M. Fernández

A copula model to analyze minimum admission scores

The Asymmetric Cubic Sections copula family is used to describe the dependence between language and mathematics scores of admission test. The parameters of the copula are annually estimated by means of a non-informative Bayesian method. The application focus on measuring the impact of conditioning language result to a mathematics minimum grade and vice-versa, this paper shows some initial results in that line. In addition, the analytical expression for each conditional expectation is shown together with a description of its monotonic behavior.

A copula-based partition Markov procedure

ABSTRACT The number of parameters needed to specify a discrete multivariate Markov chain grows exponentially with the order and dimension of the chain, and when the size of the database is not large enough, it is not possibly a consistent estimation. In this paper, we introduce a strategy to estimate a multivariate process with an order greater than the order achieved using standard procedures. The new strategy consists in obtaining a partition of the state space which is constructed from a combination of the partitions corresponding to the marginal processes and the partitions corresponding to the multivariate Markov chain.

Bounds for the cumulative conditional expectation function

We introduce the concept of cumulative conditional expectation function. This is a quantity that provides statistical support for making decisions in applied problems. The goal of this paper is to find an analytical expression for upper and lower bounds of this function, assuming stochastic dependence types as being the underlying random structure.

Bayesian sensitivity analysis for asymmetric copulas with cubic sections

The use of copulas to model the dependence between indicators leads us to observe the different methods of estimation and its applicability, given practical circumstances, such as having small databases. For this reason, Bayesian methods under the scope of copulas come to show immense utility. In this paper, we investigate how the responses of the Asymmetric Cubic Sections copula model are affected when we vary the prior distributions display over the model parameters. We use as a reference setting a non-informative prior distribution and we observe the effect of the other prior distributions in relation to it. We used this diversity of scenarios to map the possible degrees of dependence between two educational scores obtained by students of the undergraduate course of statistics at the University of Campinas in 2014.

Foreign exchange dependence through different copula models

In this paper we postulate different scenarios based on two copula models under the format C(u, v)= uv + f (u)g(v) for suitable functions f and g, see Rodriguez-Lallena & Ubeda Flores (2004) [4] and Nelsen et al. (1997) [3]. We used these copulas to model the dependence between two currencies quoted relative to the U.S. Dollar, the Canadian Dollar and the South Korean Won. We assume a Bayesian approach to estimate the copulas parameters, then we estimate the impact of losses on the South Korean Won on the Canadian Dollar.

Right tail increasing dependence between scores

In this paper we investigate the behavior of the conditional probability Prob(U > u|V > v) of two records coming from students of an undergraduate course, where U is the score of calculus I, scaled in [0, 1] and V is the score of physics scaled in [0, 1], the physics subject is part of the admission test of the university. For purposes of comparison, we consider two different undergraduate courses, electrical engineering and mechanical engineering, during nine years, from 2003 to 2011. Through a Bayesian perspective we estimate Prob(U > u|V > v) year by year and course by course. We conclude that U is right tail increasing in V, in both courses and for all the years. Moreover, over these nine years, we observe different ranges of variability for the estimated probabilities of electrical engineering when compared to the estimated probabilities of mechanical engineering.In this paper we investigate the behavior of the conditional probability Prob(U > u|V > v) of two records coming from students of an undergraduate course, where U is the score of calculus I, scaled in [0, 1] and V is the score of physics scaled in [0, 1], the physics subject is part of the admission test of the university. For purposes of comparison, we consider two different undergraduate courses, electrical engineering and mechanical engineering, during nine years, from 2003 to 2011. Through a Bayesian perspective we estimate Prob(U > u|V > v) year by year and course by course. We conclude that U is right tail increasing in V, in both courses and for all the years. Moreover, over these nine years, we observe different ranges of variability for the estimated probabilities of electrical engineering when compared to the estimated probabilities of mechanical engineering.

Confidence bands in Kendall plots

In this work we propose the construction of confidence bands for Kendall plots, based on asymptotic confidence intervals for quantiles of Kendall’s distributions. The main application explored here is from the linguistic field. We analyze specifically the relationship between values of the acoustical correlate ‘fundamental frequency’ (F0) of pretonic syllables perceived as bearing secondary stresses and values of other pretonic syllables adjacent to those, in Brazilian Portuguese (BP) and European Portuguese (EP) data. Our hypothesis is this relationship can be a cue to the secondary stress perception by BP and EP speakers. From the statistical point of view, we obtained that for the two varieties of Portuguese the dependence is modeled by Gumbel’s copulas.