Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

Structured additive regression models are perhaps the most commonly used class of models in statistical applications. It includes, among others, (generalized) linear models, (generalized) additive models, smoothing spline models, state space models, semiparametric regression, spatial and spatiotemporal models, log-Gaussian Cox processes and geostatistical and geoadditive models. We consider approximate Bayesian inference in a popular subset of structured additive regression models, latent Gaussian models, where the latent field is Gaussian, controlled by a few hyperparameters and with non-Gaussian response variables. The posterior marginals are not available in closed form owing to the non-Gaussian response variables. For such models, Markov chain Monte Carlo methods can be implemented, but they are not without problems, in terms of both convergence and computational time. In some practical applications, the extent of these problems is such that Markov chain Monte Carlo sampling is simply not an appropriate tool for routine analysis. We show that, by using an integrated nested Laplace approximation and its simplified version, we can directly compute very accurate approximations to the posterior marginals. The main benefit of these approximations is computational: where Markov chain Monte Carlo algorithms need hours or days to run, our approximations provide more precise estimates in seconds or minutes. Another advantage with our approach is its generality, which makes it possible to perform Bayesian analysis in an automatic, streamlined way, and to compute model comparison criteria and various predictive measures so that models can be compared and the model under study can be challenged.

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Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations

Statistical Analysis with Missing Data

Foreword Stephen P. Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng Introduction to MCMC, Charles J. Geyer A short history of Markov chain Monte Carlo: Subjective recollections from in-complete data, Christian Robert and George Casella Reversible jump Markov chain Monte Carlo, Yanan Fan and Scott A. Sisson Optimal proposal distributions and adaptive MCMC, Jeffrey S. Rosenthal MCMC using Hamiltonian dynamics, Radford M. Neal Inference and Monitoring Convergence, Andrew Gelman and Kenneth Shirley Implementing MCMC: Estimating with confidence, James M. Flegal and Galin L. Jones Perfection within reach: Exact MCMC sampling, Radu V. Craiu and Xiao-Li Meng Spatial point processes, Mark Huber The data augmentation algorithm: Theory and methodology, James P. Hobert Importance sampling, simulated tempering and umbrella sampling, Charles J.Geyer Likelihood-free Markov chain Monte Carlo, Scott A. Sisson and Yanan Fan MCMC in the analysis of genetic data on related individuals, Elizabeth Thompson A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data, Brian Caffo, DuBois Bowman, Lynn Eberly, and Susan Spear Bassett Partially collapsed Gibbs sampling & path-adaptive Metropolis-Hastings in high-energy astrophysics, David van Dyk and Taeyoung Park Posterior exploration for computationally intensive forward models, Dave Higdon, C. Shane Reese, J. David Moulton, Jasper A. Vrugt and Colin Fox Statistical ecology, Ruth King Gaussian random field models for spatial data, Murali Haran Modeling preference changes via a hidden Markov item response theory model, Jong Hee Park Parallel Bayesian MCMC imputation for multiple distributed lag models: A case study in environmental epidemiology, Brian Caffo, Roger Peng, Francesca Dominici, Thomas A. Louis, and Scott Zeger MCMC for state space models, Paul Fearnhead MCMC in educational research, Roy Levy, Robert J. Mislevy, and John T. Behrens Applications of MCMC in fisheries science, Russell B. Millar Model comparison and simulation for hierarchical models: analyzing rural-urban migration in Thailand, Filiz Garip and Bruce Western

Handbook of Markov Chain Monte Carlo

A detailed review of the education sector in Australia as in the data provided by the 2006 edition of the OECD's annual publication, 'Education at a Glance' is presented. While the data has shown that in almost all OECD countries educational attainment levels are on the rise, with countries showing impressive gains in university qualifications, it also reveals that a large of share of young people still do not complete secondary school, which remains a baseline for successful entry into the labour market.

/pdf/education-at-a-glance-m5vl7o68j5.pdf

Education at a Glance

Maximum likelihood estimation of models based on continuous latent variables generally requires to solve integrals that are not analytically tractable. Numerical approximations represent a possible solution to this problem. We propose to use the adaptive Gaussian---Hermite (AGH) numerical quadrature approximation for a particular class of continuous latent variable models for time-series and longitudinal data. These dynamic models are based on time-varying latent variables that follow an autoregressive process of order 1, AR(1). Two examples are the stochastic volatility models for the analysis of financial time series and the limited dependent variable models for the analysis of panel data. A comparison between the performance of AGH methods and alternative approximation methods proposed in the literature is carried out by simulation. Empirical examples are also used to illustrate the proposed approach.

Adaptive Quadrature for Maximum Likelihood Estimation of a Class of Dynamic Latent Variable Models

SUMMARY Following Cox & Wermuth (1994, 2002), we show that the distribution of a set of binary observable variables, induced by a certain discrete latent variable model, may be approximated by a quadratic exponential distribution. This discrete latent variable model is equivalent to the latent-class version of the two-parameter logistic model of Birnbaum (1968), which may be seen as a generalized version of the Rasch model (Rasch, 1960, 1961). On the basis of this result, we develop an approximate maximum likelihood estimator of the item parameters of the two-parameter logistic model which is very simply implemented. The proposed approach is illustrated through an example based on a dataset on educational assessment.

https://www.jstor.org/stable/pdfplus/20441409.pdf

On the approximation of the quadratic exponential distribution in a latent variable context

I discuss how, given a certain number of articles and citations of these articles, the h-index and the g-index are affected by the level of concentration of the citations. This offers the opportunity for a comparison between these 2 indices from a new perspective.

A comparison between the g-index and the h-index based on concentration

An exact algorithm for time-dependent variational inference for the dynamic stochastic block model

An important and yet difficult problem in fitting multivariate mixture models is determining the mixture complexity. We develop theory and a unified framework for finding the nonparametric maximum likelihood estimator of a multivariate mixing distribution and consequently estimating the mixture complexity. Multivariate mixtures provide a flexible approach to fitting high-dimensional data while offering data reduction through the number, location and shape of the component densities. The central principle of our method is to cast the mixture maximization problem in the concave optimization framework with finitely many linear inequality constraints and turn it into an unconstrained problem using a "penalty function". We establish the existence of parameter estimators and prove the convergence properties of the proposed algorithms. The role of a "sieve parameter'' in reducing the dimensionality of mixture models is demonstrated. We derive analytical machinery for building a collection of semiparametric mixture models, including the multivariate case, via the sieve parameter. The performance of the methods are shown with applications to several data sets including the cdc15 cell-cycle yeast microarray data.

Francesco Bartolucci

Papers

Adaptive Quadrature for Maximum Likelihood Estimation of a Class of Dynamic Latent Variable Models

On the approximation of the quadratic exponential distribution in a latent variable context

A comparison between the g-index and the h-index based on concentration

An exact algorithm for time-dependent variational inference for the dynamic stochastic block model

Model Building for Semiparametric Mixtures