24,330 research outputs found
Model Adequacy Checks for Discrete Choice Dynamic Models
This paper proposes new parametric model adequacy tests for possibly
nonlinear and nonstationary time series models with noncontinuous data
distribution, which is often the case in applied work. In particular, we
consider the correct specification of parametric conditional distributions in
dynamic discrete choice models, not only of some particular conditional
characteristics such as moments or symmetry. Knowing the true distribution is
important in many circumstances, in particular to apply efficient maximum
likelihood methods, obtain consistent estimates of partial effects and
appropriate predictions of the probability of future events. We propose a
transformation of data which under the true conditional distribution leads to
continuous uniform iid series. The uniformity and serial independence of the
new series is then examined simultaneously. The transformation can be
considered as an extension of the integral transform tool for noncontinuous
data. We derive asymptotic properties of such tests taking into account the
parameter estimation effect. Since transformed series are iid we do not require
any mixing conditions and asymptotic results illustrate the double simultaneous
checking nature of our test. The test statistics converges under the null with
a parametric rate to the asymptotic distribution, which is case dependent,
hence we justify a parametric bootstrap approximation. The test has power
against local alternatives and is consistent. The performance of the new tests
is compared with classical specification checks for discrete choice models
A consistent nonparametric bootstrap test of exogeneity
This paper proposes a novel way of testing exogeneity of an explanatory variable without any parametric assumptions in the presence of a "conditional" instrumental variable. A testable implication is derived that if an explanatory variable is endogenous, the conditional distribution of the outcome given the endogenous variable is not independent of its instrumental variable(s). The test rejects the null hypothesis with probability one if the explanatory variable is endogenous and it detects alternatives converging to the null at a rate n^{-1/2}. We propose a consistent nonparametric bootstrap test to implement this testable implication. We show that the proposed bootstrap test can be asymptotically justified in the sense that it produces asymptotically correct size under the null of exogeneity, and it has unit power asymptotically. Our nonparametric test can be applied to the cases in which the outcome is generated by an additively non-separable structural relation or in which the outcome is discrete, which has not been studied in the literature.Postprin
Independence clustering (without a matrix)
The independence clustering problem is considered in the following
formulation: given a set of random variables, it is required to find the
finest partitioning of into clusters such that the
clusters are mutually independent. Since mutual independence is
the target, pairwise similarity measurements are of no use, and thus
traditional clustering algorithms are inapplicable. The distribution of the
random variables in is, in general, unknown, but a sample is available.
Thus, the problem is cast in terms of time series. Two forms of sampling are
considered: i.i.d.\ and stationary time series, with the main emphasis being on
the latter, more general, case. A consistent, computationally tractable
algorithm for each of the settings is proposed, and a number of open directions
for further research are outlined
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