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...$n$ ($n$ 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 $\phi$-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 $\{X_{t_i}, i=0, ..., n\}$ with $t_i = i\Delta_n$, $i=0, 1, >..., n$, under the asymptotic scheme $\Delta_n\to0$, $n\Delta_n\to\infty$ and $n\Delta_n^2\to 0$. The class of $\phi$-divergences is wide and includes several special members like Kullback-Leibler, R\'enyi, power and $\alpha$-divergences. We derive the asymptotic distribution of the test statistics based on $\phi$-divergences. The limiting law takes different forms depending on the regularity of $\phi$. 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 $\phi$-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 $\phi$. 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 $l^p$-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 $p$. For $p=1$ we also consider the adaptive version of the Lasso estimator and establish its oracle properties

Invariant and Metric Free Proximities for Data Matching: An R Package

Data matching is a typical statistical problem in non experimental and/or observational studies or, more generally, in cross-sectional studies in which one or more data sets are to be compared. Several methods are available in the literature, most of which based on a particular metric or on statistical models, either parametric or nonparametric. In this paper we present two methods to calculate a proximity which have the property of being invariant under monotonic transformations. These methods require at most the notion of ordering. An open-source software in the form of a R package is also presented.