5,791 research outputs found
Maximal correlation and the rate of Fisher information convergence in the Central Limit Theorem
We consider the behaviour of the Fisher information of scaled sums of
independent and identically distributed random variables in the Central Limit
Theorem regime. We show how this behaviour can be related to the second-largest
non-trivial eigenvalue associated with the Hirschfeld--Gebelein--R\'{e}nyi
maximal correlation. We prove that assuming this eigenvalue satisfies a strict
inequality, an rate of convergence and a strengthened form of
monotonicity hold
Estimating the quadratic covariation matrix from noisy observations: Local method of moments and efficiency
An efficient estimator is constructed for the quadratic covariation or
integrated co-volatility matrix of a multivariate continuous martingale based
on noisy and nonsynchronous observations under high-frequency asymptotics. Our
approach relies on an asymptotically equivalent continuous-time observation
model where a local generalised method of moments in the spectral domain turns
out to be optimal. Asymptotic semi-parametric efficiency is established in the
Cram\'{e}r-Rao sense. Main findings are that nonsynchronicity of observation
times has no impact on the asymptotics and that major efficiency gains are
possible under correlation. Simulations illustrate the finite-sample behaviour.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1224 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Taming systematic uncertainties at the LHC with the central limit theorem
We study the simplifications occurring in any likelihood function in the
presence of a large number of small systematic uncertainties. We find that the
marginalisation of these uncertainties can be done analytically by means of
second-order error propagation, error combination, the Lyapunov central limit
theorem, and under mild approximations which are typically satisfied for LHC
likelihoods. The outcomes of this analysis are i) a very light treatment of
systematic uncertainties ii) a convenient way of reporting the main effects of
systematic uncertainties such as the detector effects occuring in LHC
measurements.Comment: 16 pages, 2 figures. v3: Minor changes. NPB versio
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