The Multicenter Clinical Trials Coordinating Center Statistician: “More than a Consultant”

Over the past several decades the employment of statisticians in the area of medical clinical trials in private industry, academic centers, and the federal government has increased significantly. This trend does not appear to be slowing, particularly in those organizations that have come to be termed coordinating centers. In this article we will describe the expanded role that statisticians employed in these centers are expected to be able to fill.     

Distribution of the Λ-Criterion for Sphericity Test and Its Connection to a Generalized Dirichlet Model

It is shown that the exact null distribution of the likelihood ratio criterion for sphericity test in the p-variate normal case and the marginal distribution of the first component of a (p ? 1)-variate generalized Dirichlet model with a given set of parameters are identical. The exact distribution of the likelihood ratio criterion so obtained has a general format for every p. A novel idea is introduced here through which the complicated exact null distribution of the sphericity test criterion in multivariate statistical analysis is converted into an easily tractable marginal density in a generalized Dirichlet model. It provides a direct and easiest method of computation of p-values. The computation of p-values and a table of critical points corresponding to p = 3 and 4 are also presented.     

Discussion of “Simple Estimators for Invertible Index Models” by H. Ahn,H. Ichimura,J. Powell,and P. Ruud

This is an interesting article that considers the question of inference on unknown linear index coefficients in a general class of models where reduced form parameters are invertible function of one or more linear index. Interpretable sufficient conditions such as monotonicity and or smoothness for the invertibility condition are provided. The results generalize some work in the previous literature by allowing the number of reduced form parameters to exceed the number of indices. The identification and estimation expand on the approach taken in previous work by the authors. Examples include Ahn, Powell, and Ichimura (2004 Ahn, H., Powell, J., and Ichimura, H. (2004), “Simple Estimators for Monotone Index Models,” UC Berkeley Working Paper. [Google Scholar]) for monotone single-index regression models to a multi-index setting and extended by Blundell and Powell (2004 Blundell, R. W., and Powell, J. L. (2004), “Endogeneity in Semiparametric Binary Response Models,” The Review of Economic Studies, 71, 655–679.[Crossref], [Web of Science ®] , [Google Scholar]) and Powell and Ruud (2008 Powell, J., and Ruud, P. (2008), “Simple Estimators for Semiparametric Multinomial Choice Models,” UC Berkeley Working Paper. [Google Scholar]) to models with endogenous regressors and multinomial response, respectively. A key property of the inference approach taken is that the estimator of the unknown index coefficients (up to scale) is computationally simple to obtain (relative to other estimators in the literature) in that it is closed form. Specifically, unifying an approach for all models considered in this article, the authors propose an estimator, which is the eigenvector of a matrix (defined in terms of a preliminary estimator of the reduced form parameters) corresponding to its smallest eigenvalue. Under suitable conditions, the proposed estimator is shown to be root-n-consistent and asymptotically normal.     

Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli,Marco Riani,Anthony C. Atkinson and Aldo Corbellini

This paper discusses the contribution of Cerioli et al. (Stat Methods Appl, 2018), where robust monitoring based on high breakdown point estimators is proposed for multivariate data. The results follow years of development in robust diagnostic techniques. We discuss the issues of extending data monitoring to other models with complex structure, e.g. factor analysis, mixed linear models for which S and MM-estimators exist or deviating data cells. We emphasise the importance of robust testing that is often overlooked despite robust tests being readily available once S and MM-estimators have been defined. We mention open questions like out-of-sample inference or big data issues that would benefit from monitoring.