The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate $n^{-1/2}$, $n$ being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.Comment: To appear in the Annals of the Institute of Statistical Mathematics, this http://www.ism.ac.jp/editsec/aism-e.htm

A Bayesian Modelling of Wildfires in Portugal

In the last decade wildfires became a serious problem in Portugal due to different issues such as climatic characteristics and nature of Portuguese forest. In order to analyse wildfire data, we employ beta regression for modelling the proportion of burned forest area, under a Bayesian perspective. Our main goal is to find out fire risk factors that influence the proportion of area burned and what may make a forest type susceptible or resistant to fire. Then, we analyse wildfire data in Portugal during 1990-1994 through Bayesian beta models t

Second and Third Order Bias Reduction for One-Parameter Family Models

In this paper we derive second and third order bias-corrected maximum likelihood estimates in general uniparametric models. We compare the corrected estimates and the usual maximum likelihood estimate in terms of their mean squared errors. We also obtain closed-form expressions for bias-corrected estimates in one-parameter exponential family models. Our results cover many important and commonly used distributions.Asymptotic expansion; bias correction, exponential family; maximum likelihood estimate

Bartlett Corrections for One-Parameter Exponential Family Models

In this paper we derive a general closed-form expression for the Bartlett correction for the test of H_0: \theta= \theta**(0), where "theta is a scalar parameter of a one-parameter exponential family model. Our results are general enough to cover many important and commonly used distributions. Several special cases and classes of variance functions of considerable importance are discussed, and some approximations based on asymptotic expansions are given. We also use a graphical analysis to examine how the correction varies with \theta in some special cases. Simulation results are also given.Bartlett correction, chi-squared distribution, exponential family, likelihood ratio statistic

Predicting the Evolution of a Constrained Network: A Beta Regression Model

Social network analysis allows to map and measure relationships and flows (links) between people, groups, computers, URLs, or other connected knowledge entities (nodes). In this context, a relevant issue is the treatment of constrained scale-free networks such as the network of student transfers between degree courses offered by an University, that are strongly influenced by a number of institutional decisions. In the analysis of such a system, special attention has to be paid to identify current or future \u201ccritical points\u201d, that is nodes characterized by a high number of outcoming or incoming links, on which to act in order to optimize the network. To predict the evolution of a constrained system over time in dependence of constraint modifications, a beta regression model is proposed, that fits links represented by quantities varying between 0 and 1. The algorithm was successfully applied to the network of student transfers within the University of Bologna: the link was defined by the out-transfer rate of the degree course (computed as the ratio of the number of out-transfers to the number of students enrolled) and the critical points of the system were defined by the courses characterized by a high out-transfer rate

Modelagem da fração de não-conformes em processos industriais

Em qualquer processo industrial, pode ser definido um conjunto de causas ou fatores que produzem determinado efeito sobre uma ou mais características de qualidade de um produto que pode ou não satisfazer às especificações do cliente, gerando a produção de produtos não-conformes. A modelagem da proporção ou fração de produtos não-conformes utilizando-se o modelo de regressão linear não é adequada por pelo menos duas razões: (i) pressupõe que as proporções seguem a distribuição normal, que não é correto; e (ii) possibilita a previsão de valores fora do intervalo [0,1]. Alternativas à modelagem da proporção de não-conformes são os Modelos Lineares Generalizados e os Modelos de Regressão Beta. O objetivo deste artigo é modelar a fração de não-conformes às especificações de uma indústria curtidora com enfoque nos Modelos de Regressão Beta e Modelo Linear Generalizado. Esses modelos podem ser estendidos a processos industriais que envolvam a produção de produtos não-conformes às especificações de manufatura.In any industrial process, one can enumerate causes or factors that act on one or more quality characteristics of the resulting product such that they fail to meet customers' specifications, generating items deemed as nonconforming. Modeling the fraction or proportion of nonconforming items using linear regression models is not adequate for at least two reasons: (i) proportions are assumed to follow a Normal distribution, which is not correct, and (ii) predicted responses will not necessarily be confined in the [0,1]-interval. Alternative approaches to the modeling of nonconforming proportions are based on Generalized Linear Models and Beta Regression Models. In this paper we present a case study where the objective is to model the nonconforming fraction of items emerging from a tanning process; our analysis uses Generalized Linear Models and Beta Regression Models. The developments presented in the paper may be extended to other industrial process where the proportion of nonconforming items is easily accessible