934 research outputs found
What you can do with Coordinated Samples
Sample coordination, where similar instances have similar samples, was
proposed by statisticians four decades ago as a way to maximize overlap in
repeated surveys. Coordinated sampling had been since used for summarizing
massive data sets.
The usefulness of a sampling scheme hinges on the scope and accuracy within
which queries posed over the original data can be answered from the sample. We
aim here to gain a fundamental understanding of the limits and potential of
coordination. Our main result is a precise characterization, in terms of simple
properties of the estimated function, of queries for which estimators with
desirable properties exist. We consider unbiasedness, nonnegativity, finite
variance, and bounded estimates.
Since generally a single estimator can not be optimal (minimize variance
simultaneously) for all data, we propose {\em variance competitiveness}, which
means that the expectation of the square on any data is not too far from the
minimum one possible for the data. Surprisingly perhaps, we show how to
construct, for any function for which an unbiased nonnegative estimator exists,
a variance competitive estimator.Comment: 4 figures, 21 pages, Extended Abstract appeared in RANDOM 201
Robust Bayesian Inference for Set-Identified Models
This paper reconciles the asymptotic disagreement between Bayesian and frequentist inference in setâidentified models by adopting a multipleâprior (robust) Bayesian approach. We propose new tools for Bayesian inference in setâidentified models and show that they have a wellâdefined posterior interpretation in finite samples and are asymptotically valid from the frequentist perspective. The main idea is to construct a prior class that removes the source of the disagreement: the need to specify an unrevisable prior for the structural parameter given the reducedâform parameter. The corresponding class of posteriors can be summarized by reporting the âposterior lower and upper probabilitiesâ of a given event and/or the âset of posterior meansâ and the associated ârobust credible regionâ. We show that the set of posterior means is a consistent estimator of the true identified set and the robust credible region has the correct frequentist asymptotic coverage for the true identified set if it is convex. Otherwise, the method provides posterior inference about the convex hull of the identified set. For impulseâresponse analysis in setâidentified Structural Vector Autoregressions, the new tools can be used to overcome or quantify the sensitivity of standard Bayesian inference to the choice of an unrevisable prior
Multivariate risk measures : a constructive approach based on selections
Since risky positions in multivariate portfolios can be offset by various choices of
capital requirements that depend on the exchange rules and related transaction costs, it
is natural to assume that the risk measures of random vectors are set-valued.
Furthermore, it is reasonable to include the exchange rules in the argument of the risk
and so consider risk measures of set-valued portfolios. This situation includes the
classical Kabanov's transaction costs model, where the set-valued portfolio is given by
the sum of a random vector and an exchange cone, but also a number of further cases of
additional liquidity constraints.
The definition of the selection risk measure is based on calling a set-valued portfolio
acceptable if it possesses a selection with all individually acceptable marginals. The
obtained risk measure is coherent (or convex), law invariant and has values being upper
convex closed sets. We describe the dual representation of the selection risk measure
and suggest efficient ways of approximating it from below and from above. In case of
Kabanov's exchange cone model, it is shown how the selection risk measure relates to
the set-valued risk measures considered by Kulikov (2008), Hamel and Heyde (2010),
and Hamel et al. (2013)Supported by the Spanish Ministry of Science and Innovation Grants No. MTM20IIâ22993 and ECO20ll-25706. Supported by the Chair of Excellence Programme of the Universidad Carlos III de Madrid and Banco
Santander and the Swiss National Foundation Grant No. 200021-13752
Report of the Working Group on `W Mass and QCD' (Phenomenology Workshop on LEP2 Physics, Oxford, April 1997)
The W Mass and QCD Working Group discussed a wide variety of topics relating
to present and future measurements of M(W) at LEP2, including QCD backgrounds
to W+W- production. Particular attention was focused on experimental issues
concerning the direct reconstruction and threshold mass measurements, and on
theoretical and experimental issues concerning the four jet final state. This
report summarises the main conclusions.Comment: 43 pages LaTeX and 15 encapsulated postscript figures. Uses epsfig
and ioplppt macros. Full Proceedings to be published in Journal of Physics
Asymptotically Optimal Algorithms for Budgeted Multiple Play Bandits
We study a generalization of the multi-armed bandit problem with multiple
plays where there is a cost associated with pulling each arm and the agent has
a budget at each time that dictates how much she can expect to spend. We derive
an asymptotic regret lower bound for any uniformly efficient algorithm in our
setting. We then study a variant of Thompson sampling for Bernoulli rewards and
a variant of KL-UCB for both single-parameter exponential families and bounded,
finitely supported rewards. We show these algorithms are asymptotically
optimal, both in rateand leading problem-dependent constants, including in the
thick margin setting where multiple arms fall on the decision boundary
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