Using composite estimators to improve both domain and total area estimation

In this article we propose using small area estimators to improve the estimatesof both the small and large area parameters. When the objective is to estimateparameters at both levels accurately, optimality is achieved by a mixed sampledesign of fixed and proportional allocations. In the mixed sample design, oncea sample size has been determined, one fraction of it is distributedproportionally among the different small areas while the rest is evenlydistributed among them. We use Monte Carlo simulations to assess theperformance of the direct estimator and two composite covariant-freesmall area estimators, for different sample sizes and different sampledistributions. Performance is measured in terms of Mean Squared Errors(MSE) of both small and large area parameters. It is found that the adoptionof small area composite estimators open the possibility of 1) reducingsample size when precision is given, or 2) improving precision for a givensample size.

Small-area estimation with spatial similarity

A class of composite estimators of small area quantities that exploit spatial (distancerelated)similarity is derived. It is based on a distribution-free model for the areas, but theestimators are aimed to have optimal design-based properties. Composition is applied alsoto estimate some of the global parameters on which the small area estimators depend.It is shown that the commonly adopted assumption of random effects is not necessaryfor exploiting the similarity of the districts (borrowing strength across the districts). Themethods are applied in the estimation of the mean household sizes and the proportions ofsingle-member households in the counties (comarcas) of Catalonia. The simplest version ofthe estimators is more efficient than the established alternatives, even though the extentof spatial similarity is quite modest.

Improving small area estimation by combining surveys: new perspectives in regional statistics

A national survey designed for estimating a specific population quantity is sometimes used for estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a greater sample size for the small area, and so other means of improving estimation have to be devised. We investigate such methods and assess them by a Monte Carlo study. We explore how a complementary survey can be exploited in small area estimation. We use the context of the Spanish Labour Force Survey (EPA) and the Barometer in Spain for our study.

Soybean crop area estimation by Modis/Evi data

The objective of this work was to develop a procedure to estimate soybean crop areas in Rio Grande do Sul state, Brazil. Estimations were made based on the temporal profiles of the enhanced vegetation index (Evi) calculated from moderate resolution imaging spectroradiometer (Modis) images. The methodology developed for soybean classification was named Modis crop detection algorithm (MCDA). The MCDA provides soybean area estimates in December (first forecast), using images from the sowing period, and March (second forecast), using images from the sowing and maximum crop development periods. The results obtained by the MCDA were compared with the official estimates on soybean area of the Instituto Brasileiro de Geografia e Estatística. The coefficients of determination ranged from 0.91 to 0.95, indicating good agreement between the estimates. For the 2000/2001 crop year, the MCDA soybean crop map was evaluated using a soybean crop map derived from Landsat images, and the overall map accuracy was approximately 82%, with similar commission and omission errors. The MCDA was able to estimate soybean crop areas in Rio Grande do Sul State and to generate an annual thematic map with the geographic position of the soybean fields. The soybean crop area estimates by the MCDA are in good agreement with the official agricultural statistics.

A simple and non-destructive model for individual leaf area estimation in citrus

Introduction. Leaf area is often related to plant growth, development, physiology and yield. Many non-destructive models have been proposed for leaf area estimation of several plant genotypes, demonstrating that leaf length, leaf width and leaf area are closely correlated. Thus, the objective of our study was to develop a reliable model for leaf area estimation from linear measurements of leaf dimensions for citrus genotypes. Materials and methods. Leaves of citrus genotypes were harvested, and their dimensions (length, width and area) were measured. Values of leaf area were regressed against length, width, the square of length, the square of width and the product (length x width). The most accurate equations, either linear or second-order polynomial, were regressed again with a new data set; then the most reliable equation was defined. Results and discussion. The first analysis showed that the variables length, width and the square of length gave better results in second-order polynomial equations, while the linear equations were more suitable and accurate when the width and the product (length x width) were used. When these equations were regressed with the new data set, the coefficient of determination (R(2)) and the agreement index 'd' were higher for the one that used the variable product (length x width), while the Mean Absolute Percentage Error was lower. Conclusion. The product of the simple leaf dimensions (length x width) can provide a reliable and simple non-destructive model for leaf area estimation across citrus genotypes.

Non-destructive linear model for leaf area estimation in Vernonia ferruginea Less

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

Using small area estimation and geographic information systems technology to target health services for the uninsured

The three articles that comprise this dissertation describe how small area estimation and geographic information systems (GIS) technologies can be integrated to provide useful information about the number of uninsured and where they are located. Comprehensive data about the numbers and characteristics of the uninsured are typically only available from surveys. Utilization and administrative data are poor proxies from which to develop this information. Those who cannot access services are unlikely to be fully captured, either by health care provider utilization data or by state and local administrative data. In the absence of direct measures, a well-developed estimation of the local uninsured count or rate can prove valuable when assessing the unmet health service needs of this population. However, the fact that these are “estimates” increases the chances that results will be rejected or, at best, treated with suspicion. The visual impact and spatial analysis capabilities afforded by geographic information systems (GIS) technology can strengthen the likelihood of acceptance of area estimates by those most likely to benefit from the information, including health planners and policy makers. ^ The first article describes how uninsured estimates are currently being performed in the Houston metropolitan region. It details the synthetic model used to calculate numbers and percentages of uninsured, and how the resulting estimates are integrated into a GIS. The second article compares the estimation method of the first article with one currently used by the Texas State Data Center to estimate numbers of uninsured for all Texas counties. Estimates are developed for census tracts in Harris County, using both models with the same data sets. The results are statistically compared. The third article describes a new, revised synthetic method that is being tested to provide uninsured estimates at sub-county levels for eight counties in the Houston metropolitan area. It is being designed to replicate the same categorical results provided by a current U.S. Census Bureau estimation method. The estimates calculated by this revised model are compared to the most recent U.S. Census Bureau estimates, using the same areas and population categories. ^

HPV vaccine coverage in Texas counties: An application of multilevel, small area estimation

Health departments, research institutions, policy-makers, and healthcare providers are often interested in knowing the health status of their clients/constituents. Without the resources, financially or administratively, to go out into the community and conduct health assessments directly, these entities frequently rely on data from population-based surveys to supply the information they need. Unfortunately, these surveys are ill-equipped for the job due to sample size and privacy concerns. Small area estimation (SAE) techniques have excellent potential in such circumstances, but have been underutilized in public health due to lack of awareness and confidence in applying its methods. The goal of this research is to make model-based SAE accessible to a broad readership using clear, example-based learning. Specifically, we applied the principles of multilevel, unit-level SAE to describe the geographic distribution of HPV vaccine coverage among females aged 11-26 in Texas.^ Multilevel (3 level: individual, county, public health region) random-intercept logit models of HPV vaccination (receipt of ≥ 1 dose Gardasil® ) were fit to data from the 2008 Behavioral Risk Factor Surveillance System (outcome and level 1 covariates) and a number of secondary sources (group-level covariates). Sampling weights were scaled (level 1) or constructed (levels 2 & 3), and incorporated at every level. Using the regression coefficients (and standard errors) from the final models, I simulated 10,000 datasets for each regression coefficient from the normal distribution and applied them to the logit model to estimate HPV vaccine coverage in each county and respective demographic subgroup. For simplicity, I only provide coverage estimates (and 95% confidence intervals) for counties.^ County-level coverage among females aged 11-17 varied from 6.8-29.0%. For females aged 18-26, coverage varied from 1.9%-23.8%. Aggregated to the state level, these values translate to indirect state estimates of 15.5% and 11.4%, respectively; both of which fall within the confidence intervals for the direct estimates of HPV vaccine coverage in Texas (Females 11-17: 17.7%, 95% CI: 13.6, 21.9; Females 18-26: 12.0%, 95% CI: 6.2, 17.7).^ Small area estimation has great potential for informing policy, program development and evaluation, and the provision of health services. Harnessing the flexibility of multilevel, unit-level SAE to estimate HPV vaccine coverage among females aged 11-26 in Texas counties, I have provided (1) practical guidance on how to conceptualize and conduct modelbased SAE, (2) a robust framework that can be applied to other health outcomes or geographic levels of aggregation, and (3) HPV vaccine coverage data that may inform the development of health education programs, the provision of health services, the planning of additional research studies, and the creation of local health policies.^

Grapevine Yield and Leaf Area Estimation Using Supervised Classification Methodology on RGB Images Taken under Field Conditions

The aim of this research was to implement a methodology through the generation of a supervised classifier based on the Mahalanobis distance to characterize the grapevine canopy and assess leaf area and yield using RGB images. The method automatically processes sets of images, and calculates the areas (number of pixels) corresponding to seven different classes (Grapes, Wood, Background, and four classes of Leaf, of increasing leaf age). Each one is initialized by the user, who selects a set of representative pixels for every class in order to induce the clustering around them. The proposed methodology was evaluated with 70 grapevine (V. vinifera L. cv. Tempranillo) images, acquired in a commercial vineyard located in La Rioja (Spain), after several defoliation and de-fruiting events on 10 vines, with a conventional RGB camera and no artificial illumination. The segmentation results showed a performance of 92% for leaves and 98% for clusters, and allowed to assess the grapevine’s leaf area and yield with R2 values of 0.81 (p < 0.001) and 0.73 (p = 0.002), respectively. This methodology, which operates with a simple image acquisition setup and guarantees the right number and kind of pixel classes, has shown to be suitable and robust enough to provide valuable information for vineyard management.

Vacant parking area estimation through background subtraction and transience map analysis

A method for estimating the dimensions of non-delimited free parking areas by using a static surveillance camera is proposed. The proposed method is specially designed to tackle the main challenges of urban scenarios (multiple moving objects, outdoor illumination conditions and occlusions between vehicles) with no training. The core of this work is the temporal analysis of the video frames to detect the occupancy variation of the parking areas. Two techniques are combined: background subtraction using a mixture of Gaussians to detect and track vehicles and the creation of a transience map to detect the parking and leaving of vehicles. The authors demonstrate that the proposed method yields satisfactory estimates on three real scenarios while being a low computational cost solution that can be applied in any kind of parking area covered by a single camera.

Small Area Estimation of Economic Security

The objective of this thesis is the small area estimation of an economic security indicator. Economic security is a complex concept that carries a variety of meanings. In the literature there is no a formal unambiguous definition for economic security and in this work we refer to the definition recently provided for its opposite, economic insecurity, as the “anxiety produced by the possible exposure to adverse economic events and by the anticipation of the difficulty to recover from them” (Bossert and D’Ambrosio, 2013). In the last decade interest for economic insecurity/security has grown constantly, especially since the financial crisis of 2008, but even more in the last year after the economic consequences due to the Covid-19 pandemic. In this research, economic security is measures through a longitudinal indicator that takes into account the income levels of Italian households, from 2014 to 2016. The target areas are groups of Italian provinces, for which the indicator is estimated using longitudinal data taken from EU-SILC survey. We notice that the sample size is too low to obtain reliable estimates for our target areas. Therefore we resort to some Small Area Estimation strategies to improve the reliability of the results. In particular we consider small area models specified at area level. Besides the basic Fay-Herriot area-level model, we propose to consider some longitudinal extensions, including time-specific random effects following an autoregressive processes of order 1 (AR1) and a moving average of order 1 (MA1). We found that all the small area models used show a significant efficiency gain, especially MA1 model.

Is the sword moss (Bryoxiphium) a preglacial Tertiary relict?

The disjunction of floras between East Asia, Southeast North America, West North America, and Southwest Eurasia has been interpreted in terms of the fragmentation of a once continuous mixed mesophytic forest that occurred throughout the Northern Hemisphere due to the climatic and geological changes during the late Tertiary. The sword moss, Bryoxiphium, exhibits a distribution that strikingly resembles that of the mesophytic forest elements such as Liriodendron and is considered as the only living member of an early Tertiary flora in Iceland. These hypotheses are tested here using molecular dating analyses and ancestral area estimations. The results suggest that the extant range of Bryoxiphium results from the fragmentation of a formerly wider range encompassing North America and Southeast Asia about 10 million years ago. The split of continental ancestral populations is too recent to match with a continental drift scenario but is spatially and temporally remarkably congruent with that observed in Tertiary angiosperm relict species. The timing of the colonization of Iceland from Macaronesian ancestors, about two million years ago, is, however, incompatible with the hypothesis that Bryoxiphium is the only living member of an early Tertiary flora of the island. Alaska was recurrently colonized from East Asia. The ability of Bryoxiphium to overcome large oceanic barriers is further evidenced by its occurrence on remote oceanic archipelagos. In particular, Madeira was colonized twice independently from American and East Asian ancestors, respectively. The striking range disjunction of Bryoxiphium is interpreted in terms of its mating system, as the taxon exhibits a very singular pattern of spatial segregation of the sexes.

Coordinated dispersal and pre-isthmian assembly of the Central American ichthyofauna

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

Estimation of leaf area in grapevine cv. Syrah using empirical models

Aiming to obtain empirical models for the estimation of Syrah leaf area a set of 210 fruiting shoots was randomly collected during the 2013 growing season in an adult experimental vineyard, located in Lisbon, Portugal. Samples of 30 fruiting shoots were taken periodically from the stage of inflorescences visible to veraison (7 sampling dates). At the lab, from each shoot, primary and lateral leaves were separated and numbered according to node insertion. For each leaf, the length of the central and lateral veins was recorded and then the leaf area was measured by a leaf area meter. For single leaf area estimation the best statistical models uses as explanatory variable the sum of the lengths of the two lateral leaf veins. For the estimation of leaf area per shoot it was followed the approach of Lopes & Pinto (2005), based on 3 explanatory variables: number of primary leaves and area of the largest and smallest leaves. The best statistical model for estimation of primary leaf area per shoot uses a calculated variable obtained from the average of the largest and smallest primary leaf area multiplied by the number of primary leaves. For lateral leaf area estimation another model using the same type of calculated variable is also presented. All models explain a very high proportion of variability in leaf area. Our results confirm the already reported strong importance of the three measured variables (number of leaves and area of the largest and smallest leaf) as predictors of the shoot leaf area. The proposed models can be used to accurately predict Syrah primary and secondary leaf area per shoot in any phase of the growing cycle. They are inexpensive, practical, non-destructive methods which do not require specialized staff or expensive equipment.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.