Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

Covariance matrix formula for Birnbaum-Saunders regression models

The Birnbaum-Saunders regression model is commonly used in reliability studies. We derive a simple matrix formula for second-order covariances of maximum-likelihood estimators in this class of models. The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors. Some simulation results show that the second-order covariances can be quite pronounced in small to moderate sample sizes. We also present empirical applications.

Influence diagnostics in Birnbaum-Saunders nonlinear regression models

We consider the issue of assessing influence of observations in the class of Birnbaum-Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8] which are confined to Birnbaum-Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures for studying local influence are derived under some perturbation schemes. We also give an application to a real fatigue data set.

Asymptotic skewness in Birnbaum-Saunders nonlinear regression models

The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetime data and it is widely applicable to model failure times of fatiguing materials. We give a simple matrix formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in Birnbaum-Saunders nonlinear regression models, recently introduced by Lemonte and Cordeiro (2009). The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors, in order to obtain closed-form skewness in a wide range of nonlinear regression models. Empirical and real applications are analyzed and discussed. (C) 2010 Elsevier B.V. All rights reserved.

Some restriction tests in a new class of regression models for proportions

The main purpose of this work is to study the behaviour of Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-32] adjusted likelihood ratio statistic in testing simple hypothesis in a new class of regression models proposed here. The proposed class of regression models considers Dirichlet distributed observations, and the parameters that index the Dirichlet distributions are related to covariates and unknown regression coefficients. This class is useful for modelling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in Vasconcellos and Cribari-Neto [Vasconcellos, K.L.P., Cribari-Neto, F., 2005. Improved maximum likelihood estimation in a new class of beta regression models. Brazilian journal of Probability and Statistics 19,13-31]. We show that, for our model, Skovgaard`s adjusted likelihood ratio statistics have a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with a high degree of accuracy. Some numerical simulations show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. An empirical application is also presented and discussed. (C) 2009 Elsevier B.V. All rights reserved.

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60]. We discuss maximum-likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum-likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Two empirical applications are analysed and discussed. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

An Analysis of the Telecommunications Business in China by Linear Regression

In this paper, we study the influence of the National Telecom Business Volume by the data in 2008 that have been published in China Statistical Yearbook of Statistics. We illustrate the procedure of modeling “National Telecom Business Volume” on the following eight variables, GDP, Consumption Levels, Retail Sales of Social Consumer Goods Total Renovation Investment, the Local Telephone Exchange Capacity, Mobile Telephone Exchange Capacity, Mobile Phone End Users, and the Local Telephone End Users. The testing of heteroscedasticity and multicollinearity for model evaluation is included. We also consider AIC and BIC criterion to select independent variables, and conclude the result of the factors which are the optimal regression model for the amount of telecommunications business and the relation between independent variables and dependent variable. Based on the final results, we propose several recommendations about how to improve telecommunication services and promote the economic development.

A Note on Proxy Variables and Instrument Variable Regression

This is a note about proxy variables and instruments for identification of structural parameters in regression models. We have experienced that in the econometric textbooks these two issues are treated separately, although in practice these two concepts are very often combined. Usually, proxy variables are inserted in instrument variable regressions with the motivation they are exogenous. Implicitly meaning they are exogenous in a reduced form model and not in a structural model. Actually if these variables are exogenous they should be redundant in the structural model, e.g. IQ as a proxy for ability. Valid proxies reduce unexplained variation and increases the efficiency of the estimator of the structural parameter of interest. This is especially important in situations when the instrument is weak. With a simple example we demonstrate what is required of a proxy and an instrument when they are combined. It turns out that when a researcher has a valid instrument the requirements on the proxy variable is weaker than if no such instrument exists

Electoral rules, political competition and fiscal spending: regression discontinuity evidence from brazilian municipalities

We exploit a discontinuity in Brazilian municipal election rules to investigate whether political competition has a causal impact on policy choices. In municipalities with less than 200,000 voters mayors are elected with a plurality of the vote. In municipalities with more than 200,000 voters a run-off election takes place among the top two candidates if neither achieves a majority of the votes. At a first stage, we show that the possibility of runoff increases political competition. At a second stage, we use the discontinuity as a source of exogenous variation to infer causality from political competition to fiscal policy. Our second stage results suggest that political competition induces more investment and less current spending, particularly personnel expenses. Furthermore, the impact of political competition is larger when incumbents can run for reelection, suggesting incentives matter insofar as incumbents can themselves remain in office.

Valor prognóstico das cinéticas da procalcitonina e da proteína C reativa na pneumonia associada à ventilação mecânica

Introdução A pneumonia hospitalar é a principal causa de morte dentre as infecções hospitalares. A prevalência de pneumonia hospitalar em Unidades de Tratamento Intensivo (UTI) varia de 10 a 65%, com taxas de mortalidade que podem variar de 24 a 76%. A pneumonia associada à ventilação mecânica (PAV) é um determinante de mortalidade independente em pacientes submetidos à ventilação mecânica. A adequação do tratamento empírico precoce parece ser fundamental no prognóstico. Os critérios atualmente estabelecidos para avaliar adequação do tratamento empírico utilizam parâmetros clínicos, escores de gravidade e, principalmente, a sensibilidade do germe causador da infecção aos antibióticos administrados. Estes resultados balizam a necessidade de possíveis modificações no esquema antimicrobiano. A possibilidade de utilizar a Procalcitonina (PCT), a Proteína-C Reativa (CRP) e o escore SOFA (Avaliação de Falência de Órgãos Relacionada a Sepse), como indicadores de resposta do paciente, comparando seu status no dia do início do tratamento antimicrobiano (D0) com a evolução destes indicadores no quarto dia de tratamento (D4) abre a possibilidade de comparar o paciente com ele próprio, independente da exuberância da expressão da resposta inflamatória que ele possa desenvolver. Os resultados desta cinética entre D0 e D4 podem ser preditivos de gravidade de infecção, de eficiência antimicrobiana, e possivelmente de sobrevivência ou mortalidade hospitalar nos pacientes com suspeita de PAV. Objetivos Determinar e comparar o valor prognóstico de sobrevivência da cinética da PCT, da CRP, dos escores clínicos CPIS (Escore Clínico de Infecção Pulmonar) e SOFA, e do APACHE II (Avaliação da Fisiologia Aguda e da Saúde Crônica) na PAV entre o diagnóstico e o quarto dia de tratamento, quando a adequação do tratamento é avaliada. Pacientes e Métodos Realizamos um estudo de coorte prospectivo observacional que avaliou 75 pacientes internados no Centro de Tratamento Intensivo clínico-cirúrgico de adultos do Hospital de Clínicas de Porto Alegre que desenvolveram PAV no período de outubro de 2003 a agosto de 2005. Os pacientes com suspeita clínica de PAV que se adequaram aos critérios de inclusão e exclusão do estudo foram os candidatos a participar. Os familiares ou representantes dos pacientes receberam esclarecimentos por escrito acerca dos exames a serem realizados, bem como dos objetivos gerais da pesquisa. Os que aceitaram participar do estudo assinaram o termo de Consentimento Informado. O projeto foi aprovado pelo Comitê de Ética em Pesquisa do Hospital de Clínicas de Porto Alegre. No dia do diagnóstico de PAV foram coletados aspirado traqueal quantitativo, hemoculturas e sangue para a realização de dosagens de PCT, CRP, hemograma, plaquetas, creatinina, bilirrubinas, gasometria arterial e radiografia de tórax, com o objetivo de calcular o CPIS e o escore SOFA. No terceiro dia de tratamento foram novamente coletados aspirados traqueais quantitativos e os demais exames para o cálculo do CPIS. No quarto dia foi coletado sangue para dosagens de PCT, CRP e para os demais exames necessários para o cálculo do SOFA. Os pacientes foram acompanhados por 28 dias após o diagnóstico de PAV, quando foram considerados sobreviventes. Todos os pacientes que morreram antes do vigésimo oitavo dia foram considerados não-sobreviventes. Resultados Os níveis de PCT foram mais baixos nos sobreviventes em D0 (p=0.003) e em D4 (p=0.001). Os níveis de CRP não foram diferentes em sobreviventes e nãosobreviventes em D0 (p=0.77) e em D4 (p=0.14). O CPIS não pode diferenciar sobreviventes de não-sobrevientes em D0 (p=0.32) e em D3 (p=0.45). ΔCPIS decrescente não foi correlacionado a sobrevivência (p=0.59), o mesmo ocorrendo com CPIS <6 em D3 (p=0.79). Pacientes que morreram antes de D4 não puderam ter sua cinética calculada e foram considerados casos perdidos. Variáveis incluídas no modelo de regressão logística univariável para sobrevivência foram idade, APACHE II, ΔSOFA decrescente, ΔPCT decrescente e ΔCRP decrescente. Sobrevivência foi diretamente correlacionada a ΔPCT decrescente com RC = 5.67 (1.78;18.03) p = 0.003, ΔCRP com RC = 3.78 (1.24;11.50) p = 0.02, ΔSOFA decrescente com RC = 3.08 (1.02;9.26) p = 0.05 e escore APACHE II com RC = 0.92 (0.86;0.99) p = 0.02. O modelo de regressão logística multivariável para sobrevivência incluiu todas as variáveis participantes da análise univariável. Somente ΔPCT decrescente com RC = 4.43 (1.08;18.18) p = 0.04 e ΔCRP com RC = 7.40 (1.58;34.73) p = 0.01 permaneceram significativos. A avaliação da cinética dos marcadores inflamatórios e a associação com sobrevida no estudo mostraram que: - Em 95,1% dos sobreviventes houve queda dos níveis de PCT ou de CRP. - Em 61% dos sobreviventes ambos os níveis de PCT e de CRP caíram. Apenas 4,9% dos sobreviventes tiveram níveis de PCT e CRP crescentes. Com relação aos não-sobreviventes, 78.9% tiveram pelo menos um dos dois marcadores ou ambos com níveis crescentes. Conclusão As cinéticas da PCT e da CRP, obtidas pelas dosagens de seus níveis no dia do diagnóstico e no 4º dia de tratamento, podem predizer sobrevivência em pacientes com PAV. A queda dos níveis de pelo menos um destes marcadores ou de ambos indica maior chance de sobrevivência.

Wald tests for IV regression with weak instruments

This dissertation deals with the problem of making inference when there is weak identification in models of instrumental variables regression. More specifically we are interested in one-sided hypothesis testing for the coefficient of the endogenous variable when the instruments are weak. The focus is on the conditional tests based on likelihood ratio, score and Wald statistics. Theoretical and numerical work shows that the conditional t-test based on the two-stage least square (2SLS) estimator performs well even when instruments are weakly correlated with the endogenous variable. The conditional approach correct uniformly its size and when the population F-statistic is as small as two, its power is near the power envelopes for similar and non-similar tests. This finding is surprising considering the bad performance of the two-sided conditional t-tests found in Andrews, Moreira and Stock (2007). Given this counter intuitive result, we propose novel two-sided t-tests which are approximately unbiased and can perform as well as the conditional likelihood ratio (CLR) test of Moreira (2003).

Improved combinations of parametric and nonparametric Regression estimators

This paper provides a systematic and unified treatment of the developments in the area of kernel estimation in econometrics and statistics. Both the estimation and hypothesis testing issues are discussed for the nonparametric and semiparametric regression models. A discussion on the choice of windowwidth is also presented.