arXiv subjects

Eric Mbakop

Publications and source records attributed to Eric Mbakop.

4 recordsLinked to original sources

arXiv2025

Testing the Solvability of Systems of Linear Inequalities

This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in partially identified models can be formulated as hypotheses of this form. Our approach exploits an alternative characterization of the hypothesis based on whether the value of a certain linear program is equal to zero. Building on this characterization, we develop bootstrap-based testing procedures and establish their uniform validity over large classes of data-generating processes. Simulation results demonstrate good finite-sample performance, even for moderate sample sizes. We illustrate the usefulness of the approach in two empirical applications.

econ.EM↗

arXiv2023

Identification in Some Discrete Choice Models: A Computational Approach

This paper presents an algorithm that generates the conditional moment inequalities that characterize the identified set of the common parameter of various semi-parametric panel multinomial choice models. I consider both static and dynamic models, and consider various weak stochastic restrictions on the distribution of observed and unobserved components of the models. For a broad class of such stochastic restrictions, the paper demonstrates that the inequalities characterizing the identified set of the common parameter can be obtained as solutions of multiple objective linear programs (MOLPs), thereby transforming the task of finding these inequalities into a purely computational problem. The algorithm that I provide reproduces many well-known results, including the conditional moment inequalities derived in Manski 1987, Pakes and Porter 2023, and Khan, Ponomareva, and Tamer 2023. Moreover, I use the algorithm to generate some new results, by providing characterizations of the identified set in some cases that were left open in Pakes and Porter 2023 and Khan, Ponomareva, and Tamer 2023, as well as characterizations of the identified set under alternative stochastic restrictions.

stat.ME↗

arXiv2020

Model Selection for Treatment Choice: Penalized Welfare Maximization

This paper studies a penalized statistical decision rule for the treatment assignment problem. Consider the setting of a utilitarian policy maker who must use sample data to allocate a binary treatment to members of a population, based on their observable characteristics. We model this problem as a statistical decision problem where the policy maker must choose a subset of the covariate space to assign to treatment, out of a class of potential subsets. We focus on settings in which the policy maker may want to select amongst a collection of constrained subset classes: examples include choosing the number of covariates over which to perform best-subset selection, and model selection when approximating a complicated class via a sieve. We adapt and extend results from statistical learning to develop the Penalized Welfare Maximization (PWM) rule. We establish an oracle inequality for the regret of the PWM rule which shows that it is able to perform model selection over the collection of available classes. We then use this oracle inequality to derive relevant bounds on maximum regret for PWM. An important consequence of our results is that we are able to formalize model-selection using a "hold-out" procedure, where the policy maker would first estimate various policies using half of the data, and then select the policy which performs the best when evaluated on the other half of the data.

math.ST↗

arXiv2020

Estimation of the Number of Components of Non-Parametric Multivariate Finite Mixture Models

We propose a novel estimator for the number of components (denoted by $M$) in a K-variate non-parametric finite mixture model, where the analyst has repeated observations of $K\geq2$ variables that are independent given a finitely supported unobserved variable. Under a mild assumption on the joint distribution of the observed and latent variables, we show that an integral operator $T$, that is identified from the data, has rank equal to $M$. Using this observation, and the fact that singular values are stable under perturbations, the estimator of $M$ that we propose is based on a thresholding rule which essentially counts the number of singular values of a consistent estimator of $T$ that are greater than a data-driven threshold. We prove that our estimator of $M$ is consistent, and establish non-asymptotic results which provide finite sample performance guarantees for our estimator. We present a Monte Carlo study which shows that our estimator performs well for samples of moderate size.

stat.ME↗