Related papers: Central Limit Theorem for Adaptative Multilevel Sp…
A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
The distributed Hill estimator is a divide-and-conquer algorithm for estimating the extreme value index when data are stored in multiple machines. In applications, estimates based on the distributed Hill estimator can be sensitive to the…
In computational mechanics, multiple models are often present to describe a physical system. While Bayesian model selection is a helpful tool to compare these models using measurement data, it requires the computationally expensive…
The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an…
Highly robust and efficient estimators for the generalized linear model with a dispersion parameter are proposed. The estimators are based on three steps. In the first step the maximum rank correlation estimator is used to consistently…
We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling…
Modeling and understanding multivariate extreme events is challenging, but of great importance in various applications - e.g. in biostatistics, climatology, and finance. The separating Hill estimator can be used in estimating the extreme…
Suppose (standardized) measurements or statistics are monitored to raise an alarm when a threshold is exceeded. Often, the underlying population is heterogenous with respect to important discrete variables and thus samples may consist of…
For rare events described in terms of Markov processes, truly unbiased estimation of the rare event probability generally requires the avoidance of numerical approximations of the Markov process. Recent work in the exact and…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
Datasets are often reused to perform multiple statistical analyses in an adaptive way, in which each analysis may depend on the outcomes of previous analyses on the same dataset. Standard statistical guarantees do not account for these…
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it…
The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
An important problem in space-time adaptive detection is the estimation of the large p-by-p interference covariance matrix from training signals. When the number of training signals n is greater than 2p, existing estimators are generally…
Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…
We propose a unified rare-event estimator for the performance evaluation of wireless communication systems. The estimator is derived from the well-known multilevel splitting algorithm. In its original form, the splitting algorithm cannot be…
In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…