arXiv subjects

Diego Marcondes

Publications and source records attributed to Diego Marcondes.

24 records · Page 2Linked to original sources

arXiv2019

Local Lift Dependence Scale

We propose a local and general dependence quantifier between two random variables $X$ and $Y$, which we call Local Lift Dependence Scale, that does not assume any form of dependence (e.g., linear) between $X$ and $Y$, and is defined for a large class of random variables, singular and absolutely continuous w.r.t Lebesgue measure. We argue that this dependence scale is more general and suitable to study variable dependence than other specific local dependence quantifiers and global dependence coefficients, as the Mutual Information. An outline of how this dependence scale may be useful in branches of applied probability and topics for future research are presented.

math.PR↗

arXiv2019

Random Coin Tossing with unknown bias

Consider a coin tossing experiment which consists of tossing one of two coins at a time, according to a renewal process. The first coin is fair and the second has probability $1/2 + θ$, $θ\in [-1/2,1/2]$, $θ$ unknown but fixed, of head. The biased coin is tossed at the renewal times of the process, and the fair one at all the other times. The main question about this experiment is whether or not it is possible to determine $θ$ almost surely as the number of tosses increases, given only the probabilities of the renewal process and the observed sequence of heads and tails. We will construct a confidence interval for $θ$ and determine conditions on the process for its almost sure convergence. It will be shown that recurrence is in fact a necessary condition for the almost sure convergence of the interval, although the convergence still holds if the process is null recurrent but the expected number of renewals up to and including time $N$ is $O(N^{1/2+α}), 0 \leq α< 1/2$. It solves an open problem presented by Harris and Keane (1997). We also generalize this experiment for random variables on $L^{2}$ which are sampled according to a renewal process from either one of two distributions.

math.PR↗

arXiv2018

A survey of a hurdle model for heavy-tailed data based on the generalized lambda distribution

In this survey we present an extensive research of the vast literature about the Generalized Lambda Distribution (GLD) and propose a hurdle, or two-way, model whose associated distribution is the GLD in order to meet the demand for a highly flexible model of heavy-tailed data with excess of zeros. We apply the developed models to a dataset consisting of yearly healthcare expenses, a typical example of heavy-tailed data with excess of zeros. The fitted models are compared with models based on the Generalised Pareto Distribution and it is established that the GLD models perform best.

stat.AP↗

arXiv2018

Assessing randomness in case assignment: the case study of the Brazilian Supreme Court

Sortition, i.e., random appointment for public duty, has been employed by societies throughout the years, especially for duties related to the judicial system, as a firewall designated to prevent illegitimate interference between parties in a legal case and agents of the legal system. In judicial systems of modern western countries, random procedures are mainly employed to select the jury, the court and/or the judge in charge of judging a legal case, so that they have a significant role in the course of a case. Therefore, these random procedures must comply with some principles, as statistical soundness; complete auditability; open-source programming; and procedural, cryptographical and computational security. Nevertheless, some of these principles are neglected by some random procedures in judicial systems, that are, in some cases, performed in secrecy and are not auditable by the involved parts. The assignment of cases in the Brazilian Supreme Court (Supremo Tribunal Federal) is an example of such procedures, for it is performed by a closed-source algorithm, unknown to the public and to the parts involved in the judicial cases, that allegedly assign the cases randomly to the justice chairs based on their caseload. In this context, this article presents a review of how sortition has been employed historically by societies, and discusses how Mathematical Statistics may be applied to random procedures of the judicial system, as it has been applied for almost a century on clinical trials, for example. Based on this discussion, a statistical model for assessing randomness in case assignment is proposed and applied to the Brazilian Supreme Court in order to shed light on how this assignment process is performed by the closed-source algorithm. Guidelines for random procedures are outlined and topics for further researches presented.

stat.AP↗

arXiv2017

Feature Selection based on the Local Lift Dependence Scale

This paper uses a classical approach to feature selection: minimization of a cost function applied on estimated joint distributions. However, the search space in which such minimization is performed is extended. In the original formulation, the search space is the Boolean lattice of features sets (BLFS), while, in the present formulation, it is a collection of Boolean lattices of ordered pairs (features, associated value) (CBLOP), indexed by the elements of the BLFS. In this approach, we may not only select the features that are most related to a variable Y, but also select the values of the features that most influence the variable or that are most prone to have a specific value of Y. A local formulation of Shanon's mutual information is applied on a CBLOP to select features, namely, the Local Lift Dependence Scale, an scale for measuring variable dependence in multiple resolutions. The main contribution of this paper is to define and apply this local measure, which permits to analyse local properties of joint distributions that are neglected by the classical Shanon's global measure. The proposed approach is applied to a dataset consisting of student performances on a university entrance exam, as well as on undergraduate courses. The approach is also applied to two datasets of the UCI Machine Learning Repository.

stat.CO↗

arXiv2017

A Nonparametric Statistical Approach to Content Analysis of Items

In order to use psychometric instruments to assess a multidimensional construct, we may decompose it in dimensions and, in order to assess each dimension, develop a set of items, so one may assess the construct as a whole, by assessing its dimensions. In this scenario, the content analysis of items aims to verify if the developed items are assessing the dimension they are supposed to. In the content analysis process, it is customary to request the judgement of specialists in the studied construct about the dimension that the developed items assess, what makes it a subjective process as it relies upon the personal opinion of the specialists. This paper aims to develop a nonparametric statistical approach to the content analysis of items in order to present a practical method to assess the consistency of the content analysis process, by the development of a statistical test that seeks to determine if all the specialists have the same capability to judge the items. A simulation study is conducted to assess the consistency of the test and it is applied to a real validation process.

stat.ME↗