A note on model uncertainty in linear regression

We consider model selection uncertainty in linear regression. We study theoretically and by simulation the approach of Buckland and co-workers, who proposed estimating a parameter common to all models under study by taking a weighted average over the models, using weights obtained from information criteria or the bootstrap. This approach is compared with the usual approach in which the 'best' model is used, and with Bayesian model averaging. The weighted predictor behaves similarly to model averaging, with generally more realistic mean-squared errors than the usual model-selection-based estimator.

Prediction of genomic-enabled breeding values and genome-wide association study for feedlot average daily weight gain in Nelore cattle

Pós-graduação em Genética e Melhoramento Animal - FCAV

Improving IRT parameter estimates with small sample sizes: Evaluating the efficacy of a new data augmentation technique

The 3PL model is a flexible and widely used tool in assessment. However, it suffers from limitations due to its need for large sample sizes. This study introduces and evaluates the efficacy of a new sample size augmentation technique called Duplicate, Erase, and Replace (DupER) Augmentation through a simulation study. Data are augmented using several variations of DupER Augmentation (based on different imputation methodologies, deletion rates, and duplication rates), analyzed in BILOG-MG 3, and results are compared to those obtained from analyzing the raw data. Additional manipulated variables include test length and sample size. Estimates are compared using seven different evaluative criteria. Results are mixed and inconclusive. DupER augmented data tend to result in larger root mean squared errors (RMSEs) and lower correlations between estimates and parameters for both item and ability parameters. However, some DupER variations produce estimates that are much less biased than those obtained from the raw data alone. For one DupER variation, it was found that DupER produced better results for low-ability simulees and worse results for those with high abilities. Findings, limitations, and recommendations for future studies are discussed. Specific recommendations for future studies include the application of Duper Augmentation (1) to empirical data, (2) with additional IRT models, and (3) the analysis of the efficacy of the procedure for different item and ability parameter distributions.

Evaluating atmospheric methane inversion model results for Pallas, northern Finland

A state-of-the-art inverse model, CarbonTracker Data Assimilation Shell (CTDAS), was used to optimize estimates of methane (CH4) surface fluxes using atmospheric observations of CH4 as a constraint. The model consists of the latest version of the TM5 atmospheric chemistry-transport model and an ensemble Kalman filter based data assimilation system. The model was constrained by atmospheric methane surface concentrations, obtained from the World Data Centre for Greenhouse Gases (WDCGG). Prior methane emissions were specified for five sources: biosphere, anthropogenic, fire, termites and ocean, of which bio-sphere and anthropogenic emissions were optimized. Atmospheric CH 4 mole fractions for 2007 from northern Finland calculated from prior and optimized emissions were compared with observations. It was found that the root mean squared errors of the posterior esti - mates were more than halved. Furthermore, inclusion of NOAA observations of CH 4 from weekly discrete air samples collected at Pallas improved agreement between posterior CH 4 mole fraction estimates and continuous observations, and resulted in reducing optimized biosphere emissions and their uncertainties in northern Finland.

Selection bias and the cross-validation of regression models for prediction

Strategies are compared for the development of a linear regression model with stochastic (multivariate normal) regressor variables and the subsequent assessment of its predictive ability. Bias and mean squared error of four estimators of predictive performance are evaluated in simulated samples of 32 population correlation matrices. Models including all of the available predictors are compared with those obtained using selected subsets. The subset selection procedures investigated include two stopping rules, C$\sb{\rm p}$ and S$\sb{\rm p}$, each combined with an 'all possible subsets' or 'forward selection' of variables. The estimators of performance utilized include parametric (MSEP$\sb{\rm m}$) and non-parametric (PRESS) assessments in the entire sample, and two data splitting estimates restricted to a random or balanced (Snee's DUPLEX) 'validation' half sample. The simulations were performed as a designed experiment, with population correlation matrices representing a broad range of data structures.^ The techniques examined for subset selection do not generally result in improved predictions relative to the full model. Approaches using 'forward selection' result in slightly smaller prediction errors and less biased estimators of predictive accuracy than 'all possible subsets' approaches but no differences are detected between the performances of C$\sb{\rm p}$ and S$\sb{\rm p}$. In every case, prediction errors of models obtained by subset selection in either of the half splits exceed those obtained using all predictors and the entire sample.^ Only the random split estimator is conditionally (on $\\beta$) unbiased, however MSEP$\sb{\rm m}$ is unbiased on average and PRESS is nearly so in unselected (fixed form) models. When subset selection techniques are used, MSEP$\sb{\rm m}$ and PRESS always underestimate prediction errors, by as much as 27 percent (on average) in small samples. Despite their bias, the mean squared errors (MSE) of these estimators are at least 30 percent less than that of the unbiased random split estimator. The DUPLEX split estimator suffers from large MSE as well as bias, and seems of little value within the context of stochastic regressor variables.^ To maximize predictive accuracy while retaining a reliable estimate of that accuracy, it is recommended that the entire sample be used for model development, and a leave-one-out statistic (e.g. PRESS) be used for assessment. ^

A static traffic assignment model combined with an artificial neural network delay model

As traffic congestion continues to worsen in large urban areas, solutions are urgently sought. However, transportation planning models, which estimate traffic volumes on transportation network links, are often unable to realistically consider travel time delays at intersections. Introducing signal controls in models often result in significant and unstable changes in network attributes, which, in turn, leads to instability of models. Ignoring the effect of delays at intersections makes the model output inaccurate and unable to predict travel time. To represent traffic conditions in a network more accurately, planning models should be capable of arriving at a network solution based on travel costs that are consistent with the intersection delays due to signal controls. This research attempts to achieve this goal by optimizing signal controls and estimating intersection delays accordingly, which are then used in traffic assignment. Simultaneous optimization of traffic routing and signal controls has not been accomplished in real-world applications of traffic assignment. To this end, a delay model dealing with five major types of intersections has been developed using artificial neural networks (ANNs). An ANN architecture consists of interconnecting artificial neurons. The architecture may either be used to gain an understanding of biological neural networks, or for solving artificial intelligence problems without necessarily creating a model of a real biological system. The ANN delay model has been trained using extensive simulations based on TRANSYT-7F signal optimizations. The delay estimates by the ANN delay model have percentage root-mean-squared errors (%RMSE) that are less than 25.6%, which is satisfactory for planning purposes. Larger prediction errors are typically associated with severely oversaturated conditions. A combined system has also been developed that includes the artificial neural network (ANN) delay estimating model and a user-equilibrium (UE) traffic assignment model. The combined system employs the Frank-Wolfe method to achieve a convergent solution. Because the ANN delay model provides no derivatives of the delay function, a Mesh Adaptive Direct Search (MADS) method is applied to assist in and expedite the iterative process of the Frank-Wolfe method. The performance of the combined system confirms that the convergence of the solution is achieved, although the global optimum may not be guaranteed.

A Static Traffic Assignment Model Combined with an Artificial Neural Network Delay Model

As traffic congestion continues to worsen in large urban areas, solutions are urgently sought. However, transportation planning models, which estimate traffic volumes on transportation network links, are often unable to realistically consider travel time delays at intersections. Introducing signal controls in models often result in significant and unstable changes in network attributes, which, in turn, leads to instability of models. Ignoring the effect of delays at intersections makes the model output inaccurate and unable to predict travel time. To represent traffic conditions in a network more accurately, planning models should be capable of arriving at a network solution based on travel costs that are consistent with the intersection delays due to signal controls. This research attempts to achieve this goal by optimizing signal controls and estimating intersection delays accordingly, which are then used in traffic assignment. Simultaneous optimization of traffic routing and signal controls has not been accomplished in real-world applications of traffic assignment. To this end, a delay model dealing with five major types of intersections has been developed using artificial neural networks (ANNs). An ANN architecture consists of interconnecting artificial neurons. The architecture may either be used to gain an understanding of biological neural networks, or for solving artificial intelligence problems without necessarily creating a model of a real biological system. The ANN delay model has been trained using extensive simulations based on TRANSYT-7F signal optimizations. The delay estimates by the ANN delay model have percentage root-mean-squared errors (%RMSE) that are less than 25.6%, which is satisfactory for planning purposes. Larger prediction errors are typically associated with severely oversaturated conditions. A combined system has also been developed that includes the artificial neural network (ANN) delay estimating model and a user-equilibrium (UE) traffic assignment model. The combined system employs the Frank-Wolfe method to achieve a convergent solution. Because the ANN delay model provides no derivatives of the delay function, a Mesh Adaptive Direct Search (MADS) method is applied to assist in and expedite the iterative process of the Frank-Wolfe method. The performance of the combined system confirms that the convergence of the solution is achieved, although the global optimum may not be guaranteed.

Essays on Microeconometrics

My dissertation has three chapters which develop and apply microeconometric tech- niques to empirically relevant problems. All the chapters examines the robustness issues (e.g., measurement error and model misspecification) in the econometric anal- ysis. The first chapter studies the identifying power of an instrumental variable in the nonparametric heterogeneous treatment effect framework when a binary treat- ment variable is mismeasured and endogenous. I characterize the sharp identified set for the local average treatment effect under the following two assumptions: (1) the exclusion restriction of an instrument and (2) deterministic monotonicity of the true treatment variable in the instrument. The identification strategy allows for general measurement error. Notably, (i) the measurement error is nonclassical, (ii) it can be endogenous, and (iii) no assumptions are imposed on the marginal distribution of the measurement error, so that I do not need to assume the accuracy of the measure- ment. Based on the partial identification result, I provide a consistent confidence interval for the local average treatment effect with uniformly valid size control. I also show that the identification strategy can incorporate repeated measurements to narrow the identified set, even if the repeated measurements themselves are endoge- nous. Using the the National Longitudinal Study of the High School Class of 1972, I demonstrate that my new methodology can produce nontrivial bounds for the return to college attendance when attendance is mismeasured and endogenous.

The second chapter, which is a part of a coauthored project with Federico Bugni, considers the problem of inference in dynamic discrete choice problems when the structural model is locally misspecified. We consider two popular classes of estimators for dynamic discrete choice models: K-step maximum likelihood estimators (K-ML) and K-step minimum distance estimators (K-MD), where K denotes the number of policy iterations employed in the estimation problem. These estimator classes include popular estimators such as Rust (1987)’s nested fixed point estimator, Hotz and Miller (1993)’s conditional choice probability estimator, Aguirregabiria and Mira (2002)’s nested algorithm estimator, and Pesendorfer and Schmidt-Dengler (2008)’s least squares estimator. We derive and compare the asymptotic distributions of K- ML and K-MD estimators when the model is arbitrarily locally misspecified and we obtain three main results. In the absence of misspecification, Aguirregabiria and Mira (2002) show that all K-ML estimators are asymptotically equivalent regardless of the choice of K. Our first result shows that this finding extends to a locally misspecified model, regardless of the degree of local misspecification. As a second result, we show that an analogous result holds for all K-MD estimators, i.e., all K- MD estimator are asymptotically equivalent regardless of the choice of K. Our third and final result is to compare K-MD and K-ML estimators in terms of asymptotic mean squared error. Under local misspecification, the optimally weighted K-MD estimator depends on the unknown asymptotic bias and is no longer feasible. In turn, feasible K-MD estimators could have an asymptotic mean squared error that is higher or lower than that of the K-ML estimators. To demonstrate the relevance of our asymptotic analysis, we illustrate our findings using in a simulation exercise based on a misspecified version of Rust (1987) bus engine problem.

The last chapter investigates the causal effect of the Omnibus Budget Reconcil- iation Act of 1993, which caused the biggest change to the EITC in its history, on unemployment and labor force participation among single mothers. Unemployment and labor force participation are difficult to define for a few reasons, for example, be- cause of marginally attached workers. Instead of searching for the unique definition for each of these two concepts, this chapter bounds unemployment and labor force participation by observable variables and, as a result, considers various competing definitions of these two concepts simultaneously. This bounding strategy leads to partial identification of the treatment effect. The inference results depend on the construction of the bounds, but they imply positive effect on labor force participa- tion and negligible effect on unemployment. The results imply that the difference- in-difference result based on the BLS definition of unemployment can be misleading

due to misclassification of unemployment.

Inférence robuste à la présence des valeurs aberrantes dans les enquêtes

Cette thèse comporte trois articles dont un est publié et deux en préparation. Le sujet central de la thèse porte sur le traitement des valeurs aberrantes représentatives dans deux aspects importants des enquêtes que sont : l’estimation des petits domaines et l’imputation en présence de non-réponse partielle. En ce qui concerne les petits domaines, les estimateurs robustes dans le cadre des modèles au niveau des unités ont été étudiés. Sinha & Rao (2009) proposent une version robuste du meilleur prédicteur linéaire sans biais empirique pour la moyenne des petits domaines. Leur estimateur robuste est de type «plugin», et à la lumière des travaux de Chambers (1986), cet estimateur peut être biaisé dans certaines situations. Chambers et al. (2014) proposent un estimateur corrigé du biais. En outre, un estimateur de l’erreur quadratique moyenne a été associé à ces estimateurs ponctuels. Sinha & Rao (2009) proposent une procédure bootstrap paramétrique pour estimer l’erreur quadratique moyenne. Des méthodes analytiques sont proposées dans Chambers et al. (2014). Cependant, leur validité théorique n’a pas été établie et leurs performances empiriques ne sont pas pleinement satisfaisantes. Ici, nous examinons deux nouvelles approches pour obtenir une version robuste du meilleur prédicteur linéaire sans biais empirique : la première est fondée sur les travaux de Chambers (1986), et la deuxième est basée sur le concept de biais conditionnel comme mesure de l’influence d’une unité de la population. Ces deux classes d’estimateurs robustes des petits domaines incluent également un terme de correction pour le biais. Cependant, ils utilisent tous les deux l’information disponible dans tous les domaines contrairement à celui de Chambers et al. (2014) qui utilise uniquement l’information disponible dans le domaine d’intérêt. Dans certaines situations, un biais non négligeable est possible pour l’estimateur de Sinha & Rao (2009), alors que les estimateurs proposés exhibent un faible biais pour un choix approprié de la fonction d’influence et de la constante de robustesse. Les simulations Monte Carlo sont effectuées, et les comparaisons sont faites entre les estimateurs proposés et ceux de Sinha & Rao (2009) et de Chambers et al. (2014). Les résultats montrent que les estimateurs de Sinha & Rao (2009) et de Chambers et al. (2014) peuvent avoir un biais important, alors que les estimateurs proposés ont une meilleure performance en termes de biais et d’erreur quadratique moyenne. En outre, nous proposons une nouvelle procédure bootstrap pour l’estimation de l’erreur quadratique moyenne des estimateurs robustes des petits domaines. Contrairement aux procédures existantes, nous montrons formellement la validité asymptotique de la méthode bootstrap proposée. Par ailleurs, la méthode proposée est semi-paramétrique, c’est-à-dire, elle n’est pas assujettie à une hypothèse sur les distributions des erreurs ou des effets aléatoires. Ainsi, elle est particulièrement attrayante et plus largement applicable. Nous examinons les performances de notre procédure bootstrap avec les simulations Monte Carlo. Les résultats montrent que notre procédure performe bien et surtout performe mieux que tous les compétiteurs étudiés. Une application de la méthode proposée est illustrée en analysant les données réelles contenant des valeurs aberrantes de Battese, Harter & Fuller (1988). S’agissant de l’imputation en présence de non-réponse partielle, certaines formes d’imputation simple ont été étudiées. L’imputation par la régression déterministe entre les classes, qui inclut l’imputation par le ratio et l’imputation par la moyenne sont souvent utilisées dans les enquêtes. Ces méthodes d’imputation peuvent conduire à des estimateurs imputés biaisés si le modèle d’imputation ou le modèle de non-réponse n’est pas correctement spécifié. Des estimateurs doublement robustes ont été développés dans les années récentes. Ces estimateurs sont sans biais si l’un au moins des modèles d’imputation ou de non-réponse est bien spécifié. Cependant, en présence des valeurs aberrantes, les estimateurs imputés doublement robustes peuvent être très instables. En utilisant le concept de biais conditionnel, nous proposons une version robuste aux valeurs aberrantes de l’estimateur doublement robuste. Les résultats des études par simulations montrent que l’estimateur proposé performe bien pour un choix approprié de la constante de robustesse.

Inference for nonparametric high-frequency estimators with an application to time variation in betas

We consider the problem of conducting inference on nonparametric high-frequency estimators without knowing their asymptotic variances. We prove that a multivariate subsampling method achieves this goal under general conditions that were not previously available in the literature. We suggest a procedure for a data-driven choice of the bandwidth parameters. Our simulation study indicates that the subsampling method is much more robust than the plug-in method based on the asymptotic expression for the variance. Importantly, the subsampling method reliably estimates the variability of the Two Scale estimator even when its parameters are chosen to minimize the finite sample Mean Squared Error; in contrast, the plugin estimator substantially underestimates the sampling uncertainty. By construction, the subsampling method delivers estimates of the variance-covariance matrices that are always positive semi-definite. We use the subsampling method to study the dynamics of financial betas of six stocks on the NYSE. We document significant variation in betas within year 2006, and find that tick data captures more variation in betas than the data sampled at moderate frequencies such as every five or twenty minutes. To capture this variation we estimate a simple dynamic model for betas. The variance estimation is also important for the correction of the errors-in-variables bias in such models. We find that the bias corrections are substantial, and that betas are more persistent than the naive estimators would lead one to believe.

Prediction with measurement errors in finite populations

We address the problem of selecting the best linear unbiased predictor (BLUP) of the latent value (e.g., serum glucose fasting level) of sample subjects with heteroskedastic measurement errors. Using a simple example, we compare the usual mixed model BLUP to a similar predictor based on a mixed model framed in a finite population (FPMM) setup with two sources of variability, the first of which corresponds to simple random sampling and the second, to heteroskedastic measurement errors. Under this last approach, we show that when measurement errors are subject-specific, the BLUP shrinkage constants are based on a pooled measurement error variance as opposed to the individual ones generally considered for the usual mixed model BLUP. In contrast, when the heteroskedastic measurement errors are measurement condition-specific, the FPMM BLUP involves different shrinkage constants. We also show that in this setup, when measurement errors are subject-specific, the usual mixed model predictor is biased but has a smaller mean squared error than the FPMM BLUP which points to some difficulties in the interpretation of such predictors. (C) 2011 Elsevier By. All rights reserved.

Distributed power control algorithm for multiple access systems based on Verhulst model

In this paper the continuous Verhulst dynamic model is used to synthesize a new distributed power control algorithm (DPCA) for use in direct sequence code division multiple access (DS-CDMA) systems. The Verhulst model was initially designed to describe the population growth of biological species under food and physical space restrictions. The discretization of the corresponding differential equation is accomplished via the Euler numeric integration (ENI) method. Analytical convergence conditions for the proposed DPCA are also established. Several properties of the proposed recursive algorithm, such as Euclidean distance from optimum vector after convergence, convergence speed, normalized mean squared error (NSE), average power consumption per user, performance under dynamics channels, and implementation complexity aspects, are analyzed through simulations. The simulation results are compared with two other DPCAs: the classic algorithm derived by Foschini and Miljanic and the sigmoidal of Uykan and Koivo. Under estimated errors conditions, the proposed DPCA exhibits smaller discrepancy from the optimum power vector solution and better convergence (under fixed and adaptive convergence factor) than the classic and sigmoidal DPCAs. (C) 2010 Elsevier GmbH. All rights reserved.

Método de desagregação temporal para a previsão da taxa de desemprego em Portugal

Dissertação de mestrado em Estatística

Robust response transformations based on optimal prediction

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

A priori parameterisation of the CERES soil-crop models and tests against several European data sets

Mechanistic soil-crop models have become indispensable tools to investigate the effect of management practices on the productivity or environmental impacts of arable crops. Ideally these models may claim to be universally applicable because they simulate the major processes governing the fate of inputs such as fertiliser nitrogen or pesticides. However, because they deal with complex systems and uncertain phenomena, site-specific calibration is usually a prerequisite to ensure their predictions are realistic. This statement implies that some experimental knowledge on the system to be simulated should be available prior to any modelling attempt, and raises a tremendous limitation to practical applications of models. Because the demand for more general simulation results is high, modellers have nevertheless taken the bold step of extrapolating a model tested within a limited sample of real conditions to a much larger domain. While methodological questions are often disregarded in this extrapolation process, they are specifically addressed in this paper, and in particular the issue of models a priori parameterisation. We thus implemented and tested a standard procedure to parameterize the soil components of a modified version of the CERES models. The procedure converts routinely-available soil properties into functional characteristics by means of pedo-transfer functions. The resulting predictions of soil water and nitrogen dynamics, as well as crop biomass, nitrogen content and leaf area index were compared to observations from trials conducted in five locations across Europe (southern Italy, northern Spain, northern France and northern Germany). In three cases, the model’s performance was judged acceptable when compared to experimental errors on the measurements, based on a test of the model’s root mean squared error (RMSE). Significant deviations between observations and model outputs were however noted in all sites, and could be ascribed to various model routines. In decreasing importance, these were: water balance, the turnover of soil organic matter, and crop N uptake. A better match to field observations could therefore be achieved by visually adjusting related parameters, such as field-capacity water content or the size of soil microbial biomass. As a result, model predictions fell within the measurement errors in all sites for most variables, and the model’s RMSE was within the range of published values for similar tests. We conclude that the proposed a priori method yields acceptable simulations with only a 50% probability, a figure which may be greatly increased through a posteriori calibration. Modellers should thus exercise caution when extrapolating their models to a large sample of pedo-climatic conditions for which they have only limited information.