The Fréchet mean generalizes the idea of averaging in spaces where pairwise addition is not well-defined. In general metric spaces, however, the Fréchet sample mean is not a consistent estimator of the theoretical Fréchet mean. For non-trivial examples, sequences of Fréchet sample mean sets may fail to converge in a set-analytical sense. Hence, it becomes necessary to consider other types of co...

The aim of this article is to simplify Pfanzagl’s proof of consistency for asymptotic maximum likelihood estimators, and to extend it to more general asymptotic M -estimators. The method relies on the existence of a sort of contraction of the parameter space which admits the true parameter as a fixed point. The proofs are short and elementary.

We consider the estimation of the number of hidden states (the order) of a discrete-time finite-alphabet hidden Markov model (HMM). The estimators we investigate are related to code-based order estimators: penalized maximum-likelihood (ML) estimators and penalized versions of the mixture estimator introduced by Liu and Narayan. We prove strong consistency of those estimators without assuming an...

We outline the design and operation of Pasta, a peer-topeer storage system that provides traditional file system semantics while offering the wide-spread caching and distribution required for publishing networks. Pasta allows users to manipulate shared files and folders with strong consistency semantics and to collaboratively organize them in unmanaged decentralized namespaces. Storage quotas r...

This paper deals with nonparametric estimation of a regression curve, where the estimation method should preserve possible jumps in the curve. At each point x at which one wants to estimate the regression function, the method chooses in an adaptive way among three estimates: a local linear estimate using only datapoints to the left of x, a local linear estimate based on only datapoints to the r...

Urn models are popular and useful for adaptive designs in clinical studies. Among various urn models, the drop-the-loser rule is an efficient adaptive treatment allocation scheme, recently proposed for comparing different treatments in a clinical trial. This rule is superior to other randomization schemes in terms of variability and power. In this paper, the drop-the-loser rule is generalized t...

In this paper we formulate in general terms an approach to prove strong consistency of the Empirical Risk Minimisation inductive principle applied to the prototype or distance based clustering. This approach was motivated by the Divisive Information-Theoretic Feature Clustering model in probabilistic space with Kullback-Leibler divergence, which may be regarded as a special case within the Clus...

We devise a new method of estimating a distribution in a deconvolution model with panel data and an unknown distribution of the additive errors. We prove strong consistency under a minimal condition concerning the zero sets of the involved characteristic functions.

For I a proper, countably complete ideal on P(X) for some set X , can the quotient Boolean algebra P(X)/I be complete? This question was raised by Sikorski [Si] in 1949. By a simple projection argument as for measurable cardinals, it can be assumed that X is an uncountable cardinal κ, and that I is a κ-complete ideal on P(κ) containing all singletons. In this paper we provide consequences from ...

It is expensive to maintain strong data consistency during concurrent execution. However, weak consistency levels, which are considered harmful, have been widely applied in analytical jobs. Their success challenges our belief: data consistency, which is believed to be an essential to precise computing, does not always need to be preserved. In this paper, we tackle one of the core questions rela...