arXiv subjects

Julieta Molina

Publications and source records attributed to Julieta Molina.

3 recordsLinked to original sources

arXiv2017

Robust Doubly Protected Estimators for Quantiles with Missing Data

Doubly protected estimators are widely used for estimating the population mean of an outcome Y from a sample where the response is missing in some individuals. To compensate for the missing responses, a vector X of covariates is observed at each individual, and the missing mechanism is assumed to be independent of the response, conditioned on X (missing at random). In recent years, many authors have moved from the mean to the median, and more generally, doubly protected estimators of the quantiles have been proposed, assuming a parametric regression model for the relationship between X and Y and a parametric form for the propensity score. In this work, we present doubly protected estimators for the quantiles that are also robust, in the sense that they are resistant to the presence of outliers in the sample. We also flexibilize the model for the relationship between X and Y . Thus we present robust doubly protected estimators for the quantiles of the response in the presence of missing observations, postulating a semiparametric regression model for the relationship between the response and the covariates and a parametric model for the propensity score.

stat.ME↗

arXiv2017

Models for the Propensity Score that Contemplate the Positivity Assumption and their Application to Missing Data and Causality

Generalized linear models are often assumed to fit propensity scores, which are used to compute inverse probability weighted (IPW) estimators. In order to derive the asymptotic properties of IPW estimators, the propensity score is supposed to be bounded away from cero. This condition is known in the literature as strict positivity (or positivity assumption) and, in practice, when it does not hold, IPW estimators are very unstable and have a large variability. Although strict positivity is often assumed, it is not upheld when some of the covariates are continuous. In this work, we attempt to conciliate between the strict positivity condition and the theory of generalized linear models by incorporating an extra parameter, which results in an explicit lower bound for the propensity scores.

stat.ME↗

arXiv2013

Some considerations on the back door theorem and conditional randomization

In this work we propose a different surgical modified model for the construction of counterfactual variables under non parametric structural equation models. This approach allows the simultaneous representation of counterfactual responses and observed treatment assignment, at least when the intervention is done in one node. Using the new proposal, the d-separation criterion is used verify conditions related with ignorability or conditional ignorability and a new proof of the back door theorem is provided under this framework.

math.ST↗