971,227 research outputs found
Estimating the Maximum Expected Value: An Analysis of (Nested) Cross Validation and the Maximum Sample Average
We investigate the accuracy of the two most common estimators for the maximum
expected value of a general set of random variables: a generalization of the
maximum sample average, and cross validation. No unbiased estimator exists and
we show that it is non-trivial to select a good estimator without knowledge
about the distributions of the random variables. We investigate and bound the
bias and variance of the aforementioned estimators and prove consistency. The
variance of cross validation can be significantly reduced, but not without
risking a large bias. The bias and variance of different variants of cross
validation are shown to be very problem-dependent, and a wrong choice can lead
to very inaccurate estimates
Estimating the Maximum Information Leakage
none2noopenAldini, Alessandro; DI PIERRO, A.Aldini, Alessandro; DI PIERRO, A
Estimating the GARCH Diffusion: Simulated Maximum Likelihood in Continuous Time
A new algorithm is developed to provide a simulated maximum likelihood estimation of the GARCH diffusion model of Nelson (1990) based on return data only. The method combines two accurate approximation procedures, namely, the polynomial expansion of Aït-Sahalia (2008) to approximate the transition probability density of return and volatility, and the Efficient Importance Sampler (EIS) of Richard and Zhang (2007) to integrate out the volatility. The first and second order terms in the polynomial expansion are used to generate a base-line importance density for an EIS algorithm. The higher order terms are included when evaluating the importance weights. Monte Carlo experiments show that the new method works well and the discretization error is well controlled by the polynomial expansion. In the empirical application, we fit the GARCH diffusion to equity data, perform diagnostics on the model fit, and test the finiteness of the importance weights.Ecient importance sampling; GARCH diusion model; Simulated Maximum likelihood; Stochastic volatility
Estimation of pulse heights and arrival times
The problem is studied of estimating the arrival times and heights of pulses of known shape observed with white additive noise. The main difficulty is estimating the number of pulses. When a maximum likelihood formulation is employed for the estimation problem, difficulties similar to the problem of estimating the order of an unknown system arise. The problem may be overcome using Rissanen's shortest data description approach. An estimation algorithm is described, and its consistency is proved. The results are illustrated by a simulation study using an example from seismic data processing also studied by Mendel
Sublinear Estimation of Weighted Matchings in Dynamic Data Streams
This paper presents an algorithm for estimating the weight of a maximum
weighted matching by augmenting any estimation routine for the size of an
unweighted matching. The algorithm is implementable in any streaming model
including dynamic graph streams. We also give the first constant estimation for
the maximum matching size in a dynamic graph stream for planar graphs (or any
graph with bounded arboricity) using space which also
extends to weighted matching. Using previous results by Kapralov, Khanna, and
Sudan (2014) we obtain a approximation for general graphs
using space in random order streams, respectively. In
addition, we give a space lower bound of for any
randomized algorithm estimating the size of a maximum matching up to a
factor for adversarial streams
Estimating the maximum possible earthquake magnitude using extreme value methodology: the Groningen case
The area-characteristic, maximum possible earthquake magnitude is
required by the earthquake engineering community, disaster management agencies
and the insurance industry. The Gutenberg-Richter law predicts that earthquake
magnitudes follow a truncated exponential distribution. In the geophysical
literature several estimation procedures were proposed, see for instance Kijko
and Singh (Acta Geophys., 2011) and the references therein. Estimation of
is of course an extreme value problem to which the classical methods for
endpoint estimation could be applied. We argue that recent methods on truncated
tails at high levels (Beirlant et al., Extremes, 2016; Electron. J. Stat.,
2017) constitute a more appropriate setting for this estimation problem. We
present upper confidence bounds to quantify uncertainty of the point estimates.
We also compare methods from the extreme value and geophysical literature
through simulations. Finally, the different methods are applied to the
magnitude data for the earthquakes induced by gas extraction in the Groningen
province of the Netherlands
Estimating the maximum rise in temperature according to climate models using abstract interpretation
Current climate models are complex computer programs that are typically iterated time-step by time-step to predict the next set of values of the climate-related variables. Since these iterative methods are necessarily computed only for a fixed number of iterations, they are unable to answer the natural question whether there is a limit to the rise of global temperature. In order to answer that question we propose to combine climate models with software verification techniques that can find invariant conditions for the set of program variables. In particular, we apply the constraint database approach to software verification to find that the rise in global temperature is bounded according to the common Java Climate Model that implements the Wigely/Raper Upwelling-Diffusion Energy Balance Model climate model
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