Robust inference in an heteroscedastic measurement error model

In this paper we deal with robust inference in heteroscedastic measurement error models Rather than the normal distribution we postulate a Student t distribution for the observed variables Maximum likelihood estimates are computed numerically Consistent estimation of the asymptotic covariance matrices of the maximum likelihood and generalized least squares estimators is also discussed Three test statistics are proposed for testing hypotheses of interest with the asymptotic chi-square distribution which guarantees correct asymptotic significance levels Results of simulations and an application to a real data set are also reported (C) 2009 The Korean Statistical Society Published by Elsevier B V All rights reserved

Bayesian analysis of skew-t multivariate null intercept measurement error model

The multivariate skew-t distribution (J Multivar Anal 79:93-113, 2001; J R Stat Soc, Ser B 65:367-389, 2003; Statistics 37:359-363, 2003) includes the Student t, skew-Cauchy and Cauchy distributions as special cases and the normal and skew-normal ones as limiting cases. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis of repeated measures, pretest/post-test data, under multivariate null intercept measurement error model (J Biopharm Stat 13(4):763-771, 2003) where the random errors and the unobserved value of the covariate (latent variable) follows a Student t and skew-t distribution, respectively. The results and methods are numerically illustrated with an example in the field of dentistry.

Inference and local influence assessment in skew-normal null intercept measurement error model

In this article, we discuss inferential aspects of the measurement error regression models with null intercepts when the unknown quantity x (latent variable) follows a skew normal distribution. We examine first the maximum-likelihood approach to estimation via the EM algorithm by exploring statistical properties of the model considered. Then, the marginal likelihood, the score function and the observed information matrix of the observed quantities are presented allowing direct inference implementation. In order to discuss some diagnostics techniques in this type of models, we derive the appropriate matrices to assessing the local influence on the parameter estimates under different perturbation schemes. The results and methods developed in this paper are illustrated considering part of a real data set used by Hadgu and Koch [1999, Application of generalized estimating equations to a dental randomized clinical trial. Journal of Biopharmaceutical Statistics, 9, 161-178].

Multivariate measurement error models based on scale mixtures of the skew-normal distribution

Scale mixtures of the skew-normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation-maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.

Measurement error models with a general class of error distribution

In general, the normal distribution is assumed for the surrogate of the true covariates in the classical error model. This paper considers a class of distributions, which includes the normal one, for the variables subject to error. An estimation approach yielding consistent estimators is developed and simulation studies reported.

Systematic risk estimation in symmetric models

The aim of this article is to discuss the estimation of the systematic risk in capital asset pricing models with heavy-tailed error distributions to explain the asset returns. Diagnostic methods for assessing departures from the model assumptions as well as the influence of observations on the parameter estimates are also presented. It may be shown that outlying observations are down weighted in the maximum likelihood equations of linear models with heavy-tailed error distributions, such as Student-t, power exponential, logistic II, so on. This robustness aspect may also be extended to influential observations. An application in which the systematic risk estimate of Microsoft is compared under normal and heavy-tailed errors is presented for illustration.

Credit shocks and monetary policy in Brazil: a structural FAVAR approach

This paper investigates the implications of the credit channel of the monetary policy transmission mechanism in the case of Brazil, using a structural FAVAR (SFAVAR) approach. The term structural comes from the estimation strategy, which generates factors that have a clear economic interpretation. The results show that unexpected shocks in the proxies for the external nance premium and the bank balance sheet channel produce large and persistent uctuations in in ation and economic activity accounting for more than 30% of the error forecast variance of the latter in a three-year horizon. The central bank seems to incorporate developments in credit markets especially variations in credit spreads into its reaction function, as impulse-response exercises show the Selic rate is declining in response to wider credit spreads and a contraction in the volume of new loans. Counterfactual simulations also demonstrate that the credit channel ampli ed the economic contraction in Brazil during the acute phase of the global nancial crisis in the last quarter of 2008, thus gave an important impulse to the recovery period that followed.

A simple and non-destructive model for individual leaf area estimation in citrus

Introduction. Leaf area is often related to plant growth, development, physiology and yield. Many non-destructive models have been proposed for leaf area estimation of several plant genotypes, demonstrating that leaf length, leaf width and leaf area are closely correlated. Thus, the objective of our study was to develop a reliable model for leaf area estimation from linear measurements of leaf dimensions for citrus genotypes. Materials and methods. Leaves of citrus genotypes were harvested, and their dimensions (length, width and area) were measured. Values of leaf area were regressed against length, width, the square of length, the square of width and the product (length x width). The most accurate equations, either linear or second-order polynomial, were regressed again with a new data set; then the most reliable equation was defined. Results and discussion. The first analysis showed that the variables length, width and the square of length gave better results in second-order polynomial equations, while the linear equations were more suitable and accurate when the width and the product (length x width) were used. When these equations were regressed with the new data set, the coefficient of determination (R(2)) and the agreement index 'd' were higher for the one that used the variable product (length x width), while the Mean Absolute Percentage Error was lower. Conclusion. The product of the simple leaf dimensions (length x width) can provide a reliable and simple non-destructive model for leaf area estimation across citrus genotypes.

Estimation of genetic parameters for milk yield in Murrah buffaloes by Bayesian inference

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Comparison of methodologies for degree-day estimation using numerical methods

O desenvolvimento de projetos relacionados ao desempenho de diversas culturas tem recebido aperfeiçoamento cada vez maior, incorporado a modelos matemáticos sendo indispensável à utilização de equações cada vez mais consistentes que possibilitem previsão e maior aproximação do comportamento real, diminuindo o erro na obtenção das estimativas. Entre as operações unitárias que demandam maior estudo estão aquelas relacionadas com o crescimento da cultura, caracterizadas pela temperatura ideal para o acréscimo de matéria seca. Pelo amplo uso dos métodos matemáticos na representação, análise e obtenção de estimativas de graus-dia, juntamente com a grande importância que a cultura da cana-de-açúcar tem para a economia brasileira, foi realizada uma avaliação dos modelos matemáticos comumente usados e dos métodos numéricos de integração na estimativa da disponibilidade de graus-dia para essa cultura, na região de Botucatu, Estado de São Paulo. Os modelos de integração, com discretização de 6 em 6 h, apresentaram resultados satisfatórios na estimativa de graus-dia. As metodologias tradicionais apresentaram desempenhos satisfatórios quanto à estimativa de grausdia com base na curva de temperatura horária para cada dia e para os agrupamentos de três, sete, 15 e 30 dias. Pelo método numérico de integração, a região de Botucatu, Estado de São Paulo, apresentou disponibilidade térmica anual média de 1.070,6 GD para a cultura da cana-de-açúcar.

A neural network approach for robust nonlinear parameter estimation in presence of unknown-but-bounded errors

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. This paper presents a novel approach to solve robust parameter estimation problem for nonlinear model with unknown-but-bounded errors and uncertainties. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach. Copyright (C) 2000 IFAC.

Measurement of the top quark pair production cross section in the lepton plus jets channel in proton-antiproton collisions at root s=1.96 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estimation of population profiles of two strains of the fly Megaselia scalaris (Diptera: Phoridae) by bootstrap simulation

A partir de perfis populacionais experimentais de linhagens do díptero forídeo Megaselia scalaris, foi determinado o número mínimo de perfis amostrais que devem ser repetidos, via processo de simulação bootstrap, para se ter uma estimativa confiável do perfil médio populacional e apresentar estimativas do erro-padrão como medida da precisão das simulações realizadas. Os dados originais são provenientes de populações experimentais fundadas com as linhagens SR e R4, com três réplicas cada, e que foram mantidas por 33 semanas pela técnica da transferência seriada em câmara de temperatura constante (25 ± 1,0ºC). A variável usada foi tamanho populacional e o modelo adotado para cada perfíl foi o de um processo estocástico estacionário. Por meio das simulações, os perfis de três populações experimentais foram amplificados, determinando-se, dessa forma, o tamanho mínimo de amostra. Fixado o tamanho de amostra, simulações bootstrap foram realizadas para construção de intervalos de confiança e comparação dos perfis médios populacionais das duas linhagens. Os resultados mostram que com o tamanho de amostra igual a 50 inicia-se o processo de estabilização dos valores médios.

Genetic effects on preweaning weight gain of Nelore-Hereford calves according to different models and estimation methods

Additive and nonadditive genetic effects on preweaning weight gain (PWG) of a commercial crossbred population were estimated using different genetic models and estimation methods. The data set consisted of 103,445 records on purebred and crossbred Nelore-Hereford calves raised under pasture conditions on farms located in south, southeast, and middle west Brazilian regions. In addition to breed additive and dominance effects, the models including different epistasis covariables were tested. Models considering joint additive and environment (latitude) by genetic effects interactions were also applied. In a first step, analyses were carried out under animal models. In a second step, preadjusted records were analyzed using ordinary least squares (OLS) and ridge regression (RR). The results reinforced evidence that breed additive and dominance effects are not sufficient to explain the observed variability in preweaning traits of Bos taurus x Bos indicus calves, and that genotype x environment interaction plays an important role in the evaluation of crossbred calves. Data were ill-conditioned to estimate the effects of genotype x environment interactions. Models including these effects presented multicolinearity problems. In this case, RR seemed to be a powerful tool for obtaining more plausible and stable estimates. Estimated prediction error variances and variance inflation factors were drastically reduced, and many effects that were not significant under ordinary least squares became significant under RR. Predictions of PWG based on RR estimates were more acceptable from a biological perspective. In temperate and subtropical regions, calves with intermediate genetic compositions (close to 1/2 Nelore) exhibited greater predicted PWG. In the tropics, predicted PWG increased linearly as genotype got closer to Nelore. ©2006 American Society of Animal Science. All rights reserved.

Inverse Modeling of GPS Multipath for Snow Depth Estimation-Part II: Application and Validation

GPS multipath reflectometry (GPS-MR) is a technique that uses geodetic quality GPS receivers to estimate snow depth. The accuracy and precision of GPS-MR retrievals are evaluated at three different sites: grasslands, alpine, and forested. The assessment yields a correlation of 0.98 and an rms error of 6-8 cm for observed snow depths of up to 2.5 m. GPS-MR underestimates in situ snow depth by 10%-15% at these three sites, although the validation methods do not measure the same footprint as GPS-MR.