Objectives: To evaluate the response to COVID-19 treatment through monitored convalescent plasma using ordinal logistic regression models. To determine whether the effectiveness of convalescent plasma treatment in combating COVID-19 depends more on donor or recipient characteristics, and to identify the most important variables. Methods: To assess the performance of convalescent plasma treatment, ordinal logistic regression models were used, including proportional odds models (POM), partial proportional odds models (PPOM), continuation ratio models (CRM), and stereotype models (SM) to determine which best describes the studied dataset. Results: The dataset included 2,369 patients and was divided into 6 smaller groups according to preliminary results from other studies. In all the groups analyzed, there was significance, but the fit was not satisfactory. Conclusion: Statistical evidence to prove the effectiveness of the treatment using POM, PPOM, CRM, and SM was not found. All models classified at least 98.7% of cases in the lowest severity category, due to the higher proportion of this category in the database, highlighting a considerable imbalance in category distribution. Considering the dataset, donor characteristics were not as relevant to the models as recipient
variables. In this scenario, even without satisfactory predictive results, some variables such as "Severity level upon hospitalization"and "WHO score upon hospitalization"were included in almost all models. Therefore, future investigations may consider alternative approaches to better explore these variables or include additional variables to better understand the factors influencing patient outcomes subjected to this type of treatment.

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he Item Response Theory has been increasingly used in studies that aim to estimate the latent trait and, among the existing models, the logistic ones are the most used. However, more and more studies show that the assumption that Item Characteristic Curves (ICC’s) follow the Logistic form are not valid, making it increasingly important to check this assumption. herefore, estimating the ICC in alternative, nonparametric ways can be a powerful tool to compare with the ICC generated by the logistic model and thus allow inference about the veracity of this assumption.This study proposes a nonparametric test that uses Bayesian inference, more specifically the Posterior Predictive Model Checking (PPMC) method to test this hypothesis. To compare with the ICC calculated by the Logistic Model, Isotonic and Nadaraya-Watson regressions were used to create 6 test statistics. Two analyses were done, one using a simulated data set and the other applying this test to real data from a SARESP application. The simulation results were satisfactory, with the test indicating significant differences in very few items that actually followed the 3-parameter Logistic Model, and managing to recognize well those items that had a non-monotonic ICC. Despite this, the test recognized only one item that were mixtures of distributions.For the real data, the Isotonic Regression estimators indicated different values than those indicated by the Nadaraya-Watson Regression, for the most part of items.

Artificial neural networks (ANN) are powerful tools for prediction and data modeling. Although they are becoming ever more powerful, modern improvements have compromised their calibration in favor of enhanced prediction accuracy, thus making their true confidence harder to assess. To address this problem, we propose a new post-processing quantile-based method of recalibration for ANN. To illustrate the method's mechanics we present two toy examples. In both, recalibration reduced the Mean Squared Error over the original uncalibrated models and provided a better representation of the data generative model. To further investigate the effects of the proposed recalibration procedure, we also present a simulation study comparing various parameter configurations--the recalibration successfully improved performance over the base models in all scenarios under consideration. At last, we apply the proposed method to a problem of diamond price prediction, where it was also able toimprove the overall model performance.

This Master’s Thesis proposes a hybrid model capable of forecasting hierarchical time series with multiple seasonality. This hybrid methodology consists of using aMachine Learningmodel that has variables containing time series statistical methodologies to generate cohesive forecasts. This methodology was applied to theM5-Forecasting(2020) competition available through Kaggle, in which the objective was to more accurately predict the daily sale of 3,409 products distributed in 5 levels of hierarchy by 28 days. During the dissertation, 5 different approaches were compared andtheLight Gradient Boosting Machine(LGBM) model containing a variable based on the TBATS (Trigonometric seasonity, Box-Cox transformation ARMA errors, Tred and Seasonal components) obtained an accuracy gain of 27% compared to the LGBM models without the variable mentioned. This model would have obtained the 318th place in the competition, being among the top 6% competitors.

The dissertation undertakes two distinct lines of statistical analysis on the yield curve for Brazil: the first involves the interpolation of daily observed data to estimate the complete curve. In contrast, the second focuses on extrapolating past information to forecast the yield curve. These analyses aim to model the behaviour of interest rates in Brazil, offering insights for improved macroeconomic management and supporting investment decisions. The analysis utilizes data from interest rate futures contracts traded in Brazil between January 2018 and April 2023. The second chapter is dedicated to estimating empirical models of the Term Structure of Interest Rates. Despite B3 periodically releasing yield curve estimates for monitoring the Brazilian market, various estimation techniques are considered for alternative purposes due to inherent trade-offs. The interest rate and maturity relationship holds for all terms, but daily observations are limited to specific maturities corresponding to traded securities or derivatives. Therefore, estimating the entire curve from these observed data points is crucial. This chapter evaluates empirical models, which do not impose restrictions derived from theoretical term structure models during the estimation process. These models are focused on obtaining a smooth function from observed data while adhering to specific constraints, such as the non-negativity of interest rates. The evaluation criteria include the quality of fit, robustness to outliers, and smoothness of the estimated function. This chapter contributes to literature by assessing models not previously applied to yield curve estimation and utilizing the multiple comparison procedure. Results highlight the strong fit of spline models, emphasize the greater smoothness of Nelson-Siegel family models, and recognize the noteworthy performance of the previously overlooked Loess model. The third chapter delves into modelling the yield curve dynamics through a factor model perspective to generate curve predictions. The analysis incorporates Brazilian data by implementing the Nelson-Siegel Dynamic model proposed by Diebold and Li (2006) and further developed in Diebold et al. (2006). Both original estimation procedures, two-step and one-step, are considered, focusing on the latter using the Kalman filter. Out-of-sample predictive capacity is assessed through the Diebold-Mariano test, comparing the performance of these implementations against simpler models.

Retail trade plays a crucial role in the Brazilian economy, and planning for sales volume and other factors related to the retail sector is of great importance for its growth. To effectively forecast and plan sales quantities, methodologies related to time séries can be employed. This study focuses on the development and evaluation of predictive models, which should consider typical characteristics of such data, such as hierarchical structure, the presence of multiple seasonalities in higher-level séries, and intermittent behavior in lower-level séries.

The goal of this work is to bring an approach to the modeling of count data, considering the existence of zeros in the distribution. Assuming the use of spatial data, in which the phenomenon under analysis does not present stationarity, the geographically weighted regression appears to solve this problem. Therefore, this work brings an extension of the geographically weighted negative binomial regression (GWNBR) to include a zero-inflated negative binomial distribution, entitled geographically weighted zero-inflated negative binomial regression (GWZINBR).

To verify the performance of the fit of the RBNIZGP model, some simulated data from distributions, zero-inflated poisson and zero-inflated negative binomial, without spatial space, were used. Finally, adjustment was used in the case of selection of the real quality of data on COVID-19 cases in South Korea, with data from South Korea being analyzed by (Weinstein et al., 2021).

The results of the simulations showed that the RBNIZGP model was able to model the data with Poisson, negative binomial, zero inflated Poisson and zero inflated negative binomial distributions, without spatial variation, by means of a large bandwidth. In the real case study, the results showed that locally, the adjusted models could be Poisson or negative binomial, thus refining the analysis, and showing the flexibility of the GWZINBR model.

The Weibull distribution is one of the most used models in statistics and applied areas, as it has a simple expression for the probability density function, survival function, and moments. However, the Weibull distribution is not able to fit bimodal data. In this work, we propose a new generalization of the three-parameter Weibull distribution, a new invertible bimodal Weibull model (NIBW), which can be bimodal and its cumulative distribution function and quantile function have a simple and closed form, which makes it very interesting in simulation procedures and for the calculation of risk measures in the applied areas. Several properties of the model were studied and the non-negative version of the model (NNIBW) was used in the performance of the maximumlikelihood estimates of the parameters and tested using Monte Carlo simulation. Furthermore, using four sets of temperature data, we fitted and compared our model with another bimodal distribution, calculate the return time and fit as well a regression model for one chosen dataset.

For over a century, the academic community has studied the financial market in an attempt to understand its behavior to maximize profits. This work looks for ways to maximize results in the financial market by creating a two-phase procedure that we call MAB-MMAR. First, individual generative models are established for each asset, to simulate, via Monte Carlo, future returns, using the Multifractal Model of Asset Returns, which is able to multiscale the moments of the return distribution under time scales, being an alternative to representations of the ARCH type, which are the representations that have been the focus of empirical research on the distribution of prices in recent years. Second, a Multi-Armed Bandit (MAB) structure is built by applying the Upper Confidence Bound (UCB)-Tuned algorithm on the simulated paths, in order to make choices between assets that optimize the allocation of resources. Furthermore, as a layer of protection for operations, we propose the Double Barrier Method, where the operation is terminated if a lower barrier is touched. As a performance comparison, the One-Asset, 1/n, Modern Portfolio Theory (MPT) and Axiomatic Second-order Stochastic Dominance Portfolio Theory (ASSDPT) models were tested. Our results are promising, revealing that, in general, the MAB-MMAR performed best in the most varied scenarios.

The development of computerized adaptive tests was only possible due to the technological advances of the last decades, allowing this methodology to obtain estimates for the ability of the examinees based on a reduced number of items selected specifically for each respondent from their estimated latent trait. Its difficulties arise when a small group of items is exposed frequently, jeopardizing the security of the test. Thus, this research aims to propose a method for the item selection step, based on the use of information weighted by a power of order alpha of the current proportion of respondents not exposed to each item, in order to reduce the exposure rate of the items, so that they do not have very high exposure rates or items that have never been exposed even with a degree of difficulty close to the respondent’s real skill theta. The results demonstrate the advantages of the proposed methodology in relation to those already used, presenting better performance in the proportion of overexposed items with all values of alfa for random weighted information and increasing the proportion of exposed items for higher values of alpha in the weighted maximum information method, for the simulated item bank. The weighted maximum information method with random alpha presented the best performance among all the methods discussed here when applied to the real item bank. Other advantages related to the choice of alpha values are also mentioned.