Empirical process results for exchangeable arrays
نویسندگان
چکیده
Exchangeable arrays are natural tools to model common forms of dependence between units a sample. Jointly exchangeable well suited dyadic data, where observed random variables indexed by two from the same population. Examples include trade flows countries or relationships in network. Separately multiway clustering, sharing cluster (e.g., geographical areas sectors activity when considering individual wages) may be dependent an unrestricted way. We prove uniform laws large numbers and central limit theorems for such arrays. obtain these results under moment restrictions conditions on class functions as those typically assumed with i.i.d. data. also show convergence bootstrap processes adapted
منابع مشابه
Exchangeable random arrays
These notes were written to accompany a sequence of workshop lectures at the Indian Institute of Science, Bangalore in January 2013. My lectures had two purposes. The first was to introduce some of the main ideas of exchangeability theory at a level suitable for graduate students (assuming familiarity with measure-theoretic probability). The second was to show the key rôle exchangeability has p...
متن کاملRe-sampling and exchangeable arrays
The non-parametric, or re-sampling, bootstrap for a single unstructured sample corresponds to the algebraic operation of monoid composition, with a uniform distribution on the monoid. With this interpretation, the notion of re-sampling can be extended to designs having a certain group-invariance property. Two types of exchangeable array structures are considered in some detail, namely the one-w...
متن کاملComparison results for exchangeable credit risk portfolios
This paper is dedicated to the risk analysis of credit portfolios. Assuming that default indicators form an exchangeable sequence of Bernoulli random variables and as a consequence of de Finetti’s theorem, default indicators are Binomial mixtures. We can characterize the supermodular order between two exchangeable Bernoulli random vectors in terms of the convex ordering of their corresponding m...
متن کاملBaire category results for exchangeable copulas
Considering two different metrics on the space of two-dimensional copulas C we prove some Baire category results for important subclasses of copulas, including the families of exchangeable, associative, and Archimedean copulas. From the point of view of Baire categories, with respect to the uniform metric d∞, a typical copula is not symmetric and a typical symmetric copula is not associative, w...
متن کاملRequirements of Process Modeling Languages - Results from an Empirical Investigation
The majority of large and mid-sized companies are active in Business Process Management (BPM). Documenting business processes is a key task of BPM, but the variety of process modeling languages makes it difficult to determine ‘the best’ one. Basically, the suitability of a process modeling language depends on the companies’ requirements. In this paper we adopt a bird’s eye view on the issue: By...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Statistics
سال: 2021
ISSN: ['0090-5364', '2168-8966']
DOI: https://doi.org/10.1214/20-aos1981