111,671 research outputs found
Empirical-likelihood-based confidence interval for the mean with a heavy-tailed distribution
Empirical-likelihood-based confidence intervals for a mean were introduced by
Owen [Biometrika 75 (1988) 237-249], where at least a finite second moment is
required. This excludes some important distributions, for example, those in the
domain of attraction of a stable law with index between 1 and 2. In this
article we use a method similar to Qin and Wong [Scand.
J. Statist. 23 (1996) 209-219] to derive an empirical-likelihood-based
confidence interval for the mean when the underlying distribution has heavy
tails. Our method can easily be extended to obtain a confidence interval for
any order of moment of a heavy-tailed distribution
Optimal Quantum Measurements of Expectation Values of Observables
Experimental characterizations of a quantum system involve the measurement of
expectation values of observables for a preparable state |psi> of the quantum
system. Such expectation values can be measured by repeatedly preparing |psi>
and coupling the system to an apparatus. For this method, the precision of the
measured value scales as 1/sqrt(N) for N repetitions of the experiment. For the
problem of estimating the parameter phi in an evolution exp(-i phi H), it is
possible to achieve precision 1/N (the quantum metrology limit) provided that
sufficient information about H and its spectrum is available. We consider the
more general problem of estimating expectations of operators A with minimal
prior knowledge of A. We give explicit algorithms that approach precision 1/N
given a bound on the eigenvalues of A or on their tail distribution. These
algorithms are particularly useful for simulating quantum systems on quantum
computers because they enable efficient measurement of observables and
correlation functions. Our algorithms are based on a method for efficiently
measuring the complex overlap of |psi> and U|psi>, where U is an implementable
unitary operator. We explicitly consider the issue of confidence levels in
measuring observables and overlaps and show that, as expected, confidence
levels can be improved exponentially with linear overhead. We further show that
the algorithms given here can typically be parallelized with minimal increase
in resource usage.Comment: 22 page
Monte Carlo-based tail exponent estimator
In this paper we propose a new approach to estimation of the tail exponent in
financial stock markets. We begin the study with the finite sample behavior of
the Hill estimator under {\alpha}-stable distributions. Using large Monte Carlo
simulations, we show that the Hill estimator overestimates the true tail
exponent and can hardly be used on samples with small length. Utilizing our
results, we introduce a Monte Carlo-based method of estimation for the tail
exponent. Our proposed method is not sensitive to the choice of tail size and
works well also on small data samples. The new estimator also gives unbiased
results with symmetrical confidence intervals. Finally, we demonstrate the
power of our estimator on the international world stock market indices. On the
two separate periods of 2002-2005 and 2006-2009, we estimate the tail exponent
Software timing analysis for complex hardware with survivability and risk analysis
The increasing automation of safety-critical real-time systems, such as those in cars and planes, leads, to more complex and performance-demanding on-board software and the subsequent adoption of multicores and accelerators. This causes software's execution time dispersion to increase due to variable-latency resources such as caches, NoCs, advanced memory controllers and the like. Statistical analysis has been proposed to model the Worst-Case Execution Time (WCET) of software running such complex systems by providing reliable probabilistic WCET (pWCET) estimates. However, statistical models used so far, which are based on risk analysis, are overly pessimistic by construction. In this paper we prove that statistical survivability and risk analyses are equivalent in terms of tail analysis and, building upon survivability analysis theory, we show that Weibull tail models can be used to estimate pWCET distributions reliably and tightly. In particular, our methodology proves the correctness-by-construction of the approach, and our evaluation provides evidence about the tightness of the pWCET estimates obtained, which allow decreasing them reliably by 40% for a railway case study w.r.t. state-of-the-art exponential tails.This work is a collaboration between Argonne National Laboratory and the Barcelona Supercomputing Center within the Joint Laboratory for Extreme-Scale Computing. This research is supported by the
U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under contract number DE-AC02-
06CH11357, program manager Laura Biven, and by the Spanish Government (SEV2015-0493), by the Spanish Ministry of Science and Innovation (contract TIN2015-65316-P), by Generalitat de Catalunya (contract 2014-SGR-1051).Peer ReviewedPostprint (author's final draft
Characterization of the frequency of extreme events by the Generalized Pareto Distribution
Based on recent results in extreme value theory, we use a new technique for
the statistical estimation of distribution tails. Specifically, we use the
Gnedenko-Pickands-Balkema-de Haan theorem, which gives a natural limit law for
peak-over-threshold values in the form of the Generalized Pareto Distribution
(GPD). Useful in finance, insurance, hydrology, we investigate here the
earthquake energy distribution described by the Gutenberg-Richter seismic
moment-frequency law and analyze shallow earthquakes (depth h < 70 km) in the
Harvard catalog over the period 1977-2000 in 18 seismic zones. The whole GPD is
found to approximate the tails of the seismic moment distributions quite well
above moment-magnitudes larger than mW=5.3 and no statistically significant
regional difference is found for subduction and transform seismic zones. We
confirm that the b-value is very different in mid-ocean ridges compared to
other zones (b=1.50=B10.09 versus b=1.00=B10.05 corresponding to a power law
exponent close to 1 versus 2/3) with a very high statistical confidence. We
propose a physical mechanism for this, contrasting slow healing ruptures in
mid-ocean ridges with fast healing ruptures in other zones. Deviations from the
GPD at the very end of the tail are detected in the sample containing
earthquakes from all major subduction zones (sample size of 4985 events). We
propose a new statistical test of significance of such deviations based on the
bootstrap method. The number of events deviating from the tails of GPD in the
studied data sets (15-20 at most) is not sufficient for determining the
functional form of those deviations. Thus, it is practically impossible to give
preference to one of the previously suggested parametric families describing
the ends of tails of seismic moment distributions.Comment: pdf document of 21 pages + 2 tables + 20 figures (ps format) + one
file giving the regionalizatio
Underlying Dynamics of Typical Fluctuations of an Emerging Market Price Index: The Heston Model from Minutes to Months
We investigate the Heston model with stochastic volatility and exponential
tails as a model for the typical price fluctuations of the Brazilian S\~ao
Paulo Stock Exchange Index (IBOVESPA). Raw prices are first corrected for
inflation and a period spanning 15 years characterized by memoryless returns is
chosen for the analysis. Model parameters are estimated by observing volatility
scaling and correlation properties. We show that the Heston model with at least
two time scales for the volatility mean reverting dynamics satisfactorily
describes price fluctuations ranging from time scales larger than 20 minutes to
160 days. At time scales shorter than 20 minutes we observe autocorrelated
returns and power law tails incompatible with the Heston model. Despite major
regulatory changes, hyperinflation and currency crises experienced by the
Brazilian market in the period studied, the general success of the description
provided may be regarded as an evidence for a general underlying dynamics of
price fluctuations at intermediate mesoeconomic time scales well approximated
by the Heston model. We also notice that the connection between the Heston
model and Ehrenfest urn models could be exploited for bringing new insights
into the microeconomic market mechanics.Comment: 20 pages, 9 figures, to appear in Physica
Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks
Quantile regression is an increasingly important empirical tool in economics
and other sciences for analyzing the impact of a set of regressors on the
conditional distribution of an outcome. Extremal quantile regression, or
quantile regression applied to the tails, is of interest in many economic and
financial applications, such as conditional value-at-risk, production
efficiency, and adjustment bands in (S,s) models. In this paper we provide
feasible inference tools for extremal conditional quantile models that rely
upon extreme value approximations to the distribution of self-normalized
quantile regression statistics. The methods are simple to implement and can be
of independent interest even in the non-regression case. We illustrate the
results with two empirical examples analyzing extreme fluctuations of a stock
return and extremely low percentiles of live infants' birthweights in the range
between 250 and 1500 grams.Comment: 41 pages, 9 figure
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