Discussion on the paper by Peter Müller,Fernando A. Quintana,and Garritt L. Page

The article by Müller, Quintana, and Page reviews a variety of Bayesian nonparametric models and demonstrates them in a few applications. They emphasize applications in spatial data on which our discussion focuses as well. In particular, we consider two types of mixture models based on species sampling models (SSM) for spatial clustering and apply them to the Chilean mathematics testing score data analyzed by the authors. We conclude that only the mixture model of SSM with spatial locations as part of observations renders spatially non-overlapping clusters.     

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 “On simulation and properties of the stable law” by L. Devroye and L. James

We contribute to the discussion of the paper by Devroye and James, by reviewing some of the most meaningful results that relate the unilateral stable distribution with the asymptotic behavior of the so-called Ewens-Pitman sampling model. Our focus is then on how these results have been exploited in the context of Bayesian nonparametric inference for species sampling problems.     

A comment on “An analysis of global warming in the Alpine Region based on nonlinear nonstationary time series models” by F. Battaglia and M. K. Protopapas

We discuss the paper by Battaglia and Protopapas concerning the analysis of global warming phenomenon in the Alpine Region. The Authors consider a nonlinear model which takes into account regimes in time and levels. In this contribution some of the statistical results presented in the paper are commented and a different approach to the problem is proposed. It is based on a temporal aggregation analysis and it can help to highlight some features in the data.     

Comment “On the role of data,statistics and decisions in a pandemic” by Jahn et al.

AStA Advances in Statistical Analysis - We comment the paper by Jahn et al. (On the role of data, statistics and decisions in a pandemic, 2022).     

Comments on “Sums,Products, and Ratios of Non-Central Beta Variables” by Saralees Nadarajah

Brief comments on “Sums, Products, and Ratios of Non-Central Beta Variables” by Saralees Nadarajah, which appeared in Communications in Statistics – Theory and Methods, Volume 34, Issue 1, pp. 89–100.