stratified sample surveys usually it is not possible to use the individual optimum allocations for sample sizes to various strata for one reason or another. In such situations some criterion is needed to work out an allocation which is optimum for all characteristics in some sense. Such an allocation may be called an optimum compromise allocation. This paper examines the problem of determining an optimum compromise allocation in multivariate stratified random sampling, when the population means of several characteristics are to be estimated. Formulating the problem of allocation as an all integer nonlinear programming problem, the paper develops a solution procedure using a dynamic programming technique. The compromise allocation discussed is optimal in the sense that it minimizes a weighted sum of the sampling variances of the estimates of the population means of various characteristics under study. A numerical example illustrates the solution procedure and shows how it compares with Cochran's average allocation and proportional allocation.

Relative indices of abundance are key to providing science advice for the management of many fish stocks. Historical focus has been on design-based estimation, wherein mathematical formulae for aggregating data into a single index are directly informed by the underlying sampling design. Recent efforts have moved toward using index standardization models instead. However, the impacts sampling designs and allocation schemes have on these index standardization models have not been fully examined. Using a spatio-temporal multinomial index standardization model developed for survey data obtained with longline fishing gear, we develop a simulation framework to analyze the effects of five different combinations of sampling designs and allocation schemes under various conditions. These simulations expose bias in model-based indices caused by non-proportional-to-area designs, which are common in surveys that have historically utilized design-based estimation. We explore the impact of robust statistical alternatives on this bias. This effort highlights an important source of bias and the importance of periodically reassessing allocation schemes and sampling designs for scientific surveys.

To use computable phenotypes for characterization of patients and identification of outcomes in studies conducted using healthcare claims and electronic health record data. Chart review studies establish reference labels against which computable phenotypes are compared to understand their measurement characteristics (the quantity of interest), for instance, the positive predictive value. We describe a method to adaptively evaluate a quantity of interest over sequential samples of charts, with the goal to minimize the number of charts reviewed. With the help of a simultaneous confidence band, we stop the reviewing once the confidence band meets a pre-specified stopping threshold. The contribution of this work is threefold. First, we test the use of an adaptive approach called Neyman's sampling versus random or stratified random sampling. Second, we propose frequentist confidence bands and Bayesian credible intervals to sequentially evaluate the quantity of interest. Third, we propose a tool to predict the stopping time (defined as the number of charts reviewed) at which the chart review would be complete. We observe that Bayesian credible intervals prove to be tighter than its frequentist confidence band counterparts. Moreover, we observe that simple random sampling often performs similarly to Neyman's sampling. We conclude that random sampling in connection with Bayesian credible intervals allows for an efficient validation of a response of interest for both binary and continuous outcomes.