39 research outputs found
Sharp detection of smooth signals in a high-dimensional sparse matrix with indirect observations
We consider a matrix-valued Gaussian sequence model, that is, we observe a
sequence of high-dimensional matrices of heterogeneous Gaussian
random variables for , and . The standard deviation of our observations is \ep k^s for
some \ep >0 and .
We give sharp rates for the detection of a sparse submatrix of size with active components. A component is said active if the sequence
have mean within a Sobolev ellipsoid of
smoothness and total energy larger than
some r^2_\ep. Our rates involve relationships between and
tending to infinity such that , and \ep tend to 0, such that a
test procedure that we construct has asymptotic minimax risk tending to 0.
We prove corresponding lower bounds under additional assumptions on the
relative size of the submatrix in the large matrix of observations. Except for
these additional conditions our rates are asymptotically sharp. Lower bounds
for hypothesis testing problems mean that no test procedure can distinguish
between the null hypothesis (no signal) and the alternative, i.e. the minimax
risk for testing tends to 1
Bayesian optimal adaptive estimation using a sieve prior
We derive rates of contraction of posterior distributions on nonparametric
models resulting from sieve priors. The aim of the paper is to provide general
conditions to get posterior rates when the parameter space has a general
structure, and rate adaptation when the parameter space is, e.g., a Sobolev
class. The conditions employed, although standard in the literature, are
combined in a different way. The results are applied to density, regression,
nonlinear autoregression and Gaussian white noise models. In the latter we have
also considered a loss function which is different from the usual l2 norm,
namely the pointwise loss. In this case it is possible to prove that the
adaptive Bayesian approach for the l2 loss is strongly suboptimal and we
provide a lower bound on the rate.Comment: 33 pages, 2 figure
Bayesian inference for CoVaR
Recent financial disasters emphasised the need to investigate the consequence
associated with the tail co-movements among institutions; episodes of contagion
are frequently observed and increase the probability of large losses affecting
market participants' risk capital. Commonly used risk management tools fail to
account for potential spillover effects among institutions because they provide
individual risk assessment. We contribute to analyse the interdependence
effects of extreme events providing an estimation tool for evaluating the
Conditional Value-at-Risk (CoVaR) defined as the Value-at-Risk of an
institution conditioned on another institution being under distress. In
particular, our approach relies on Bayesian quantile regression framework. We
propose a Markov chain Monte Carlo algorithm exploiting the Asymmetric Laplace
distribution and its representation as a location-scale mixture of Normals.
Moreover, since risk measures are usually evaluated on time series data and
returns typically change over time, we extend the CoVaR model to account for
the dynamics of the tail behaviour. Application on U.S. companies belonging to
different sectors of the Standard and Poor's Composite Index (S&P500) is
considered to evaluate the marginal contribution to the overall systemic risk
of each individual institutio
A test of goodness-of-fit for the copula densities
We consider the problem of testing hypotheses on the copula density from
bi-dimensional observations. We wish to test the null hypothesis characterized
by a parametric class against a composite nonparametric alternative. Each
density under the alternative is separated in the -norm from any density
lying in the null hypothesis. The copula densities under consideration are
supposed to belong to a range of Besov balls. According to the minimax
approach, the testing problem is solved in an adaptive framework: it leads to a
term loss in the minimax rate of testing in comparison with the
non-adaptive case. A smoothness-free test statistic that achieves the minimax
rate is proposed. The lower bound is also proved. Besides, the empirical
performance of the test procedure is demonstrated with both simulated and real
data
Parametric estimation in noisy blind deconvolution model: a new estimation procedure
In a parametric framework, the paper is devoted to the study of a new
estimation procedure for the inverse filter and the level noise in a complex
noisy blind discrete deconvolution model. Our estimation method is a
consequence of the sharp exploitation of the specifical properties of the
Hankel forms. The distribution of the input signal is also estimated. The
strong consistency and the asymptotic distribution of all estimates are
established. A consistent simulation study is added in order to demonstrate
empirically the computational performance of our estimation procedures.Comment: Submitted to the Electronic Journal of Statistics
(http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics
(http://www.imstat.org
Bayesian Tail Risk Interdependence Using Quantile Regression
Recent financial disasters emphasised the need to investigate the consequences associated with the tail co-movements among institutions; episodes of contagion are frequently observed and increase the probability of large losses affecting market participants’ risk capital. Commonly used risk management tools fail to account for potential spillover effects among institutions because they only provide individual risk assessment. We contribute to the analysis of the interdependence effects of extreme events, providing an estimation tool for evaluating the co-movement Value-at-Risk. In particular, our approach relies on a Bayesian quantile regression framework. We propose a Markov chain Monte Carlo algorithm, exploiting the representation of the Asymmetric Laplace distribution as a location-scale mixture of Normals. Moreover, since risk measures are usually evaluated on time series data and returns typically change over time, we extend the model to account for the dynamics of the tail behaviour. We apply our model to a sample of U.S. companies belonging to different sectors of the Standard and Poor’s Composite Index and we provide an evaluation of the marginal contribution to the overall risk of each individual institutio