GMM Based Inference with Standard Stratified Samples when the Aggregate Shares are Known

We show how to do efficient moment based inference using the generalized method of moments (GMM) when data is collected by standard stratified sampling and the maintained assumption is that the aggregate shares are known.

Variance estimation with highly stratified sampling designs with unequal probabilities

It is common practice to design a survey with a large number of strata. However, in this case the usual techniques for variance estimation can be inaccurate. This paper proposes a variance estimator for estimators of totals. The method proposed can be implemented with standard statistical packages without any specific programming, as it involves simple techniques of estimation, such as regression fitting.

Stratified Sampling Applied to Estimation of the Volumetric Fraction of Alumina in Cast Metal Matrix Composites

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Moment Based Inference with Stratified Data

Many datasets used by economists and other social scientists are collected by stratified sampling. The sampling scheme used to collect the data induces a probability distribution on the observed sample that differs from the target or underlying distribution for which inference is to be made. If this effect is not taken into account, subsequent statistical inference can be seriously biased. This paper shows how to do efficient semiparametric inference in moment restriction models when data from the target population is collected by three widely used sampling schemes: variable probability sampling, multinomial sampling, and standard stratified sampling.

Bacteria in shrimp pond sediments: their role in mineralizing nutrients and some suggested sampling strategies

Strategies for sampling sediment bacteria were examined in intensive shrimp, Penaeus monodon (Fabricius), ponds in tropical Australia. Stratified sampling of bacteria at the end of the production season showed that the pond centre, containing flocculated sludge, had significantly higher bacterial counts (15.5 X 10(9) g(-1) dw) than the pond periphery (8.1 X 10(9) g(-1) dw), where the action of aerators had swept the pond floor. The variation in bacterial counts between these two zones within a pond was higher than that between sites within each zone or between ponds. Therefore, sampling effort should be focused within these zones: for example, sampling two ponds at six locations within each of the two zones resulted in a coefficient of variation of approximate to 5%. Bacterial numbers in the sediment were highly correlated with sediment grain size, probably because eroded soil particles and organic waste both accumulated in the centre of the pond. Despite high inputs of organic matter added to the ponds, principally as pelleted feeds, the mean bacterial numbers and nutrient concentrations (i.e. organic carbon, nitrogen and phosphorus) in the sediment were similar to those found in mangrove sediments. This suggests that bacteria are rapidly remineralizing particulates into soluble compounds. Bacterial numbers were highly correlated with organic carbon and total kjeldahl nitrogen in the sediment, suggesting that these were limiting factors to bacterial growth.

Soil sampling design and sampling techniques for soil properties monitoring – common difficulties related to forest soils

Mathematical models and statistical analysis are key instruments in soil science scientific research as they can describe and/or predict the current state of a soil system. These tools allow us to explore the behavior of soil related processes and properties as well as to generate new hypotheses for future experimentation. A good model and analysis of soil properties variations, that permit us to extract suitable conclusions and estimating spatially correlated variables at unsampled locations, is clearly dependent on the amount and quality of data and of the robustness techniques and estimators. On the other hand, the quality of data is obviously dependent from a competent data collection procedure and from a capable laboratory analytical work. Following the standard soil sampling protocols available, soil samples should be collected according to key points such as a convenient spatial scale, landscape homogeneity (or non-homogeneity), land color, soil texture, land slope, land solar exposition. Obtaining good quality data from forest soils is predictably expensive as it is labor intensive and demands many manpower and equipment both in field work and in laboratory analysis. Also, the sampling collection scheme that should be used on a data collection procedure in forest field is not simple to design as the sampling strategies chosen are strongly dependent on soil taxonomy. In fact, a sampling grid will not be able to be followed if rocks at the predicted collecting depth are found, or no soil at all is found, or large trees bar the soil collection. Considering this, a proficient design of a soil data sampling campaign in forest field is not always a simple process and sometimes represents a truly huge challenge. In this work, we present some difficulties that have occurred during two experiments on forest soil that were conducted in order to study the spatial variation of some soil physical-chemical properties. Two different sampling protocols were considered for monitoring two types of forest soils located in NW Portugal: umbric regosol and lithosol. Two different equipments for sampling collection were also used: a manual auger and a shovel. Both scenarios were analyzed and the results achieved have allowed us to consider that monitoring forest soil in order to do some mathematical and statistical investigations needs a sampling procedure to data collection compatible to established protocols but a pre-defined grid assumption often fail when the variability of the soil property is not uniform in space. In this case, sampling grid should be conveniently adapted from one part of the landscape to another and this fact should be taken into consideration of a mathematical procedure.

Central corneal thickness, intraocular pressure, and degree of myopia in an adult myopic population aged 20 to 40 years in southeast Spain: determination and relationships

Objective: To determine the values of, and study the relationships among, central corneal thickness (CCT), intraocular pressure (IOP), and degree of myopia (DM) in an adult myopic population aged 20 to 40 years in Almeria (southeast Spain). To our knowledge this is first study of this kind in this region. Methods: An observational, descriptive, cross-sectional study was done in which a sample of 310 myopic patients (620 eyes) aged 20 to 40 years was selected by gender- and age-stratified sampling, which was proportionally fixed to the size of the population strata for which a 20% prevalence of myopia, 5% epsilon, and a 95% confidence interval were hypothesized. We studied IOP, CCT, and DM and their relationships by calculating the mean, standard deviation, 95% confidence interval for the mean, median, Fisher’s asymmetry coefficient, range (maximum, minimum), and the Brown-Forsythe’s robust test for each variable (IOP, CCT, and DM). Results: In the adult myopic population of Almeria aged 20 to 40 years (mean of 29.8), the mean overall CCT was 550.12 μm. The corneas of men were thicker than those of women (P = 0.014). CCT was stable as no significant differences were seen in the 20- to 40-year-old subjects’ CCT values. The mean overall IOP was 13.60 mmHg. Men had a higher IOP than women (P = 0.002). Subjects over 30 years (13.83) had a higher IOP than those under 30 (13.38) (P = 0.04). The mean overall DM was −4.18 diopters. Men had less myopia than women (P < 0.001). Myopia was stable in the 20- to 40-year-old study population (P = 0.089). A linear relationship was found between CCT and IOP (R2 = 0.152, P ≤ 0.001). CCT influenced the IOP value by 15.2%. However no linear relationship between DM and IOP, or between CCT and DM, was found. Conclusions: CCT was found to be similar to that reported in other studies in different populations. IOP tends to increase after the age of 30 and is not accounted for by alterations in CCT values.

Central corneal thickness, intraocular pressure, and degree of myopia in an adult myopic population aged 20 to 40 years in southeast Spain: determination and relationships.

Objective: To determine the values of, and study the relationships among, central corneal thickness (CCT), intraocular pressure (IOP), and degree of myopia (DM) in an adult myopic population aged 20 to 40 years in Almeria (southeast Spain). To our knowledge this is first study of this kind in this region. Methods: An observational, descriptive, cross-sectional study was done in which a sample of 310 myopic patients (620 eyes) aged 20 to 40 years was selected by gender- and age-stratified sampling, which was proportionally fixed to the size of the population strata for which a 20% prevalence of myopia, 5% epsilon, and a 95% confidence interval were hypothesized. We studied IOP, CCT, and DM and their relationships by calculating the mean, standard deviation, 95% confidence interval for the mean, median, Fisher’s asymmetry coefficient, range (maximum, minimum), and the Brown-Forsythe’s robust test for each variable (IOP, CCT, and DM). Results: In the adult myopic population of Almeria aged 20 to 40 years (mean of 29.8), the mean overall CCT was 550.12 μm. The corneas of men were thicker than those of women (P = 0.014). CCT was stable as no significant differences were seen in the 20- to 40-year-old subjects’ CCT values. The mean overall IOP was 13.60 mmHg. Men had a higher IOP than women (P = 0.002). Subjects over 30 years (13.83) had a higher IOP than those under 30 (13.38) (P = 0.04). The mean overall DM was −4.18 diopters. Men had less myopia than women (P < 0.001). Myopia was stable in the 20- to 40-year-old study population (P = 0.089). A linear relationship was found between CCT and IOP (R2 = 0.152, P ≤ 0.001). CCT influenced the IOP value by 15.2%. However no linear relationship between DM and IOP, or between CCT and DM, was found. Conclusions: CCT was found to be similar to that reported in other studies in different populations. IOP tends to increase after the age of 30 and is not accounted for by alterations in CCT values.

A stratified approach for modeling the distribution of a threatened ant species in the Swiss National Park

We present models predicting the potential distribution of a threatened ant species, Formica exsecta Nyl., in the Swiss National Park ( SNP). Data to fit the models have been collected according to a random-stratified design with an equal number of replicates per stratum. The basic aim of such a sampling strategy is to allow the formal testing of biological hypotheses about those factors most likely to account for the distribution of the modeled species. The stratifying factors used in this study were: vegetation, slope angle and slope aspect, the latter two being used as surrogates of solar radiation, considered one of the basic requirements of F. exsecta. Results show that, although the basic stratifying predictors account for more than 50% of the deviance, the incorporation of additional non-spatially explicit predictors into the model, as measured in the field, allows for an increased model performance (up to nearly 75%). However, this was not corroborated by permutation tests. Implementation on a national scale was made for one model only, due to the difficulty of obtaining similar predictors on this scale. The resulting map on the national scale suggests that the species might once have had a broader distribution in Switzerland. Reasons for its particular abundance within the SNP might possibly be related to habitat fragmentation and vegetation transformation outside the SNP boundaries.

Which is the optimal sampling strategy for habitat suitability modelling

Designing an efficient sampling strategy is of crucial importance for habitat suitability modelling. This paper compares four such strategies, namely, 'random', 'regular', 'proportional-stratified' and 'equal -stratified'- to investigate (1) how they affect prediction accuracy and (2) how sensitive they are to sample size. In order to compare them, a virtual species approach (Ecol. Model. 145 (2001) 111) in a real landscape, based on reliable data, was chosen. The distribution of the virtual species was sampled 300 times using each of the four strategies in four sample sizes. The sampled data were then fed into a GLM to make two types of prediction: (1) habitat suitability and (2) presence/ absence. Comparing the predictions to the known distribution of the virtual species allows model accuracy to be assessed. Habitat suitability predictions were assessed by Pearson's correlation coefficient and presence/absence predictions by Cohen's K agreement coefficient. The results show the 'regular' and 'equal-stratified' sampling strategies to be the most accurate and most robust. We propose the following characteristics to improve sample design: (1) increase sample size, (2) prefer systematic to random sampling and (3) include environmental information in the design'

Uncertainties in annual riverine phosphorus load estimation: Impact of load estimation methodology, sampling frequency, baseflow index and catchment population density

Models developed to identify the rates and origins of nutrient export from land to stream require an accurate assessment of the nutrient load present in the water body in order to calibrate model parameters and structure. These data are rarely available at a representative scale and in an appropriate chemical form except in research catchments. Observational errors associated with nutrient load estimates based on these data lead to a high degree of uncertainty in modelling and nutrient budgeting studies. Here, daily paired instantaneous P and flow data for 17 UK research catchments covering a total of 39 water years (WY) have been used to explore the nature and extent of the observational error associated with nutrient flux estimates based on partial fractions and infrequent sampling. The daily records were artificially decimated to create 7 stratified sampling records, 7 weekly records, and 30 monthly records from each WY and catchment. These were used to evaluate the impact of sampling frequency on load estimate uncertainty. The analysis underlines the high uncertainty of load estimates based on monthly data and individual P fractions rather than total P. Catchments with a high baseflow index and/or low population density were found to return a lower RMSE on load estimates when sampled infrequently than those with a tow baseflow index and high population density. Catchment size was not shown to be important, though a limitation of this study is that daily records may fail to capture the full range of P export behaviour in smaller catchments with flashy hydrographs, leading to an underestimate of uncertainty in Load estimates for such catchments. Further analysis of sub-daily records is needed to investigate this fully. Here, recommendations are given on load estimation methodologies for different catchment types sampled at different frequencies, and the ways in which this analysis can be used to identify observational error and uncertainty for model calibration and nutrient budgeting studies. (c) 2006 Elsevier B.V. All rights reserved.

Parallel Monte Carlo sampling scheme for sphere and hemisphere

The sampling of certain solid angle is a fundamental operation in realistic image synthesis, where the rendering equation describing the light propagation in closed domains is solved. Monte Carlo methods for solving the rendering equation use sampling of the solid angle subtended by unit hemisphere or unit sphere in order to perform the numerical integration of the rendering equation. In this work we consider the problem for generation of uniformly distributed random samples over hemisphere and sphere. Our aim is to construct and study the parallel sampling scheme for hemisphere and sphere. First we apply the symmetry property for partitioning of hemisphere and sphere. The domain of solid angle subtended by a hemisphere is divided into a number of equal sub-domains. Each sub-domain represents solid angle subtended by orthogonal spherical triangle with fixed vertices and computable parameters. Then we introduce two new algorithms for sampling of orthogonal spherical triangles. Both algorithms are based on a transformation of the unit square. Similarly to the Arvo's algorithm for sampling of arbitrary spherical triangle the suggested algorithms accommodate the stratified sampling. We derive the necessary transformations for the algorithms. The first sampling algorithm generates a sample by mapping of the unit square onto orthogonal spherical triangle. The second algorithm directly compute the unit radius vector of a sampling point inside to the orthogonal spherical triangle. The sampling of total hemisphere and sphere is performed in parallel for all sub-domains simultaneously by using the symmetry property of partitioning. The applicability of the corresponding parallel sampling scheme for Monte Carlo and Quasi-D/lonte Carlo solving of rendering equation is discussed.

Risk factors relating to helminth infections in cows during the peripartum

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sampling density and proportion for the characterization of the variability of Oxisol attributes on different materials

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Spatial methods for plot-based sampling of wildlife populations

Classical sampling methods can be used to estimate the mean of a finite or infinite population. Block kriging also estimates the mean, but of an infinite population in a continuous spatial domain. In this paper, I consider a finite population version of block kriging (FPBK) for plot-based sampling. The data are assumed to come from a spatial stochastic process. Minimizing mean-squared-prediction errors yields best linear unbiased predictions that are a finite population version of block kriging. FPBK has versions comparable to simple random sampling and stratified sampling, and includes the general linear model. This method has been tested for several years for moose surveys in Alaska, and an example is given where results are compared to stratified random sampling. In general, assuming a spatial model gives three main advantages over classical sampling: (1) FPBK is usually more precise than simple or stratified random sampling, (2) FPBK allows small area estimation, and (3) FPBK allows nonrandom sampling designs.