Particle filtering for partially observed Gaussian state space models

Summary. Solving Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data has many applications for dynamic models. A large number of algorithms based on particle filtering methods, also known as sequential Monte Carlo algorithms, have recently been proposed to solve these problems. We propose a special particle filtering method which uses random mixtures of normal distributions to represent the posterior distributions of partially observed Gaussian state space models. This algorithm is based on a marginalization idea for improving efficiency and can lead to substantial gains over standard algorithms. It differs from previous algorithms which were only applicable to conditionally linear Gaussian state space models. Computer simulations are carried out to evaluate the performance of the proposed algorithm for dynamic tobit and probit models.     

Wavelet Estimation of a Density in a GARCH-type Model

We consider the GARCH-type model: S = σ² Z, where σ² and Z are independent random variables. The density of σ² is unknown whereas the one of Z is known. We want to estimate the density of σ² from n observations of S under some dependence assumption (the exponentially strongly mixing dependence). Adopting the wavelet methodology, we construct a nonadaptive estimator based on projections and an adaptive estimator based on the hard thresholding rule. Taking the mean integrated squared error over Besov balls, we prove that the adaptive one attains a sharp rate of convergence.     

On the estimation of female births missing due to prenatal sex selection

This research note is prompted by a paper by Kashyap (Is prenatal sex selection associated with lower female child mortality? Population Studies 73(1): 57–78). Kashyap’s paper, which provides 40 original estimates of missing female births, relies on an alternative definition of missing female births, leading to estimates of about half the magnitude of other estimates. There appears, therefore, a real need to take stock of the concept of missing female births widely used by statisticians around the world for assessing the demographic consequences of prenatal sex selection. This research note starts with a brief review of the history of the concept and the difference between Amartya Sen’s original method and the alternative method found elsewhere to compute missing female births. We then put forward three different arguments (deterministic and probabilistic approaches, and consistency analysis) in support of the original computation procedure based on the number of observed male births and the expected sex ratio at birth.     

The Valuation of Non-Monetary Consumption in Household Surveys

Many social indicators are based on household consumption information. The valuation of non-monetary operations is crucial for the analysis of consumption surveys in developing countries because of the importance of own-consumption and transfers in kind. What are the price statistics used in the valuation of consumption indicators? How is the available price information exploited to produce consumption indicators? How can the different steps of the valuation process be analysed? We explore these questions by presenting the valuation method for the consumption used in rural Rwanda for the 1983 consumption survey, and by proposing a general model of valuation algorithm. This is useful not only for improving such algorithms, but also for assessing the impact of the valuation process on economic analyses.     

Directors’ human capital,firm strategy,and firm performance

Ideally, corporations are directed by boards whose directors provide valuable human capital that match the firms’ strategy. We investigate how directors’ human capital (international experience, industrial know-how, CEO experience, and financial know-how) affects firm performance including the firm’s strategy (diversification and internationalization) and how human capital is related to acquisition strategies (non-diversifying and international acquisitions). Our sample consists of 560 firm-year observations in Switzerland. We find empirical evidence that directors’ human capital affects firm performance and that this relationship depends on the firm’s strategy. Furthermore, human capital is also correlated with acquisition strategy. The study shows that focusing on board independence and compliance issues may be unrewarding in board research and practice.     

Beyond support in two-stage variable selection

Numerous variable selection methods rely on a two-stage procedure, where a sparsity-inducing penalty is used in the first stage to predict the support, which is then conveyed to the second stage for estimation or inference purposes. In this framework, the first stage screens variables to find a set of possibly relevant variables and the second stage operates on this set of candidate variables, to improve estimation accuracy or to assess the uncertainty associated to the selection of variables. We advocate that more information can be conveyed from the first stage to the second one: we use the magnitude of the coefficients estimated in the first stage to define an adaptive penalty that is applied at the second stage. We give the example of an inference procedure that highly benefits from the proposed transfer of information. The procedure is precisely analyzed in a simple setting, and our large-scale experiments empirically demonstrate that actual benefits can be expected in much more general situations, with sensitivity gains ranging from 50 to 100 % compared to state-of-the-art.     

Model-based clustering of Gaussian copulas for mixed data

Clustering of mixed data is important yet challenging due to a shortage of conventional distributions for such data. In this article, we propose a mixture model of Gaussian copulas for clustering mixed data. Indeed copulas, and Gaussian copulas in particular, are powerful tools for easily modeling the distribution of multivariate variables. This model clusters data sets with continuous, integer, and ordinal variables (all having a cumulative distribution function) by considering the intra-component dependencies in a similar way to the Gaussian mixture. Indeed, each component of the Gaussian copula mixture produces a correlation coefficient for each pair of variables and its univariate margins follow standard distributions (Gaussian, Poisson, and ordered multinomial) depending on the nature of the variable (continuous, integer, or ordinal). As an interesting by-product, this model generalizes many well-known approaches and provides tools for visualization based on its parameters. The Bayesian inference is achieved with a Metropolis-within-Gibbs sampler. The numerical experiments, on simulated and real data, illustrate the benefits of the proposed model: flexible and meaningful parameterization combined with visualization features.