9,670 research outputs found
When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators
The use of improved covariance matrix estimators as an alternative to the
sample estimator is considered an important approach for enhancing portfolio
optimization. Here we empirically compare the performance of 9 improved
covariance estimation procedures by using daily returns of 90 highly
capitalized US stocks for the period 1997-2007. We find that the usefulness of
covariance matrix estimators strongly depends on the ratio between estimation
period T and number of stocks N, on the presence or absence of short selling,
and on the performance metric considered. When short selling is allowed,
several estimation methods achieve a realized risk that is significantly
smaller than the one obtained with the sample covariance method. This is
particularly true when T/N is close to one. Moreover many estimators reduce the
fraction of negative portfolio weights, while little improvement is achieved in
the degree of diversification. On the contrary when short selling is not
allowed and T>N, the considered methods are unable to outperform the sample
covariance in terms of realized risk but can give much more diversified
portfolios than the one obtained with the sample covariance. When T<N the use
of the sample covariance matrix and of the pseudoinverse gives portfolios with
very poor performance.Comment: 30 page
Probabilistic performance estimators for computational chemistry methods: the empirical cumulative distribution function of absolute errors
Benchmarking studies in computational chemistry use reference datasets to
assess the accuracy of a method through error statistics. The commonly used
error statistics, such as the mean signed and mean unsigned errors, do not
inform end-users on the expected amplitude of prediction errors attached to
these methods. We show that, the distributions of model errors being neither
normal nor zero-centered, these error statistics cannot be used to infer
prediction error probabilities. To overcome this limitation, we advocate for
the use of more informative statistics, based on the empirical cumulative
distribution function of unsigned errors, namely (1) the probability for a new
calculation to have an absolute error below a chosen threshold, and (2) the
maximal amplitude of errors one can expect with a chosen high confidence level.
Those statistics are also shown to be well suited for benchmarking and ranking
studies. Moreover, the standard error on all benchmarking statistics depends on
the size of the reference dataset. Systematic publication of these standard
errors would be very helpful to assess the statistical reliability of
benchmarking conclusions.Comment: Supplementary material: https://github.com/ppernot/ECDF
Reliable inference for complex models by discriminative composite likelihood estimation
Composite likelihood estimation has an important role in the analysis of
multivariate data for which the full likelihood function is intractable. An
important issue in composite likelihood inference is the choice of the weights
associated with lower-dimensional data sub-sets, since the presence of
incompatible sub-models can deteriorate the accuracy of the resulting
estimator. In this paper, we introduce a new approach for simultaneous
parameter estimation by tilting, or re-weighting, each sub-likelihood component
called discriminative composite likelihood estimation (D-McLE). The
data-adaptive weights maximize the composite likelihood function, subject to
moving a given distance from uniform weights; then, the resulting weights can
be used to rank lower-dimensional likelihoods in terms of their influence in
the composite likelihood function. Our analytical findings and numerical
examples support the stability of the resulting estimator compared to
estimators constructed using standard composition strategies based on uniform
weights. The properties of the new method are illustrated through simulated
data and real spatial data on multivariate precipitation extremes.Comment: 29 pages, 4 figure
Uncertainty and sensitivity analysis of functional risk curves based on Gaussian processes
A functional risk curve gives the probability of an undesirable event as a
function of the value of a critical parameter of a considered physical system.
In several applicative situations, this curve is built using phenomenological
numerical models which simulate complex physical phenomena. To avoid cpu-time
expensive numerical models, we propose to use Gaussian process regression to
build functional risk curves. An algorithm is given to provide confidence
bounds due to this approximation. Two methods of global sensitivity analysis of
the models' random input parameters on the functional risk curve are also
studied. In particular, the PLI sensitivity indices allow to understand the
effect of misjudgment on the input parameters' probability density functions
Point and Interval Estimation on the Degree and the Angle of Polarization. A Bayesian approach
Linear polarization measurements provide access to two quantities, the degree
(DOP) and the angle of polarization (AOP). The aim of this work is to give a
complete and concise overview of how to analyze polarimetric measurements. We
review interval estimations for the DOP with a frequentist and a Bayesian
approach. Point estimations for the DOP and interval estimations for the AOP
are further investigated with a Bayesian approach to match observational needs.
Point and interval estimations are calculated numerically for frequentist and
Bayesian statistics. Monte Carlo simulations are performed to clarify the
meaning of the calculations.
Under observational conditions, the true DOP and AOP are unknown, so that
classical statistical considerations - based on true values - are not directly
usable. In contrast, Bayesian statistics handles unknown true values very well
and produces point and interval estimations for DOP and AOP, directly. Using a
Bayesian approach, we show how to choose DOP point estimations based on the
measured signal-to-noise ratio. Interval estimations for the DOP show great
differences in the limit of low signal-to-noise ratios between the classical
and Bayesian approach. AOP interval estimations that are based on observational
data are presented for the first time. All results are directly usable via
plots and parametric fits.Comment: 11 pages, 14 figures, 3 table
Robust Estimators in Generalized Pareto Models
This paper deals with optimally-robust parameter estimation in generalized
Pareto distributions (GPDs). These arise naturally in many situations where one
is interested in the behavior of extreme events as motivated by the
Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have
in mind is calculation of the regulatory capital required by Basel II for a
bank to cover operational risk. In this context the tail behavior of the
underlying distribution is crucial. This is where extreme value theory enters,
suggesting to estimate these high quantiles parameterically using, e.g. GPDs.
Robust statistics in this context offers procedures bounding the influence of
single observations, so provides reliable inference in the presence of moderate
deviations from the distributional model assumptions, respectively from the
mechanisms underlying the PBHT.Comment: 26pages, 6 figure
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