International Statistical Review最新文献

Many models for spatial and spatio-temporal data assume that ‘near things are more related than distant things’, which is known as the first law of geography. While geography may be important, it may not be all-important, for at least two reasons. First, technology helps bridge distance, so that regions separated by large distances may be more similar than would be expected based on geographical distance. Second, geographical, political and social divisions can make neighbouring regions dissimilar. We develop a flexible Bayesian approach for learning from spatial data in which units are close in an unobserved socio-demographic space and hence which units are similar. While classic approaches based on nearest-neighbour adjacency matrices may not fully capture all of the spatial correlation, the proposed approach learns neighbourhoods from data, and averages over all possible neighbourhood structures. We demonstrate the advantages of the proposed approach by presenting simulations along with applications to county-level American Community Survey data on median household income in the US states of Florida, North Carolina and South Carolina.

Statistical depth is the act of gauging how representative a point is compared with a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied and with much experimental success, little theoretical progress has been made in analysing functional depths. This article highlights how the common $�h$-depth and related depths from functional data analysis can be viewed as a kernel mean embedding, widely used in statistical machine learning. This facilitates answers to several open questions regarding the statistical properties of functional depths. We show that (i) $�h$-depth has the interpretation of a kernel-based method; (ii) several $�h$-depths possess explicit expressions, without the need to estimate them using Monte Carlo procedures; (iii) under minimal assumptions, $�h$-depths and their maximisers are uniformly strongly consistent and asymptotically Gaussian (also in infinite-dimensional spaces and for imperfectly observed functional data); and (iv) several $�h$-depths uniquely characterise probability distributions in separable Hilbert spaces. In addition, we also provide a link between the depth and empirical characteristic function based procedures for functional data. Finally, the unveiled connections enable to design an extension of the $�h$-depth towards regression problems.

This article develops a novel feature screening procedure for ultrahigh dimensional mixed data based on Wasserstein distance, termed as Wasserstein-SIS. To handle the mixture of continuous and discrete data, we use Wasserstein distance as a new marginal utility to measure the difference between the joint distribution and the product of marginal distributions. In theory, we establish the sure screening property under less restrictive assumptions on data types. The proposed procedure does not require model specification, gives a more effective geometric measure to compare the discrepancy between distributions and avoids introducing biases caused by the choice of slicing rules for continuous data. Numerical comparison indicates that the proposed Wasserstein-SIS method performs better than existing methods in various models. A real data application also validates the better practicability of Wasserstein-SIS.

Estimating the parameter $�n$ when $�p$ is known or simultaneous estimation of $�n$ and $�p$ of the binomial distribution based on $�k�\ge �1$ independent observations has been considered by many authors over the last several decades. A range of estimators have been proposed, and questions regarding asymptotic and small sample properties received adequate treatment. In this paper, we provide an extensive review and a comprehensive performance comparison of the estimators from the literature. We propose a conceptually simple estimator of $�n$ that uses the marginal likelihood when $�p$ is integrated out by simultaneous optimisation w.r.t. $�n$ and the hyperparameters. We compare the proposed estimator with various existing estimators and find its performance competitive and, in some scenarios, superior.