Association of Under-Approximation Techniques for Generating Tests from Models

International audienceIn this paper we present a Model-Based Testing approach with which we generate tests from an abstraction of a source behavioural model. We show a new algorithm that computes the abstraction as an under-approximation of the source model. Our first contribution is to combine two previous approaches proposed by Ball and Pasareanu et al. to compute May, Must+ and Must- abstract transition relations. Prooftechniques are used to compute these transition relations. The tests obtained by covering the abstract transitions have to be instantiated from the source model. So, following Pasareanu et al., our algorithm additionally computes a concrete transition relation: the tests obtained as sequences of concrete transitions need not be instantiated from the source model. Another contribution is to propose a choice of relevant paramaters and heuristics to pilot the tests computation. We experiment our approach and compare it with a previous approach of ours to compute tests from an abstraction that over-approximates the source model

Specification Tests of Parametric Dynamic Conditional Quantiles

This article proposes omnibus specification tests of parametric dynamic quantile regression models. Contrary to the existing procedures, we allow for a flexible and general specification framework where a possibly continuum of quantiles are simultaneously specified. This is the case for many econometric applications for both time series and cross section data which require a global diagnostic tool. We study the asymptotic distribution of the test statistics under fairly weak conditions on the serial dependence in the underlying data generating process. It turns out that the asymptotic null distribution depends on the data generating process and the hypothesized model. We propose a subsampling procedure for approximating the asymptotic critical values of the tests. An appealing property of the proposed tests is that they do not require estimation of the non-parametric (conditional) sparsity function. A Monte Carlo study compares the proposed tests and shows that the asymptotic results provide good approximations for small sample sizes. Finally, an application to some European stock indexes provides evidence that our methodology is a powerful and flexible alternative to standard backtesting procedures in evaluating market risk by using information from a range of quantiles in the lower tail of returns.

Estimation of latent variable models for ordinal data via fully exponential Laplace approximation

Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function can arise since analytical solutions do not exist. Numerical approximations, like the widely used Gauss Hermite (GH) quadrature, are generally applied to solve these problems. However, GH becomes unfeasible as the number of latent variables increases. Thus, alternative solutions have to be found. In this paper, we propose an extended version of the Laplace method for approximating the integrals, known as fully exponential Laplace approximation. It is computational feasible also in presence of many latent variables, and it is more accurate than the classical Laplace method

Detecting multivariate interactions in spatial point patterns with Gibbs models and variable selection

We propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology develops high dimensional data understanding in the point process setting. The method is based on modelling the patterns using a flexible Gibbs point process model to directly characterise point-to-point interactions at different spatial scales. By using the Gibbs framework significant interactions can also be captured at small scales. Subsequently, the Gibbs point process is fitted using a pseudo-likelihood approximation, and we select significant interactions automatically using the group lasso penalty with this likelihood approximation. Thus we estimate the multivariate interactions stably even in this setting. We demonstrate the feasibility of the method with a simulation study and show its power by applying it to a large and complex rainforest plant population data set of 83 species