scholarly journals Relative efficiencies of two‐stage sampling schemes for mean estimation in multilevel populations when cluster size is informative

2018 ◽  
Vol 38 (10) ◽  
pp. 1817-1834
Author(s):  
Francesco Innocenti ◽  
Math J.J.M. Candel ◽  
Frans E.S. Tan ◽  
Gerard J.P. Breukelen
Keyword(s):  
Cluster Size ◽  
Two Stage ◽  
Sampling Schemes ◽  
Mean Estimation

scholarly journals Optimal two-stage sampling for mean estimation in multilevel populations when cluster size is informative

2020 ◽  
pp. 096228022095283
Author(s):  
Francesco Innocenti ◽  
Math JJM Candel ◽  
Frans ES Tan ◽  
Gerard JP van Breukelen
Keyword(s):  
Cluster Size ◽  
Simple Random Sampling ◽  
Equal Probability ◽  
Outcome Variable ◽  
Two Stage ◽  
Mean Estimation ◽  
Informative Cluster Size ◽  
The Mean ◽  
Two Stages ◽  
Number Of Individuals

To estimate the mean of a quantitative variable in a hierarchical population, it is logistically convenient to sample in two stages (two-stage sampling), i.e. selecting first clusters, and then individuals from the sampled clusters. Allowing cluster size to vary in the population and to be related to the mean of the outcome variable of interest (informative cluster size), the following competing sampling designs are considered: sampling clusters with probability proportional to cluster size, and then the same number of individuals per cluster; drawing clusters with equal probability, and then the same percentage of individuals per cluster; and selecting clusters with equal probability, and then the same number of individuals per cluster. For each design, optimal sample sizes are derived under a budget constraint. The three optimal two-stage sampling designs are compared, in terms of efficiency, with each other and with simple random sampling of individuals. Sampling clusters with probability proportional to size is recommended. To overcome the dependency of the optimal design on unknown nuisance parameters, maximin designs are derived. The results are illustrated, assuming probability proportional to size sampling of clusters, with the planning of a hypothetical survey to compare adolescent alcohol consumption between France and Italy.

scholarly journals An Estimation of Sensitive Attribute Applying Geometric Distribution under Probability Proportional to Size Sampling

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1102
Author(s):  
Gi-Sung Lee ◽  
Ki-Hak Hong ◽  
Chang-Kyoon Son
Keyword(s):  
Sampling Methods ◽  
Geometric Distribution ◽  
Equal Probability ◽  
Two Stage ◽  
Generalized Model ◽  
Sampling Schemes ◽  
Variance Estimators ◽  
Numerical Studies ◽  
Sensitive Attribute ◽  
S Model

In this paper, we extended Yennum et al.’s model, in which geometric distribution is used as a randomization device for a population that consists of different-sized clusters, and clusters are obtained by probability proportional to size (PPS) sampling. Estimators of a sensitive parameter, their variances, and their variance estimators are derived under PPS sampling and equal probability two-stage sampling, respectively. We also applied these sampling schemes to Yennum et al.’s generalized model. Numerical studies were carried out to compare the efficiencies of the proposed sampling methods for each case of Yennum et al.’s model and Yennum et al.’s generalized model.

Forest inventory: further results for optimal sampling schemes based on the anticipated variance

2001 ◽  
Vol 31 (10) ◽  
pp. 1845-1853 ◽  
Author(s):  
Daniel Mandallaz ◽  
Adrian Lanz
Keyword(s):  
Forest Inventory ◽  
Optimal Allocation ◽  
Optimality Criterion ◽  
Second Phase ◽  
Optimal Sampling ◽  
Two Stage ◽  
Two Phase ◽  
Sampling Density ◽  
Sampling Schemes ◽  
Inclusion Probabilities

This work presents optimal allocation rules for two-phase, two-stage sampling schemes in which the sampling density and the costs of the second phase can vary over domains. The optimality criterion is based on the anticipated variance. It also gives an improved version of discrete approximation for the resulting inclusion probabilities. An example illustrates the theory.

scholarly journals Two-stage sector sampling for estimating small woodlot attributes

2011 ◽  
Vol 41 (9) ◽  
pp. 1819-1826 ◽  
Author(s):  
Piermaria Corona ◽  
Lorenzo Fattorini ◽  
Sara Franceschi
Keyword(s):  
Large Scale ◽  
Sampling Strategy ◽  
Sampling Variance ◽  
Sampling Strategies ◽  
Fixed Size ◽  
Two Stage ◽  
Sampling Schemes ◽  
Second Stage ◽  
Forest Inventories ◽  
Plot Sampling

A two-stage sampling strategy is proposed to assess small woodlots outside the forests scattered on extensive territories. The first stage is performed to select a sample of small woodlots using fixed-size sampling schemes, and the second stage is performed to sample trees within woodlots selected at first stage. Usually, fixed- or variable-area plots are adopted to sample trees. However, the use of plot sampling in small patches such as woodlots is likely to induce a relevant amount of bias owing to edge effects. In this framework, sector sampling proves to be particularly effective. The present paper investigates the statistical properties of two-stage sampling strategies for estimating forest attributes of woodlot populations when sector sampling is adopted at the second stage. A two-stage estimator of population totals is derived together with a conservative estimator of its sampling variance. By means of a simulation study, the performance of the proposed estimator is checked and compared with that achieved using traditional plot sampling with edge corrections. Simulation results prove the adequacy of sector sampling and provide some guidelines for the effective planning of the strategy. In some countries, the proposed strategy can be performed with few modifications within the framework of large-scale forest inventories.

Forest inventory with optimal two-phase two-stage sampling schemes based on the anticipated variance

1999 ◽  
Vol 29 (11) ◽  
pp. 1691-1708 ◽  
Author(s):  
Daniel Mandallaz ◽  
Ronghua Ye
Keyword(s):  
Spatial Distribution ◽  
Forest Inventory ◽  
Poisson Model ◽  
Optimal Sampling ◽  
Two Stage ◽  
Two Phase ◽  
Sampling Schemes ◽  
One Stage ◽  
Sampling Procedures

This work presents optimal sampling schemes for forest inventory. The sampling procedures are optimal in the sense that they minimize the anticipated variance for given costs or conversely, the anticipated variance is the average of the design-based variance under a local Poisson model for the spatial distribution of the trees. The resulting optimal inclusion rules are either probability proportional to size, in one-stage procedures, or a combination of probability proportional to prediction and probability proportional to error, in two-stage procedures. Best feasible approximations of the exact optimal sampling schemes are also given.

Production and STEM examination of controlled-size silver clusters

1983 ◽  
Vol 41 ◽  
pp. 338-339
Author(s):  
M. A. Listvan ◽  
R. P. Andres
Keyword(s):  
Cluster Size ◽  
Metal Clusters ◽  
Experimental Parameter ◽  
Carbon Films ◽  
Metal Species ◽  
Silver Clusters ◽  
Free Jet ◽  
Size Dependent ◽  
Cluster Properties ◽  
Controllable Size

Knowledge of the function and structure of small metal clusters is one goal of research in catalysis. One important experimental parameter is cluster size. Ideally, one would like to produce metal clusters of regulated size in order to characterize size-dependent cluster properties.A source has been developed which is capable of producing microscopic metal clusters of controllable size (in the range 5-500 atoms) This source, the Multiple Expansion Cluster Source, with a Free Jet Deceleration Filter (MECS/FJDF) operates as follows. The bulk metal is heated in an oven to give controlled concentrations of monomer and dimer which were expanded sonically. These metal species were quenched and condensed in He and filtered to produce areosol particles of a controlled size as verified by mass spectrometer measurements. The clusters were caught on pre-mounted, clean carbon films. The grids were then transferred in air for microscopic examination. MECS/FJDF was used to produce two different sizes of silver clusters for this study: nominally Ag6 and Ag50.

Two-stage self-seeding method for preparation of single crystals of poly(phenylene sulfide)

1989 ◽  
Vol 47 ◽  
pp. 368-369
Author(s):  
Sengshiu Chung ◽  
Peggy Cebe
Keyword(s):  
Single Crystals ◽  
High Performance ◽  
Dilute Solution ◽  
Two Stage ◽  
Annealing Behavior ◽  
High Performance Polymers ◽  
Seeding Method ◽  
Phenylene Sulfide

We are studying the crystallization and annealing behavior of high performance polymers, like poly(p-pheny1ene sulfide) PPS, and poly-(etheretherketone), PEEK. Our purpose is to determine whether PPS, which is similar in many ways to PEEK, undergoes reorganization during annealing. In an effort to address the issue of reorganization, we are studying solution grown single crystals of PPS as model materials.Observation of solution grown PPS crystals has been reported. Even from dilute solution, embrionic spherulites and aggregates were formed. We observe that these morphologies result when solutions containing uncrystallized polymer are cooled. To obtain samples of uniform single crystals, we have used two-stage self seeding and solution replacement techniques.

364: Two stage "Progressive Elongation of Spermatic Cord" Technique in Criptorchidism with very short Spermatic Vessels

2007 ◽  
Vol 177 (4S) ◽  
pp. 121-121
Author(s):  
Antonio Dessanti ◽  
Diego Falchetti ◽  
Marco Iannuccelli ◽  
Susanna Milianti ◽  
Gian P. Strusi ◽  
...  
Keyword(s):  
Spermatic Cord ◽  
Two Stage
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