Nonlinear set-membership estimation: a support vector machine approach

In this paper a support vector machine (SVM) approach for characterizing the feasible parameter set (FPS) in non-linear set-membership estimation problems is presented. It iteratively solves a regression problem from which an approximation of the boundary of the FPS can be determined. To guarantee convergence to the boundary the procedure includes a no-derivative line search and for an appropriate coverage of points on the FPS boundary it is suggested to start with a sequential box pavement procedure. The SVM approach is illustrated on a simple sine and exponential model with two parameters and an agro-forestry simulation model.

Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

A critical revision of the estimation of the latent heat flux from two-wavelength scintillometry

Simultaneous scintillometer measurements at multiple wavelengths (pairing visible or infrared with millimetre or radio waves) have the potential to provide estimates of path-averaged surface fluxes of sensible and latent heat. Traditionally, the equations to deduce fluxes from measurements of the refractive index structure parameter at the two wavelengths have been formulated in terms of absolute humidity. Here, it is shown that formulation in terms of specific humidity has several advantages. Specific humidity satisfies the requirement for a conserved variable in similarity theory and inherently accounts for density effects misapportioned through the use of absolute humidity. The validity and interpretation of both formulations are assessed and the analogy with open-path infrared gas analyser density corrections is discussed. Original derivations using absolute humidity to represent the influence of water vapour are shown to misrepresent the latent heat flux. The errors in the flux, which depend on the Bowen ratio (larger for drier conditions), may be of the order of 10%. The sensible heat flux is shown to remain unchanged. It is also verified that use of a single scintillometer at optical wavelengths is essentially unaffected by these new formulations. Where it may not be possible to reprocess two-wavelength results, a density correction to the latent heat flux is proposed for scintillometry, which can be applied retrospectively to reduce the error.

Rainfall estimation by rain gauge-radar combination: a concurrent multiplicative-additive approach

A procedure (concurrent multiplicative-additive objective analysis scheme [CMA-OAS]) is proposed for operational rainfall estimation using rain gauges and radar data. On the basis of a concurrent multiplicative-additive (CMA) decomposition of the spatially nonuniform radar bias, within-storm variability of rainfall and fractional coverage of rainfall are taken into account. Thus both spatially nonuniform radar bias, given that rainfall is detected, and bias in radar detection of rainfall are handled. The interpolation procedure of CMA-OAS is built on Barnes' objective analysis scheme (OAS), whose purpose is to estimate a filtered spatial field of the variable of interest through a successive correction of residuals resulting from a Gaussian kernel smoother applied on spatial samples. The CMA-OAS, first, poses an optimization problem at each gauge-radar support point to obtain both a local multiplicative-additive radar bias decomposition and a regionalization parameter. Second, local biases and regionalization parameters are integrated into an OAS to estimate the multisensor rainfall at the ground level. The procedure is suited to relatively sparse rain gauge networks. To show the procedure, six storms are analyzed at hourly steps over 10,663 km2. Results generally indicated an improved quality with respect to other methods evaluated: a standard mean-field bias adjustment, a spatially variable adjustment with multiplicative factors, and ordinary cokriging.

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

On estimation and influence diagnostics for log-Birnbaum-Saunders Student-t regression models: Full Bayesian analysis

The purpose of this paper is to develop a Bayesian approach for log-Birnbaum-Saunders Student-t regression models under right-censored survival data. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the considered model. In order to attenuate the influence of the outlying observations on the parameter estimates, we present in this paper Birnbaum-Saunders models in which a Student-t distribution is assumed to explain the cumulative damage. Also, some discussions on the model selection to compare the fitted models are given and case deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback-Leibler divergence. The developed procedures are illustrated with a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Improved likelihood inference for the shape parameter in Weibull regression

We obtain adjustments to the profile likelihood function in Weibull regression models with and without censoring. Specifically, we consider two different modified profile likelihoods: (i) the one proposed by Cox and Reid [Cox, D.R. and Reid, N., 1987, Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B, 49, 1-39.], and (ii) an approximation to the one proposed by Barndorff-Nielsen [Barndorff-Nielsen, O.E., 1983, On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.], the approximation having been obtained using the results by Fraser and Reid [Fraser, D.A.S. and Reid, N., 1995, Ancillaries and third-order significance. Utilitas Mathematica, 47, 33-53.] and by Fraser et al. [Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple formula for tail probabilities for frequentist and Bayesian inference. Biometrika, 86, 655-661.]. We focus on point estimation and likelihood ratio tests on the shape parameter in the class of Weibull regression models. We derive some distributional properties of the different maximum likelihood estimators and likelihood ratio tests. The numerical evidence presented in the paper favors the approximation to Barndorff-Nielsen`s adjustment.

Local Influence Under Parameter Constraints

Calculations of local influence curvatures and leverage have been well developed when the parameters are unrestricted. In this article, we discuss the assessment of local influence and leverage under linear equality parameter constraints with extensions to inequality constraints. Using a penalized quadratic function we express the normal curvature of local influence for arbitrary perturbation schemes and the generalized leverage matrix in interpretable forms, which depend on restricted and unrestricted components. The results are quite general and can be applied in various statistical models. In particular, we derive the normal curvature under three useful perturbation schemes for generalized linear models. Four illustrative examples are analyzed by the methodology developed in the article.

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.

Modified Fixed Effects Estimation of Technical Inefficiency

We consider method of moment fixed effects (FE) estimation of technical inefficiency. When N, the number of cross sectional observations, is large it ispossible to obtain consistent central moments of the population distribution of the inefficiencies. It is well-known that the traditional FE estimator may be seriously upward biased when N is large and T, the number of time observations, is small. Based on the second central moment and a single parameter distributional assumption on the inefficiencies, we obtain unbiased technical inefficiencies in large N settings. The proposed methodology bridges traditional FE and maximum likelihood estimation – bias is reduced without the random effects assumption.

Genetic heterogeneity of residual variance : estimation of variance components using double hierarchical generalized linear models

Background: The sensitivity to microenvironmental changes varies among animals and may be under genetic control. It is essential to take this element into account when aiming at breeding robust farm animals. Here, linear mixed models with genetic effects in the residual variance part of the model can be used. Such models have previously been fitted using EM and MCMC algorithms. Results: We propose the use of double hierarchical generalized linear models (DHGLM), where the squared residuals are assumed to be gamma distributed and the residual variance is fitted using a generalized linear model. The algorithm iterates between two sets of mixed model equations, one on the level of observations and one on the level of variances. The method was validated using simulations and also by re-analyzing a data set on pig litter size that was previously analyzed using a Bayesian approach. The pig litter size data contained 10,060 records from 4,149 sows. The DHGLM was implemented using the ASReml software and the algorithm converged within three minutes on a Linux server. The estimates were similar to those previously obtained using Bayesian methodology, especially the variance components in the residual variance part of the model. Conclusions: We have shown that variance components in the residual variance part of a linear mixed model can be estimated using a DHGLM approach. The method enables analyses of animal models with large numbers of observations. An important future development of the DHGLM methodology is to include the genetic correlation between the random effects in the mean and residual variance parts of the model as a parameter of the DHGLM.

A Gradient-Type Method For Real-Time State Estimation Of Water Distribution Networks

Drinking water distribution networks risk exposure to malicious or accidental contamination. Several levels of responses are conceivable. One of them consists to install a sensor network to monitor the system on real time. Once a contamination has been detected, this is also important to take appropriate counter-measures. In the SMaRT-OnlineWDN project, this relies on modeling to predict both hydraulics and water quality. An online model use makes identification of the contaminant source and simulation of the contaminated area possible. The objective of this paper is to present SMaRT-OnlineWDN experience and research results for hydraulic state estimation with sampling frequency of few minutes. A least squares problem with bound constraints is formulated to adjust demand class coefficient to best fit the observed values at a given time. The criterion is a Huber function to limit the influence of outliers. A Tikhonov regularization is introduced for consideration of prior information on the parameter vector. Then the Levenberg-Marquardt algorithm is applied that use derivative information for limiting the number of iterations. Confidence intervals for the state prediction are also given. The results are presented and discussed on real networks in France and Germany.

Estimation of DSGE Models: A Monte Carlo Analysis

Neste trabalho investigamos as propriedades em pequena amostra e a robustez das estimativas dos parâmetros de modelos DSGE. Tomamos o modelo de Smets and Wouters (2007) como base e avaliamos a performance de dois procedimentos de estimação: Método dos Momentos Simulados (MMS) e Máxima Verossimilhança (MV). Examinamos a distribuição empírica das estimativas dos parâmetros e sua implicação para as análises de impulso-resposta e decomposição de variância nos casos de especificação correta e má especificação. Nossos resultados apontam para um desempenho ruim de MMS e alguns padrões de viés nas análises de impulso-resposta e decomposição de variância com estimativas de MV nos casos de má especificação considerados.

Influence of data structure on the estimation of the additive genetic direct and maternal covariance for early growth traits in Nellore cattle

The objective of the present study was to investigate the effect of data structure on estimated genetic parameters and predicted breeding values of direct and maternal genetic effects for weaning weight (WW) and weight gain from birth to weaning (BWG), including or not the genetic covariance between direct and maternal effects. Records of 97,490 Nellore animals born between 1993 and 2006, from the Jacarezinho cattle raising farm, were used. Two different data sets were analyzed: DI_all, which included all available progenies of dams without their own performance; DII_all, which included DI_all + 20% of recorded progenies with maternal phenotypes. Two subsets were obtained from each data set (DI_all and DII_all): DI_1 and DII_1, which included only dams with three or fewer progenies; DI_5 and DII_5, which included only dams with five or more progenies. (Co)variance components and heritabilities were estimated by Bayesian inference through Gibbs sampling using univariate animal models. In general, for the population and traits studied, the proportion of dams with known phenotypic information and the number of progenies per dam influenced direct and maternal heritabilities, as well as the contribution of maternal permanent environmental variance to phenotypic variance. Only small differences were observed in the genetic and environmental parameters when the genetic covariance between direct and maternal effects was set to zero in the data sets studied. Thus, the inclusion or not of the genetic covariance between direct and maternal effects had little effect on the ranking of animals according to their breeding values for WW and BWG. Accurate estimation of genetic correlations between direct and maternal genetic effects depends on the data structure. Thus, this covariance should be set to zero in Nellore data sets in which the proportion of dams with phenotypic information is low, the number of progenies per dam is small, and pedigree relationships are poorly known. (c) 2012 Elsevier B.V. All rights reserved.

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)