4 research outputs found
Kernel Conditional Moment Test via Maximum Moment Restriction
We propose a new family of specification tests called kernel conditional
moment (KCM) tests. Our tests are built on a novel representation of
conditional moment restrictions in a reproducing kernel Hilbert space (RKHS)
called conditional moment embedding (CMME). After transforming the conditional
moment restrictions into a continuum of unconditional counterparts, the test
statistic is defined as the maximum moment restriction (MMR) within the unit
ball of the RKHS. We show that the MMR not only fully characterizes the
original conditional moment restrictions, leading to consistency in both
hypothesis testing and parameter estimation, but also has an analytic
expression that is easy to compute as well as closed-form asymptotic
distributions. Our empirical studies show that the KCM test has a promising
finite-sample performance compared to existing tests.Comment: In Proceedings of the 36th Conference on Uncertainty in Artificial
Intelligence (UAI2020
Functional Generalized Empirical Likelihood Estimation for Conditional Moment Restrictions
Important problems in causal inference, economics, and, more generally,
robust machine learning can be expressed as conditional moment restrictions,
but estimation becomes challenging as it requires solving a continuum of
unconditional moment restrictions. Previous works addressed this problem by
extending the generalized method of moments (GMM) to continuum moment
restrictions. In contrast, generalized empirical likelihood (GEL) provides a
more general framework and has been shown to enjoy favorable small-sample
properties compared to GMM-based estimators. To benefit from recent
developments in machine learning, we provide a functional reformulation of GEL
in which arbitrary models can be leveraged. Motivated by a dual formulation of
the resulting infinite dimensional optimization problem, we devise a practical
method and explore its asymptotic properties. Finally, we provide kernel- and
neural network-based implementations of the estimator, which achieve
state-of-the-art empirical performance on two conditional moment restriction
problems