516 research outputs found
Digit analysis for Covid-19 reported data
The coronavirus which appeared in December 2019 in Wuhan has spread out
worldwide and caused the death of more than 280,000 people (as of May, 11
2020). Since February 2020, doubts were raised about the numbers of confirmed
cases and deaths reported by the Chinese government. In this paper, we examine
data available from China at the city and provincial levels and we compare them
with Canadian provincial data, US state data and French regional data. We
consider cumulative and daily numbers of confirmed cases and deaths and examine
these numbers through the lens of their first two digits and in particular we
measure departures of these first two digits to the Newcomb-Benford
distribution, often used to detect frauds. Our finding is that there is no
evidence that cumulative and daily numbers of confirmed cases and deaths for
all these countries have different first or second digit distributions. We also
show that the Newcomb-Benford distribution cannot be rejected for these data
Expectiles for subordinated Gaussian processes with applications
In this paper, we introduce a new class of estimators of the Hurst exponent
of the fractional Brownian motion (fBm) process. These estimators are based on
sample expectiles of discrete variations of a sample path of the fBm process.
In order to derive the statistical properties of the proposed estimators, we
establish asymptotic results for sample expectiles of subordinated stationary
Gaussian processes with unit variance and correlation function satisfying
(\kappa\in \RR) with . Via a
simulation study, we demonstrate the relevance of the expectile-based
estimation method and show that the suggested estimators are more robust to
data rounding than their sample quantile-based counterparts
Asymptotic properties of the maximum pseudo-likelihood estimator for stationary Gibbs point processes including the Lennard-Jones model
This paper presents asymptotic properties of the maximum pseudo-likelihood
estimator of a vector \Vect{\theta} parameterizing a stationary Gibbs point
process. Sufficient conditions, expressed in terms of the local energy function
defining a Gibbs point process, to establish strong consistency and asymptotic
normality results of this estimator depending on a single realization, are
presented.These results are general enough to no longer require the local
stability and the linearity in terms of the parameters of the local energy
function. We consider characteristic examples of such models, the Lennard-Jones
and the finite range Lennard-Jones models. We show that the different
assumptions ensuring the consistency are satisfied for both models whereas the
assumptions ensuring the asymptotic normality are fulfilled only for the finite
range Lennard-Jones model
Variational approach for spatial point process intensity estimation
We introduce a new variational estimator for the intensity function of an
inhomogeneous spatial point process with points in the -dimensional
Euclidean space and observed within a bounded region. The variational estimator
applies in a simple and general setting when the intensity function is assumed
to be of log-linear form where is a spatial
covariate function and the focus is on estimating . The variational
estimator is very simple to implement and quicker than alternative estimation
procedures. We establish its strong consistency and asymptotic normality. We
also discuss its finite-sample properties in comparison with the maximum first
order composite likelihood estimator when considering various inhomogeneous
spatial point process models and dimensions as well as settings were is
completely or only partially known.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ516 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Poisson intensity parameter estimation for stationary Gibbs point processes of finite interaction range
We introduce a semi-parametric estimator of the Poisson intensity parameter
of a spatial stationary Gibbs point process. Under very mild assumptions
satisfied by a large class of Gibbs models, we establish its strong consistency
and asymptotic normality. We also consider its finite-sample properties in a
simulation study
Stein estimation of the intensity of a spatial homogeneous Poisson point process
In this paper, we revisit the original ideas of Stein and propose an
estimator of the intensity parameter of a homogeneous Poisson point process
defined in and observed in a bounded window. The procedure is based on a
new general integration by parts formula for Poisson point processes. We show
that our Stein estimator outperforms the maximum likelihood estimator in terms
of mean squared error. In particular, we show that in many practical situations
we have a gain larger than 30\%
Convex and non-convex regularization methods for spatial point processes intensity estimation
This paper deals with feature selection procedures for spatial point
processes intensity estimation. We consider regularized versions of estimating
equations based on Campbell theorem derived from two classical functions:
Poisson likelihood and logistic regression likelihood. We provide general
conditions on the spatial point processes and on penalty functions which ensure
consistency, sparsity and asymptotic normality. We discuss the numerical
implementation and assess finite sample properties in a simulation study.
Finally, an application to tropical forestry datasets illustrates the use of
the proposed methods
- …