132 research outputs found
Data-driven rate-optimal specification testing in regression models
We propose new data-driven smooth tests for a parametric regression function.
The smoothing parameter is selected through a new criterion that favors a large
smoothing parameter under the null hypothesis. The resulting test is adaptive
rate-optimal and consistent against Pitman local alternatives approaching the
parametric model at a rate arbitrarily close to 1/\sqrtn. Asymptotic critical
values come from the standard normal distribution and the bootstrap can be used
in small samples. A general formalization allows one to consider a large class
of linear smoothing methods, which can be tailored for detection of additive
alternatives.Comment: Published at http://dx.doi.org/10.1214/009053604000001200 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Conditional Moment Models under Semi-Strong Identification
We consider models defined by conditional moment restrictions under semi-strong identification. Identification strength is directly defined through the conditional mo- ments that flatten as the sample size increases. The framework allows for different iden- tification strengths across parameter’s components. We propose a minimum distance estimator that is robust to semi-strong identification and does not rely on the choice of a user-chosen parameter, such as the number of instruments or any other smoothing parameter. Our method yields consistent and asymptotically normal estimators of each parameter’s components. Heteroskedasticity-robust inference is possible through Wald testing without prior knowledge of the identification pattern. In simulations, we find that our estimator is competitive with alternative estimators based on many instruments. In particular, it is well-centered with better coverage rates for confidence intervals.Asset Markets, Uncertainty, Experimental Economics
One for all and all for one: regression checks with many regressors
We develop a novel approach to build checks of parametric regression models when many regressors are present, based on a class of sufficiently rich semiparametric alternatives, namely single-index models. We propose an omnibus test based on the kernel method that performs against a sequence of directional nonparametric alternatives as if there was one regressor only, whatever the number of regressors. This test can be viewed as a smooth version of the integrated conditional moment (ICM) test of Bierens. Qualitative information can be easily incorporated into the procedure to enhance power. In an extensive comparative simulation study, we find that our test is little sensitive to the smoothing parameter and performs well in multidimensional settings. We then apply it to a cross-country growth regression model.Dimensionality, Hypothesis testing, Nonparametric methods
One for All and All for One:Regression Checks With Many Regressors
We develop a novel approach to build checks of parametric regression models when many regressors are present, based on a class of rich enough semiparametric alternatives, namely single-index models. We propose an omnibus test based on the kernel method that performs against a sequence of directional nonparametric alternatives as if there was one regressor only, whatever the number of regressors. This test can be viewed as a smooth version of the integrated conditional moment (ICM) test of Bierens. Qualitative information can be easily incorporated in the procedure to enhance power. Our test is little sensitive to the smoothing parameter and performs better than several known lack-of-fit tests in multidimensional settings, as illustrated by extensive simulations and an application to a cross-country growth regression.Dimensionality, Hypothesis testing, Nonparametric methods
DATA-DRIVEN RATE-OPTIMAL SPECIFICATION TESTING IN REGRESSION MODELS
We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/\sqrt{n}. Asymptotic critical values come from the standard normal distribution and bootstrap can be used in small samples. A general formalization allows to consider a large class of linear smoothing methods, which can be tailored for detection of additive alternatives.Hypothesis testing, nonparametric adaptive tests, selection methods
Powerful nonparametric checks for quantile regression
We address the issue of lack-of-fit testing for a parametric quantile
regression. We propose a simple test that involves one-dimensional kernel
smoothing, so that the rate at which it detects local alternatives is
independent of the number of covariates. The test has asymptotically gaussian
critical values, and wild bootstrap can be applied to obtain more accurate ones
in small samples. Our procedure appears to be competitive with existing ones in
simulations. We illustrate the usefulness of our test on birthweight data.Comment: 32 pages, 2 figure
A Significance Test for Covariates in Nonparametric Regression
We consider testing the significance of a subset of covariates in a
nonparametric regression. These covariates can be continuous and/or discrete.
We propose a new kernel-based test that smoothes only over the covariates
appearing under the null hypothesis, so that the curse of dimensionality is
mitigated. The test statistic is asymptotically pivotal and the rate of which
the test detects local alternatives depends only on the dimension of the
covariates under the null hypothesis. We show the validity of wild bootstrap
for the test. In small samples, our test is competitive compared to existing
procedures.Comment: 42 pages, 6 figure
Model Equivalence Tests in a Parametric Framework
In empirical research, one commonly aims to obtain evidence in favor of re-
strictions on parameters, appearing as an economic hypothesis, a consequence of
economic theory, or an econometric modeling assumption. I propose a new theoret-
ical framework based on the Kullback-Leibler information to assess the approximate
validity of multivariate restrictions in parametric models. I construct tests that are
locally asymptotically maximin and locally asymptotically uniformly most powerful
invariant. The tests are applied to three different empirical problems
Assessing the Approximate Validity of Moment Restrictions
We propose a new theoretical framework to assess the approximate validity of overidentifying moment restrictions. Their validity is evaluated by the divergence between the true probability measure and the closest measure that imposes the moment restrictions of interest. The divergence can be chosen as any of the Cressie-Read family. The considered alternative hypothesis states that the
divergence is smaller than some user-chosen tolerance. Tests are constructed based on the minimum empirical divergence that attain the local semiparametric power envelope of invariant tests. We show how the tolerance can be chosen by reformulating the hypothesis under test as a set of admissible misspecifications. Two empirical applications illustrate the practical usefulness of the new tests for providing evidence on the potential extent of misspecification
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