Reliability in its broad sense refers to the probability that a component or system is able to perform its intended function satisfactorily during a specified period of time under normal operating conditions. It is estimated as the fraction of time the unit/system is available for operation. For...

We adopt an `epistemic' interpretation of social decisions: there is an objectively correct choice, each voter receives a `noisy signal' of the correct choice, and the social objective is to aggregate these signals to make the best possible guess about the correct choice. One epistemic method is...

In this paper, we establish some new central limit theorems for generalized U-statistics of dependent processes under some mild conditions. Such central limit theorems complement existing existing results available from both the econometrics literature and statistics literature. We then look at...

Capturing dependence among a large number of high dimensional random vectors is a very important and challenging problem. By arranging n random vectors of length p in the form of a matrix, we develop a linear spectral statistic of the constructed matrix to test whether the n random vectors are...

Nicolas Bernoulli suggested the St Petersburg game, nearly 300 years ago, which is widely believed to produce a paradox in decision theory. This belief stems from a long standing mathematical error in the original calculation of the expected value of the game. This article argues that, in...

Standardized slowly varying regressors are shown to be $L_p$-approximable. This fact allows one to relax the assumption on linear processes imposed in central limit results by P.C.B. Phillips, as well as provide alternative proofs for some other statements.

The phenomenon of high volatility in financial markets stemming from the increased complexity of financial instruments traded, as well as the evidence of losses due to natural and man-made catastrophes, highlight the need for sophisticated risk management practices. The analysis concerning the...

The most part of the paper is about modeling (or approximating) nonstochastic regressors. Examples of regressors which are (not) L2-approximable are given. Applications to central limit theory and OLS estimator asymptotics are provided.

This paper puts forward a technique based on the characteristic function to tackle the problem of the sum of stochastic variables. We consider independent processes whose reduced variables are identically distributed, including those that violate the conditions for the central limit theorem to...