High Dimensional Semiparametric Gaussian Copula Graphical Models

In this paper, we propose a semiparametric approach, named nonparanormal skeptic, for efficiently and robustly estimating high dimensional undirected graphical models. To achieve modeling flexibility, we consider Gaussian Copula graphical models (or the nonparanormal) as proposed by Liu et al. (2009). To achieve estimation robustness, we exploit nonparametric rank-based correlation coefficient estimators, including Spearman's rho and Kendall's tau. In high dimensional settings, we prove that the nonparanormal skeptic achieves the optimal parametric rate of convergence in both graph and parameter estimation. This celebrating result suggests that the Gaussian copula graphical models can be used as a safe replacement of the popular Gaussian graphical models, even when the data are truly Gaussian. Besides theoretical analysis, we also conduct thorough numerical simulations to compare different estimators for their graph recovery performance under both ideal and noisy settings. The proposed methods are then applied on a large-scale genomic dataset to illustrate their empirical usefulness. The R language software package huge implementing the proposed methods is available on the Comprehensive R Archive Network: http://cran. r-project.org/.Comment: 34 pages, 10 figures; the Annals of Statistics, 201

Diderot´s rule

Like many new products, newly released creative goods such as books, music records and movies are sometimes ‘surprise’ hits but often flops. Experimental and empirical research suggests that it is hard to predict the demand for a new creative good, and therefore its success, even for industry experts. Rules of thumb on the quantitative properties of demand uncertainty exist for various creative industries – including a rule by Denis Diderot (1763) according to which one out of ten published books is a commercial success. Yet, representative evidence on any industry’s new-product success rate is scarce. This paper studies new-product success in a random sample of novels. Its empirical strategy to identify success – a simple characterization of author-publisher bargaining combined with a parsimonious model of new-product diffusion – is based on the common observation that word-of-mouth is a crucial success factor in creative industries. Parametric and semi-parametric estimation results corroborate Diderot’s rule: between 10 and 15% of novels enjoy significantly positive effects of word-of-mouth. -- Neu veröffentlichte Kreativgüter wie Bücher, Musikalben und Filme sind, ähnlich anderen neuen Produkten, zwar manchmal "Überraschungserfolge", meistens jedoch Flops. Laut experimentellem und empirischem Forschungsstand ist es selbst für Branchenexperten schwierig, die Nachfrage nach einem neuen Kreativgut, und damit seinen kommerziellen Erfolg, vorherzusagen. Daumenregeln zu den quantitativen Eigenschaften dieser Nachfrageunsicherheit existieren in einigen kreativen Branchen – unter anderem eine Regel von Denis Diderot (1763), wonach eines von zehn veröffentlichten Büchern ein kommerzieller Erfolg ist. Allerdings mangelt es an repräsentativer Evidenz zu der Erfolgsrate neuer Produkte, gleich in welcher Branche. Dieses Papier untersucht den Erfolg neuer Produkte in einer zufälligen Stichprobe von Romanen. Die verwendete empirische Strategie zur Identifikation von Erfolg - eine einfache Charakterisierung der Verhandlungen zwischen Autor und Verlag, kombiniert mit einem überschaubaren Modell der Diffusion neuer Produkte - basiert auf der verbreiteten Beobachtung, dass Mundpropaganda ein entscheidender Erfolgsfaktor in kreativen Branchen ist. Parametrische und semiparametrische Schätzergebnisse bestätigen Diderot's Daumenregel: zwischen 10 und 15% der Romane profitieren von einem signifikant positiven Einfluß von Mundpropaganda.new-product success rate,demand uncertainty,word-of-mouth,creative industries