Estatística - Interinstitucional (PIPGEs) https://repositorio.ufscar.br/handle/ufscar/8205 2019-10-22T13:46:52Z Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process https://repositorio.ufscar.br/handle/ufscar/11925 Statistical inference for non-homogeneous Poisson process with competing risks: a repairable systems approach under power-law process In this thesis, the main objective is to study certain aspects of modeling failure time data of repairable systems under a competing risks framework. We consider two different models and propose more efficient Bayesian methods for estimating the parameters. In the first model, we discuss inferential procedures based on an objective Bayesian approach for analyzing failures from a single repairable system under independent competing risks. We examined the scenario where a minimal repair is performed at each failure, thereby resulting in that each failure mode appropriately follows a power-law intensity. Besides, it is proposed that the power-law intensity is reparametrized in terms of orthogonal parameters. Then, we derived two objective priors known as the Jeffreys prior and reference prior. Moreover, posterior distributions based on these priors will be obtained in order to find properties which may be optimal in the sense that, for some cases, we prove that these posterior distributions are proper and are also matching priors. In addition, in some cases, unbiased Bayesian estimators of simple closed-form expressions are derived. In the second model, we analyze data from multiple repairable systems under the presence of dependent competing risks. In order to model this dependence structure, we adopted the well-known shared frailty model. This model provides a suitable theoretical basis for generating dependence between the components’ failure times in the dependent competing risks model. It is known that the dependence effect in this scenario influences the estimates of the model parameters. Hence, under the assumption that the cause-specific intensities follow a PLP, we propose a frailty-induced dependence approach to incorporate the dependence among the cause-specific recurrent processes. Moreover, the misspecification of the frailty distribution may lead to errors when estimating the parameters of interest. Because of this, we considered a Bayesian nonparametric approach to model the frailty density in order to offer more flexibility and to provide consistent estimates for the PLP model, as well as insights about heterogeneity among the systems. Both simulation studies and real case studies are provided to illustrate the proposed approaches and demonstrate their validity. 2019-08-30T00:00:00Z Modelo geométrico de ordem k correlacionado https://repositorio.ufscar.br/handle/ufscar/11914 Modelo geométrico de ordem k correlacionado In this work we propose the correlated geometric distribution of order k, k≥1, with parameters π and ρ; π ∈(0,1), max{−1,−1−π π } ≤ρ < 1, as an extension of the generalized geometric distribution proposed by Philippou e Muwaﬁ (1980) and considering the ideas of Kolev, Minkova e Neytchev (2000) for generalizations of discrete distributions by including an additional parameter ρ. Thus, it is also a re-reading of the geometric distribution of order k by Aki e Hirano (1993). Some properties of the proposed distribution are presented. Regression models are developed using classical and Bayesian estimation methods. Simulated data studies show the behavior of the distributions and some properties of the estimators. The main motivation in this research, besides contribute to generalizations of discrete distributions, is to propose na alternative analysis and even more suitable for real data, since the effect of the individual correlation is taken into account through the existence of the parameter. The ﬁtted models are evaluated and the residual analysis and diagnosis of inﬂuence or divergence are also presented. 2019-08-29T00:00:00Z Modelos não lineares assimétricos com efeitos mistos https://repositorio.ufscar.br/handle/ufscar/11867 Modelos não lineares assimétricos com efeitos mistos This work aims to develop asymmetric nonlinear regression models with mixed-effects, which provide alternatives to the use of normal distribution and other symmetric distributions, in order to avoid the sensitivity in the estimates to atypical observations and asymmetry. Nonlinear models with mixed-effects are explored in several areas of knowledge, especially when data are correlated, such as longitudinal data, repeated measures and multilevel data, in particular, for their flexibility in dealing with measures of areas such as biology and pharmacokinetics. However, there are difficulties in obtaining explicit estimators for the parameters in these models. At present, many studies have been developed with the family scale mixtures of skew-normal distribution (SMSN) that encompasses distributions with light and heavy tails, such as skew-normal, skew-Student-t, skew-contaminated normal and skew-slash, as well as symmetrical versions of these distributions. In this work, nonlinear regression models with mixed-effects are presented in which the random components have distributions belonging to the SMSN family. For the parameters estimation, a numerical solution via the EM algorithm and its extensions and Newton-Raphson algorithm is obtained. Analyzes for real data sets are performed with this new proposal, such as the study of drug kinetics in humans, as well as diagnostic analyzes, through residual analysis and influence diagnostics. Simulation studies are conducted to verify the maximum likelihood properties of the estimators. 2019-08-02T00:00:00Z Neural networks as an optimization tool for regression https://repositorio.ufscar.br/handle/ufscar/11853 Neural networks as an optimization tool for regression Neural networks are a tool to solve prediction problems that have gained much prominence recently. In general, neural networks are used as a predictive method, that is, their are used to estimate a regression function. Instead, this work presents the use of neural networks as an optimization tool to combine existing regression estimators in order to obtain more accurate predictions and to fit local linear models more efficiently. Several tests were conducted to show the greater efficiency of these methods when compared to the usual ones. 2019-09-02T00:00:00Z