Não vício assintótico, consistência forte e uniformemente forte de estimadores do tipo núcleo para dados direcionais sobre uma esfera unitária k-dimensional

In this work we studied the asymptotic unbiasedness, the strong and the uniform strong consistencies of a class of kernel estimators fn as an estimator of the density function f taking values on a k-dimensional sphere

Métodos numéricos para resolução de equações diferenciais ordinárias lineares baseados em interpolação por spline

In this work we have elaborated a spline-based method of solution of inicial value problems involving ordinary differential equations, with emphasis on linear equations. The method can be seen as an alternative for the traditional solvers such as Runge-Kutta, and avoids root calculations in the linear time invariant case. The method is then applied on a central problem of control theory, namely, the step response problem for linear EDOs with possibly varying coefficients, where root calculations do not apply. We have implemented an efficient algorithm which uses exclusively matrix-vector operations. The working interval (till the settling time) was determined through a calculation of the least stable mode using a modified power method. Several variants of the method have been compared by simulation. For general linear problems with fine grid, the proposed method compares favorably with the Euler method. In the time invariant case, where the alternative is root calculation, we have indications that the proposed method is competitive for equations of sifficiently high order.

Estimadores do tipo núcleo para Variávei s I.I.D. com espaço de estados geral

In this work, the paper of Campos and Dorea [3] was detailed. In that article a Kernel Estimator was applied to a sequence of random variables with general state space, which were independent and identicaly distributed. In chapter 2, the estimator´s properties such as asymptotic unbiasedness, consistency in quadratic mean, strong consistency and asymptotic normality were verified. In chapter 3, using R software, numerical experiments were developed in order to give a visual idea of the estimate process

Estimação clássica e Bayesiana em modelos de sobrevida com fração de cura

In Survival Analysis, long duration models allow for the estimation of the healing fraction, which represents a portion of the population immune to the event of interest. Here we address classical and Bayesian estimation based on mixture models and promotion time models, using different distributions (exponential, Weibull and Pareto) to model failure time. The database used to illustrate the implementations is described in Kersey et al. (1987) and it consists of a group of leukemia patients who underwent a certain type of transplant. The specific implementations used were numeric optimization by BFGS as implemented in R (base::optim), Laplace approximation (own implementation) and Gibbs sampling as implemented in Winbugs. We describe the main features of the models used, the estimation methods and the computational aspects. We also discuss how different prior information can affect the Bayesian estimates

Uma estratégia aleatória chamada de MOSES

This paper we study a random strategy called MOSES, which was introduced in 1996 by Fran¸cois. Asymptotic results of this strategy; behavior of the stationary distributions of the chain associated to strategy, were derived by Fran¸cois, in 1998, of the theory of Freidlin and Wentzell [8]. Detailings of these results are in this work. Moreover, we noted that an alternative approach the convergence of this strategy is possible without making use of theory of Freidlin and Wentzell, yielding the visit almost certain of the strategy to uniform populations which contain the minimum. Some simulations in Matlab are presented in this work

Análise de resíduos em modelos de tempo de falha acelerado com efeito aleatório

We present residual analysis techniques to assess the fit of correlated survival data by Accelerated Failure Time Models (AFTM) with random effects. We propose an imputation procedure for censored observations and consider three types of residuals to evaluate different model characteristics. We illustrate the proposal with the analysis of AFTM with random effects to a real data set involving times between failures of oil well equipment

Algoritmos genéticos canônico e elitista: uma abordagem comparativa

Universidade Federal do Rio Grande do Norte

Consequências da análise inadequada de um experimento fatorial 2k am parcelas subdivididas e sem replicação

Em experimentos com vários fatores em que alguns são mais difíceis de mudar que outros, pode ser inconveniente executar as provas do experimento em uma forma completamente aleatória, levando o pesquisador a criar naturalmente uma restrição na ordem de execução para poupar tempo ou reduzir os custos. Este tipo de restrição pode resultar em uma generalização do planejamento fatorial, conhecida como experimentos em parcelas subdivididas. Na prática, é comum executar um experimento em parcelas subdivididas e analisá-lo como se fosse completamente aleatorizado. O objetivo principal do trabalho é avaliar o impacto de analisar um experimento com restrição na aleatorização como completamente aleatorizado

A teoria da ruína aplicada em um modelo de empresa financeira com risco de crédito

In this work we study a new risk model for a firm which is sensitive to its credit quality, proposed by Yang(2003): Are obtained recursive equations for finite time ruin probability and distribution of ruin time and Volterra type integral equation systems for ultimate ruin probability, severity of ruin and distribution of surplus before and after ruin

Controle on-line para o número de não-conformidades em um ítem inspecionado

The on-line processes control for attributes consists of inspecting a single item at every m produced ones. If the examined item is conforming, the production continues; otherwise, the process stops for adjustment. However, in many practical situations, the interest consist of monitoring the number of non-conformities among the examined items. In this case, if the number of non-conformities is higher than an upper control limit, the process needs to be stopped and some adjustment is required. The contribution of this paper is to propose a control system for the number of nonconforming of the inspected item. Employing properties of an ergodic Markov chain, an expression for the expected cost per item of the control system was obtained and it will be minimized by two parameters: the sampling interval and the upper limit control of the non-conformities of the examined item. Numerical examples illustrate the proposed procedure

Métodos estatisticos em cadeias de Markov

Este trabalho tem como objetivo o estudo do comportamento assintótico da estatística de Pearson (1900), que é o aparato teórico do conhecido teste qui-quadrado ou teste x2 como também é usualmente denotado. Inicialmente estudamos o comportamento da distribuição da estatística qui-quadrado de Pearson (1900) numa amostra {X1, X2,...,Xn} quando n → ∞ e pi = pi0 , 8n. Em seguida detalhamos os argumentos usados em Billingley (1960), os quais demonstram a convergência em distribuição de uma estatística, semelhante a de Pearson, baseada em uma amostra de uma cadeia de Markov, estacionária, ergódica e com espaço de estados finitos S

Estimação paramétrica e não-paramétrica em modelos de markov ocultos

In this work we study the Hidden Markov Models with finite as well as general state space. In the finite case, the forward and backward algorithms are considered and the probability of a given observed sequence is computed. Next, we use the EM algorithm to estimate the model parameters. In the general case, the kernel estimators are used and to built a sequence of estimators that converge in L1-norm to the density function of the observable process

Estimador do Tipo Núcleo para Densidades Limites de Cadeias de Markov com Espaço de Estados Geral

In this work we studied the consistency for a class of kernel estimates of f f (.) in the Markov chains with general state space E C Rd case. This study is divided into two parts: In the first one f (.) is a stationary density of the chain, and in the second one f (x) v (dx) is the limit distribution of a geometrically ergodic chain

Teoria da Ruína em um Modelo de Markov com dois Estados

In this work, we present a risk theory application in the following scenario: In each period of time we have a change in the capital of the ensurance company and the outcome of a two-state Markov chain stabilishs if the company pays a benece it heat to one of its policyholders or it receives a Hightimes c > 0 paid by someone buying a new policy. At the end we will determine once again by the recursive equation for expectation the time ruin for this company

Estimativa de expoentes críticos em Percolação

In Percolation Theory, functions like the probability that a given site belongs to the infinite cluster, average size of clusters, etc. are described through power laws and critical exponents. This dissertation uses a method called Finite Size Scaling to provide a estimative of those exponents. The dissertation is divided in four parts. The first one briefly presents the main results for Site Percolation Theory for d = 2 dimension. Besides, some important quantities for the determination of the critical exponents and for the phase transistions understanding are defined. The second shows an introduction to the fractal concept, dimension and classification. Concluded the base of our study, in the third part the Scale Theory is mentioned, wich relates critical exponents and the quantities described in Chapter 2. In the last part, through the Finite Size Scaling method, we determine the critical exponents fi and. Based on them, we used the previous Chapter scale relations in order to determine the remaining critical exponents