Influence Functions of the Spearman and Kendall Correlation Measures

Mathematics Subject Classification (2000) 62G35 · 62F99

PAYMENT FOR ENVIRONMENTAL SERVICES IN A MUNICIPALITY IN THE STATE OF SÃO PAULO: EQUIVALENT UNIFORM ANNUAL COST

The implementation and discussion of Payment for Environmental Services (PES) programs has gained prominence in environmental policy. However, there are still knowledge gaps regarding economic indicators that are fundamental for the analysis of the viability and financing of PES projects. Thus, obtaining information related to the analysis of investment projects in PES programs can contribute to future decision-making. In this context, the objective was to estimate the Equivalent Uniform Annual Cost (EUAC) of investment projects for PES in subwatersheds in the State of São Paulo under conditions of uncertainty, as well as to analyze whether the EUAC allows attesting to the economic viability of these investment projects. From the costs of the PES actions, the EUAC was used and then the Monte Carlo method was applied to incorporate stochastic solutions. The average EUAC of the PES investment projects for the priority and non-priority subwatersheds is USD 1,814.11 and USD 1,675.54, respectively. The costs associated with the purchase of organic fertilizer and fence posts have the greatest impact on the EUAC in both the priority and non-priority areas. The EUAC, combined with Spearman's correlation, allows for the analysis of the economic viability of investment projects and thus assists in the decision-making process regarding the prioritization of resource allocation in sub-watersheds

Spatial Sign Correlation

A new robust correlation estimator based on the spatial sign covariance matrix (SSCM) is proposed. We derive its asymptotic distribution and influence function at elliptical distributions. Finite sample and robustness properties are studied and compared to other robust correlation estimators by means of numerical simulations.Comment: 20 pages, 7 figures, 2 table

THE EFFECT OF CLASSROOM ACOUSTICS ON STUDENTS’ LEARNING PROCESSES: SELECTION OF OBJECTIVE PARAMETERS AND PROVISION OF A MEASUREMENT PROTOCOL

Since the students’ learning process is affected by classroom acoustics, this work is based on a literature review aiming at identifying the acoustical parameters that have major influence on students’ academic performances. The review strategy involved three different approaches and resulted in more than 30 selected papers, of which only a few provided information on the effects of the acoustics of the environment on learning. The indexes that turned out to have the greater influence on students' performance were therefore considered on the evaluation of acoustical quality in elementary school classrooms through in-field measurements. Room acoustics and intelligibility indices in both occupied and unoccupied conditions of twenty-nine first-grade classrooms belonging to 13 school buildings in Turin that differ in location and typology, were gathered in the study. Then, the association between objective parameters was assessed with linear regression analysis and results of previous studies were confirmed. In addition to that, new important considerations useful for the creation of a simplified protocol that can be universally applied when performing acoustic measurements in classrooms emerged, so that comparisons across several environments can be performed

Influence Function-based Empirical Likelihood Method for Kendall Rank Correlation Coefficient

Correlation coefficients are used in statistics to measure the dependence between two variables. Kendall rank correlation coefficient is routinely used as a measure of association between two random variables in a number of circumstances in which the use of the Pearson correlation coefficient is inappropriate. In this thesis, we develop an influence function-based empirical likelihood interval for the Kendall rank correlation coefficient. Simulation studies are conducted to show good finite sample properties and robustness of the proposed method compared with existing methods. The proposed method is illustrated on a real UCLA graduate dataset

BLUE-GREEN INFRASTRUCTURE DISTRIBUTION IN PIAUÍ, BRAZIL

Studies of blue-green infrastructure (BGI) are still incipient in Brazil. Since its access and benefits may not be well-distributed among the population, it is important to evaluate BGI distribution to base territorial and environmental planning. This is especially true for less urbanized and developed states, like Piauí. Thus, this study aimed to assess urbanization, socioeconomic and BGI parameters in Piauí municipalities. We conducted a quantitative assessment through descriptive and correlation statistical analysis and spatial data visualization considering absolute population, population density, relative built area, and built area per inhabitant as urbanization parameters; per capita income, poverty, GINI inequality, and human development indexes as socioeconomic parameters; and relative forest area, forest area per inhabitant, relative BGI area, and BGI area per inhabitant as BGI parameters. Strong correlations were found between BGI and urbanization, while important but weak correlations were found between BGI and socioeconomic variables. Municipalities with more BGI are less urbanized and have worse socioeconomic conditions. Results reinforce that the urbanization processes of Piauí municipalities need to ensure open spaces for urban BGI, therefore pursuing environmental justice and BGI access and benefits for all.

Robust high-dimensional precision matrix estimation

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in high-dimensions, it cannot be used to obtain a precision matrix estimator. A popular high-dimensional estimator is the graphical lasso, but it lacks robustness. We consider the high-dimensional independent contamination model. Here, even a small percentage of contaminated cells in the data matrix may lead to a high percentage of contaminated rows. Downweighting entire observations, which is done by traditional robust procedures, would then results in a loss of information. In this paper, we formally prove that replacing the sample covariance matrix in the graphical lasso with an elementwise robust covariance matrix leads to an elementwise robust, sparse precision matrix estimator computable in high-dimensions. Examples of such elementwise robust covariance estimators are given. The final precision matrix estimator is positive definite, has a high breakdown point under elementwise contamination and can be computed fast