Relatórios de Pesquisa

13/2008 Diagnostics analysis for skew normal regression models
C. S. Ferreira, Heleno Bolfarine

The skew normal model (Azzalini, 1985) is being used successfully in various statistical applications. The main purpose of this paper is to consider local influence analysis, which is a well-recognized important step of data analysis. In this paper local influence measures are developed via Zhu and Lee's (2001) approach, that is closely related to the EM-algorithm. The diagnostic measures derived under this approach are invariant under reparameterization. Some useful perturbation schemes are discussed. The Cook's approach is also calculated and compared with Zhu and Lee's approach. Results that are obtained from analysis of a real data example are presented to illustrate the developed methodologies.Primary 20M20, 93B29; Secondary 22E46.


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12/2008 Fractional Term Structure Models: No-Arbitrage and Consistency
Alberto M. F. Ohashi

In this work we introduce Heath-Jarrow-Morton (HJM) interest rate models driven by fractional Brownian motions. By using support arguments we prove that the resulting model is arbitrage-free under proportional transaction costs in the same spirit of Guasoni et al [20, 21, 22]. In particular, we obtain a drift condition which is similar in nature to the classical HJM no-arbitrage drift restriction. The second part of this paper deals with consistency problems related to the fractional HJM dynamics. We give a fairly complete characterization of finitedimensional invariant manifolds for HJM models with fractional Brownian motion by means of Nagumo-type conditions. As an application, we investigate consistency of Nelson-Siegel family with respect to Ho-Lee and Hull-White models. It turns out that similar to the Brownian case such family does not go well with the fractional HJM dynamics with deterministic volatility. In fact, there is no nontrivial fractional interest rate model consistent with the Nelson-Siegel family.


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11/2008 Distribuições Subexponenciais: Introdução e Exemplos
Diego Fernando de Bernardini
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10/2008 Asymptotic Robustness of Hotteling's Statistic
Mario A. Gneri, Emanuel P. Barbosa

We show that under quite general distributional conditions the asymptotic distribution of Hotteling's $T^2$ statistic is the chi-square distribution, which is also the asymptotic distribution of $T^2$ under the assumption of normality.


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9/2008 The Probability Density Function to the Random Linear Transport Equation
Lúcio T. Santos, Fábio A. Dorini, Maria Cristina C. Cunha

We present a formula to calculate the probability density function to the solution of the random linear transport equation in terms of the density functions of the velocity and the initial condition. We also present an expression to the joint probability density function of the solution in two different points. Our results have shown good agreement with Monte Carlo simulations.


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8/2008 Correlates of Rhythm in Written Texts of Brazilian and European Portuguese
Antônio Galves, Charlotte Galves, Nancy L. Garcia, Claudia Peixoto

We address the question of detecting fingerprints of rhythm in written texts. We study texts from 20th century Brazilian and Portuguese authors. In these texts we codify the syllables according to whether they carry main stress or not, and whether they are at the beginning of a phonological word or not. Additionally, periods are also marked. Modeling the sequences of symbols obtained with this codification as Variable Length Markov Chains, we estimate the patterns for each text. This probabilistic model discriminates European Portuguese from Brazilian Portuguese. Moreover, the model obtained for each language has a clear linguistic interpretation, as it captures structural features which have long been conjectured in the literature.address the question of detecting fingerprints of rhythm in written texts. We study texts from 20th century Brazilian and Portuguese authors. In these texts we codify the syllables according to whether they carry main stress or not, and whether they are at the beginning of a phonological word or not. Additionally, periods are also marked. Modeling the sequences of symbols obtained with this codification as Variable Length Markov Chains, we estimate the patterns for each text. This probabilistic model discriminates European Portuguese from Brazilian Portuguese. Moreover, the model obtained for each language has a clear linguistic interpretation, as it captures structural features which have long been conjectured in the literature.


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7/2008 Group Classification of Burgers' Equations
Igor Leite Freire

In this work we carry out a complete group classification of Burgers' equations.


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6/2008 Equação do Telégrafo Fracionária e as Funções de Mittag-Leffler
R. Figueiredo Camargo, Ary O. Chiacchio, Edmundo Capelas de Oliveira

Utilizando métodos de cálculo diferencial e integral fracionários são apresentados e discutidos dois modos distintos de se calcular a função de Green, associada ao caso unidimensional, da assimchamada equação do telégrafo fracionária. Esta é uma equação diferencial parcial com coeficientes constantes e é resolvida através da metodologia da justaposição das transformadas de Fourier, na parte espacial, e Laplace, na parte temporal. Utilizando manipulações algébricas, i.e., efetuando os cálculos de um modo alternativo, obtemos uma outra expressão para a função de Green, num particular caso, ou seja, a solução é dada de uma outra maneira. Através da comparação entre os resultados obtidos a partir das duas maneiras, são obtidas novas relações e um teorema de adição para as funções deMittag-Leffler. É apresentada uma demonstração formal do teorema assim obtido e casos particulares do mesmo são discutidos.

5/2008 Pseudo Periodic Orbits of the Planar Collision Restricted 3-Body Problem in Rotating Coordinates
Jaume Llibre, Luci Any Roberto

By using the continuation method of Poincar\'{e}, we characterize the periodic circular orbits and the symmetric periodic elliptic orbits that can be prolonged from the planar Kepler problem in rotating coordinates to pseudo periodic orbits of the planar restricted 3--body problem in rotating coordinates with the two primaries moving in an elliptic collision orbit.


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4/2008 Branching of Periodic Orbits in Reversible Hamiltonian Systems
Cláudio A. Buzzi, Luci Any Roberto, Marco A. Teixeira

This paper deals with the dynamics of time-reversible Hamiltonian vector fields with 2 and 3 degrees of freedom around an elliptic equilibrium point in presence of symplectic involutions. The main results discuss the existence of one-parameter families of reversible periodic solutions terminating at the equilibrium. The main techniques used are Birkhoff and Belitskii normal forms combined with the Liapunov-Schmidt reduction.


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