A GEE-type approach to untangle structural and random zeros in predictors

Count outcomes with excessive zeros are common in behavioral and social studies, and zero-inflated count models such as zero-inflated Poisson (ZIP) and zero-inflated Negative Binomial (ZINB) can be applied when such zero-inflated count data are used as response variable. However, when the zero-inflated count data are used as predictors, ignoring the difference of structural and random zeros can result in biased estimates. In this paper, a generalized estimating equation (GEE)-type mixture model is proposed to jointly model the response of interest and the zero-inflated count predictors. Simulation studies show that the proposed method performs well for practical settings and is more robust for model misspecification than the likelihood-based approach. A case study is also provided for illustration.

Random zeros on complex manifolds: conditional expectations

We study the conditional distribution of zeros of a Gaussian system of random polynomials (and more generally, holomorphic sections), given that the polynomials or sections vanish at a point p (or a fixed finite set of points). The conditional distribution is analogous to the pair correlation function of zeros but we show that it has quite a different small distance behaviour. In particular, the conditional distribution does not exhibit repulsion of zeros in dimension 1. To prove this, we give universal scaling asymptotics for around p. The key tool is the conditional Szegő kernel and its scaling asymptotics.

Speaking Stata: I. J. Good and Quasi-Bayes Smoothing of Categorical Frequencies

I. J. Good (1916–2009) was a prolific scientist who contributed to many fields, mostly from a Bayesian standpoint. This column explains his idea of quasi-Bayes (a.k.a. pseudo-Bayes) estimation or smoothing of categorical frequencies in a contingency table, which is especially useful as a way of dealing with awkward sampling or random zeros. It shows how the method can be implemented, almost calculator-style, using a combination of Stata and Mata. Convenience commands qsbayesi and qsbayes are also introduced.