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.

Preparation and characterization of ordered intermetallic platinum phases for electrocatalytic applications

Ordered intermetallic phases of Pt with several transition metals have been prepared and their electrocatalytic properties studied. In light of these tests it is proposed that these catalysts could be used as electrodes in fuel cells, as they combine an excellent capacity to adsorb organic fuels at the Pt sites with low susceptibility to being poisoned by intermediates and reaction products at the transition-metal sites. An experimental procedure used to obtain the four intermetallic phases Pt-M (M = Mn, Pb, Sb and Sn) is described. The phases thus produced were characterized by X-ray diffraction, scanning electron microscopy with surface analysis by energy-dispersive X-ray spectrometry, scanning tunneling microscopy and X-ray photoelectron spectroscopy. The data thus obtained support the conclusion that the method described here is highly effective for the preparation of Pt-M phases featuring a range of structural and electronic modifications that will allow a useful relation to be established between their physicochemical properties and predicted electrocatalytic activity. (C) 2007 Elsevier Ltd. 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

Correcting the fixed-effect estimator for endogenous switching

In this paper, we propose a two-step estimator for panel data models in which a binary covariate is endogenous. In the first stage, a random-effects probit model is estimated, having the endogenous variable as the left-hand side variable. Correction terms are then constructed and included in the main regression.

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.

An analysis of quit and dismissal determinants between 1988 and 1999 using the bivariate probit model

Excessive labor turnover may be considered, to a great extent, an undesirable feature of a given economy. This follows from considerations such as underinvestment in human capital by firms. Understanding the determinants and the evolution of turnover in a particular labor market is therefore of paramount importance, including policy considerations. The present paper proposes an econometric analysis of turnover in the Brazilian labor market, based on a partial observability bivariate probit model. This model considers the interdependence of decisions taken by workers and firms, helping to elucidate the causes that lead each of them to end an employment relationship. The Employment and Unemployment Survey (PED) conducted by the State System of Data Analysis (SEADE) and by the Inter-Union Department of Statistics and Socioeconomic Studies (DIEESE) provides data at the individual worker level, allowing for the estimation of the joint probabilities of decisions to quit or stay on the job on the worker’s side, and to maintain or fire the employee on the firm’s side, during a given time period. The estimated parameters relate these estimated probabilities to the characteristics of workers, job contracts, and to the potential macroeconomic determinants in different time periods. The results confirm the theoretical prediction that the probability of termination of an employment relationship tends to be smaller as the worker acquires specific skills. The results also show that the establishment of a formal employment relationship reduces the probability of a quit decision by the worker, and also the firm’s firing decision in non-industrial sectors. With regard to the evolution of quit probability over time, the results show that an increase in the unemployment rate inhibits quitting, although this tends to wane as the unemployment rate rises.