814 research outputs found
Average treatment effect estimation via random recursive partitioning
A new matching method is proposed for the estimation of the average treatment
effect of social policy interventions (e.g., training programs or health care
measures). Given an outcome variable, a treatment and a set of pre-treatment
covariates, the method is based on the examination of random recursive
partitions of the space of covariates using regression trees. A regression tree
is grown either on the treated or on the untreated individuals {\it only} using
as response variable a random permutation of the indexes 1... ( being the
number of units involved), while the indexes for the other group are predicted
using this tree. The procedure is replicated in order to rule out the effect of
specific permutations. The average treatment effect is estimated in each tree
by matching treated and untreated in the same terminal nodes. The final
estimator of the average treatment effect is obtained by averaging on all the
trees grown. The method does not require any specific model assumption apart
from the tree's complexity, which does not affect the estimator though. We show
that this method is either an instrument to check whether two samples can be
matched (by any method) and, when this is feasible, to obtain reliable
estimates of the average treatment effect. We further propose a graphical tool
to inspect the quality of the match. The method has been applied to the
National Supported Work Demonstration data, previously analyzed by Lalonde
(1986) and others
Divergences Test Statistics for Discretely Observed Diffusion Processes
In this paper we propose the use of -divergences as test statistics to
verify simple hypotheses about a one-dimensional parametric diffusion process
\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t, from discrete
observations with , , under the asymptotic scheme , and
. The class of -divergences is wide and includes
several special members like Kullback-Leibler, R\'enyi, power and
-divergences. We derive the asymptotic distribution of the test
statistics based on -divergences. The limiting law takes different forms
depending on the regularity of . These convergence differ from the
classical results for independent and identically distributed random variables.
Numerical analysis is used to show the small sample properties of the test
statistics in terms of estimated level and power of the test
On a family of test statistics for discretely observed diffusion processes
We consider parametric hypotheses testing for multidimensional ergodic
diffusion processes observed at discrete time. We propose a family of test
statistics, related to the so called -divergence measures. By taking into
account the quasi-likelihood approach developed for studying the stochastic
differential equations, it is proved that the tests in this family are all
asymptotically distribution free. In other words, our test statistics weakly
converge to the chi squared distribution. Furthermore, our test statistic is
compared with the quasi likelihood ratio test. In the case of contiguous
alternatives, it is also possible to study in detail the power function of the
tests.
Although all the tests in this family are asymptotically equivalent, we show
by Monte Carlo analysis that, in the small sample case, the performance of the
test strictly depends on the choice of the function . Furthermore, in
this framework, the simulations show that there are not uniformly most powerful
tests
On penalized estimation for dynamical systems with small noise
We consider a dynamical system with small noise for which the drift is
parametrized by a finite dimensional parameter. For this model we consider
minimum distance estimation from continuous time observations under
-penalty imposed on the parameters in the spirit of the Lasso approach
with the aim of simultaneous estimation and model selection. We study the
consistency and the asymptotic distribution of these Lasso-type estimators for
different values of . For we also consider the adaptive version of the
Lasso estimator and establish its oracle properties
IFSM representation of Brownian motion with applications to simulation
Several methods are currently available to simulate paths of the Brownian
motion. In particular, paths of the BM can be simulated using the properties of
the increments of the process like in the Euler scheme, or as the limit of a
random walk or via L2 decomposition like the Kac-Siegert/Karnounen-Loeve
series.
In this paper we first propose a IFSM (Iterated Function Systems with Maps)
operator whose fixed point is the trajectory of the BM. We then use this
representation of the process to simulate its trajectories. The resulting
simulated trajectories are self-affine, continuous and fractal by construction.
This fact produces more realistic trajectories than other schemes in the sense
that their geometry is closer to the one of the true BM's trajectories. The
IFSM trajectory of the BM can then be used to generate more realistic solutions
of stochastic differential equations
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