Flavio Santi

Design-based estimation in environmental surveys with positional errors

The recent increased availability of information about the micro-geographic positions of population units in environmental surveys has led to important developments in spatial sampling methodologies and, as a result, has improved the estimation accuracy. In real data, however, information about the location of units is often affected by inaccuracy about their exact spatial positions, and these non-sampling errors can affect the estimation procedure. This paper aims to investigate the effects of positional errors on total estimation through a Monte-Carlo simulation study based on real populations of trees. Starting from perfect positioning, we examine two typical types of coarsening that frequently impact two different species of trees. The simulation results show that the exploitation of spatial information to estimate population totals continues to be relevant in the context of environmental surveys, even in the presence of inaccuracies.

Fitting spatial regressions to large datasets using unilateral approximations

ABSTRACT Maximum likelihood estimation of a spatial model typically requires a sizeable computational capacity, even in relatively small samples, and becomes unfeasible in very large datasets. The unilateral approximation approach to spatial model estimation (suggested in Besag 1974) provides a viable alternative to maximum likelihood estimation that reduces substantially the computing time and the storage required. In this article, we extend the method, originally proposed for conditionally specified processes, to simultaneous and to general bilateral spatial processes over rectangular lattices. We prove the estimators’ consistency and study their finite-sample properties via Monte Carlo simulations.

A Graphical Tool for Interpreting Regression Coefficients of Trinomial Logit Models

ABSTRACT Multinomial logit (also termed multi-logit) models permit the analysis of the statistical relation between a categorical response variable and a set of explicative variables (called covariates or regressors). Although multinomial logit is widely used in both the social and economic sciences, the interpretation of regression coefficients may be tricky, as the effect of covariates on the probability distribution of the response variable is nonconstant and difficult to quantify. The ternary plots illustrated in this article aim at facilitating the interpretation of regression coefficients and permit the effect of covariates (either singularly or jointly considered) on the probability distribution of the dependent variable to be quantified. Ternary plots can be drawn both for ordered and for unordered categorical dependent variables, when the number of possible outcomes equals three (trinomial response variable); these plots allow not only to represent the covariate effects over the whole parameter space of the dependent variable but also to compare the covariate effects of any given individual profile. The method is illustrated and discussed through analysis of a dataset concerning the transition of master’s graduates of the University of Trento (Italy) from university to employment.

Likelihood-based risk estimation for variance-gamma models

Although the variance-gamma distribution is a flexible model for log-returns of financial assets, so far it has found rather limited applications in finance and risk management. One of the reasons is that maximum likelihood estimation of its parameters is not straightforward. We develop an EM-type algorithm based on Nitithumbundit and Chan (An ECM algorithm for skewed multivariate variance gamma distribution in normal mean–variance representation, arXiv:1504.01239, 2015) that bypasses the evaluation of the full likelihood, which may be difficult because the density is not in closed form and is unbounded for small values of the shape parameter. Moreover, we study the relative efficiency of our approach with respect to the maximum likelihood estimation procedures implemented in the VarianceGamma and ghyp R packages. Extensive simulation experiments and real-data analyses suggest that the multicycle ECM algorithm gives the best results in terms of root-mean-squared-error, for both parameter and value-at-risk estimation. The performance of the routines in the ghyp R package is similar but not as good, whereas the VarianceGamma package produces worse results, especially when the shape parameter is small.

La sopravvivenza immediata delle start-up italiane del settore manifatturiero sanitario: un’analisi multilevel

L’obiettivo del presente lavoro e quello di fornire nuove evidenze circa le determinanti della probabilita di sopravvivenza di breve periodo delle start-up italiane attive nel settore farmaceutico e nel settore della produzione di dispositivi medico-sanitari. Al fine di valutare l’effetto di caratteristiche specifiche delle singole imprese, e di tener conto delle variabili di contesto osservate e non osservate, la probabilita di sopravvivenza a tre anni viene descritta mediante un modello logistico multilevel. L’analisi si basa sulle osservazioni a livello di popolazione raccolte e gestite dall’ISTAT in conformita con le direttive dell’OCSE e di EUROSTAT sulla demografia d’impresa, in grado di garantire la coerenza delle informazioni raccolte con particolare riferimento alle entrate e alle uscite delle imprese dal mercato. L’elevato numero di effetti random e la conseguente elevata dimensionalita dell’in¬tegrazione richiesta dal processo di stima rendono le tecniche di stima standard poco affidabili. Le stime sono state quindi effettuate mediante il metodo del-l’entropia relativa per l’ottimizzazione di funzioni con rumore (Bee et al., 2015).

La crescita economica nelle regioni europee nuts 3: un’analisi delle economie alpine nel contesto dell’unione europea

In questo lavoro gli autori analizzano le economie delle regioni alpine nel contesto delle altre economie regionali europee a livello NUTS 3, prendendo in considerazione sia gli aspetti strutturali, sia le performance in termini di crescita economica, sia le dinamiche di interazione tra le economie delle regioni confinanti e i processi di convergenza del reddito pro capite. Con riferimento al primo aspetto le regioni vengono confrontate rispetto al contributo dato al valore aggiunto lordo da sei macro settori (agricoltura; costruzioni; industria; trasporti, distribuzione e ristorazioni; finanza e altri servizi; servizi non di mercato) distinguendo tra regioni alpine e non alpine e, all’interno di esse, tra le regioni a basso, medio e alto grado di urbanizzazione. Secondo la medesima disaggregazione le performance delle regioni vengono analizzate rispetto ai tassi di crescita settoriali del valore aggiunto lordo e al contributo che questi danno alla crescita economica complessiva. Rilievo particolare e riservato alle economie delle provincie autonome di Trento e Bolzano, essendo le due maggiori provincie italiane interamente alpine. Le dinamiche di convergenza tra le regioni europee sono analizzate mediante un’analisi longitudinale sulla β-convergenza che tiene conto sia dell’in¬terazione tra le economie geograficamente vicine (dipendenza spaziale), sia della presenza di ritardi e inerzia nelle variabili economiche (dipendenza spaziale). Viene quindi illustrata un’analisi di tipo panel sul tasso di crescita del PIL reale pro capite con componente autoregressiva spaziale della variabile dipendente e autocorrelazione temporale nell’errore. Infine, viene proposta un’analisi sul grado di interdipendenza delle economie regionali.

A Cross-Entropy Approach to the Estimation of Generalised Linear Multilevel Models

ABSTRACT In this article, we use the cross-entropy method for noisy optimization for fitting generalized linear multilevel models through maximum likelihood. We propose specifications of the instrumental distributions for positive and bounded parameters that improve the computational performance. We also introduce a new stopping criterion, which has the advantage of being problem-independent. In a second step we find, by means of extensive Monte Carlo experiments, the most suitable values of the input parameters of the algorithm. Finally, we compare the method to the benchmark estimation technique based on numerical integration. The cross-entropy approach turns out to be preferable from both the statistical and the computational point of view. In the last part of the article, the method is used to model the probability of firm exits in the healthcare industry in Italy. Supplemental materials are available online.