Mathematical Modeling of Concentration Risk under the Default Risk Charge Using Probability and Statistics TheoryRead the full article
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Extreme Value Distributions: An Overview of Estimation and Simulation
The generalized extreme value distribution (GEVD) and various extreme value distributions are commonly applied in air pollution, telecommunications, operational risk management, finance, insurance, material sciences, economics, and hydrology, among many other industries that deal with extreme events. Extreme value distributions (EVDs) typically limit the distribution of maximum and minimum values for many random observations drawn from the same arbitrary distribution. Besides that, it is a crucial method for forecasting future events and emerged as critical method for predicting future events. As a result, prior research is required to select the best estimation method to obtain a reliable value for the parameters of extreme value distributions. This study provides an overview of three-parameter estimation methods based on goodness-of-fit statistics and root mean square error (RMSE). This paper reviewed and compared three estimation methods used to approximate values of parameters for simulated observations taken from the EVD and GEVD. The method of moments (MOMs), maximum likelihood estimator (MLE), and maximum product of spacing (MPS) were the methods investigated in this study. Our findings indicated that the MPS performed better based on the mean square errors (MSEs); meanwhile, the MPS had similar goodness-of-fit statistic values compared to the MLE.
Interpretability of Composite Indicators Based on Principal Components
Principal component approaches are often used in the construction of composite indicators to summarize the information of input variables. The gain of dimension reduction comes at the cost of difficulties in interpretation, inaccurate targeting, and possible conflicts with the theoretical framework when the signs in the loading are not aligned with the expected direction of impact. In this study, we propose an adjustment in the construction of principal component approaches to avoid these problems. The effectiveness of the proposed approach is illustrated in defining the Food and Agriculture Organization of the United Nations’ Resilience Capacity Index, which is used to measure household-level resilience to food insecurity. We conclude that the robustness gain of using the new method improves the reliability of the composite indicator.
NetDA: An R Package for Network-Based Discriminant Analysis Subject to Multilabel Classes
In this paper, we introduce the R package NetDA, which aims to deal with multiclassification with network structures in predictors accommodated. To address the natural feature of network structures, we apply Gaussian graphical models to characterize dependence structures of the predictors and directly estimate the precision matrix. After that, the estimated precision matrix is employed to linear discriminant functions and quadratic discriminant functions. The R package NetDA is now available on CRAN, and the demonstration of functions is summarized as a vignette in the online documentation.
Some Improved Classes of Estimators in Stratified Sampling Using Bivariate Auxiliary Information
This manuscript considers some improved combined and separate classes of estimators of population mean using bivariate auxiliary information under stratified simple random sampling. The expressions of bias and mean square error of the proposed classes of estimators are determined to the first order of approximation. It is exhibited that under some particular conditions, the proposed classes of estimators dominate the existing prominent estimators. The theoretical findings are supported by a simulation study performed over a hypothetically generated population.
D-Optimal Design for a Causal Structure for Completely Randomized and Random Blocked Experiments
Most experimental design literature on causal inference focuses on establishing a causal relationship between variables, but there is no literature on how to identify a design that results in the optimal parameter estimates for a structural equation model (SEM). In this research, search algorithms are used to produce a D-optimal design for a SEM for three-stage least squares and full information maximum likelihood estimators. Then, a D-optimal design for the estimate of the model parameters of a mixed-effects SEM is obtained. The efficiency of each of the D-optimal designs for SEMs is compared with univariate optimal and uniform designs. In each case, the causal relationship changed the optimal designs dramatically and the new D-optimal designs were more efficient.
On Hierarchical Bayesian Spatial Small Area Model for Binary Data under Spatial Misalignment
Small area models have become popular methods for producing reliable estimates for sub-populations (small geographic areas in this study). Small area modeling may be carried out via model-assisted approaches within the model-based approaches or design-based paradigm. When there are medium or large samples, a model-assisted approach may be reliable. However, when data are scarce, a model-based technique may be required. Model-based Bayesian analysis is popular for its ability to combine information from several sources as well as taking account uncertainties in the analysis and spatial prediction of spatial data. Nevertheless, things become more complex when the geographic boundaries of interest are misaligned. Some authors have addressed the problem of misalignment under hierarchical Bayesian approach. In this study, we developed non-trivial extension of existing hierarchical Bayesian model for a binary outcome variable under spatial misalignment with three contributions. First, the model uses unit-level survey data and area-level auxiliary data to predict the posterior mean proportion spatially at the second geographic area level. Second, the linking model is changed to logit-normal model in the proposed model. Lastly, the mean process was considered to overcome the multicollinearity between the true predictors and the spatial random effect. Sensitivity analysis was also done via simulation.