3,249 research outputs found
On large-sample estimation and testing via quadratic inference functions for correlated data
Hansen (1982) proposed a class of "generalized method of moments" (GMMs) for
estimating a vector of regression parameters from a set of score functions.
Hansen established that, under certain regularity conditions, the estimator
based on the GMMs is consistent, asymptotically normal and asymptotically
efficient. In the generalized estimating equation framework, extending the
principle of the GMMs to implicitly estimate the underlying correlation
structure leads to a "quadratic inference function" (QIF) for the analysis of
correlated data. The main objectives of this research are to (1) formulate an
appropriate estimated covariance matrix for the set of extended score functions
defining the inference functions; (2) develop a unified large-sample
theoretical framework for the QIF; (3) derive a generalization of the QIF test
statistic for a general linear hypothesis problem involving correlated data
while establishing the asymptotic distribution of the test statistic under the
null and local alternative hypotheses; (4) propose an iteratively reweighted
generalized least squares algorithm for inference in the QIF framework; and (5)
investigate the effect of basis matrices, defining the set of extended score
functions, on the size and power of the QIF test through Monte Carlo simulated
experiments.Comment: 32 pages, 2 figure
Adaptive Test of Conditional Moment Inequalities
In this paper, I construct a new test of conditional moment inequalities,
which is based on studentized kernel estimates of moment functions with many
different values of the bandwidth parameter. The test automatically adapts to
the unknown smoothness of moment functions and has uniformly correct asymptotic
size. The test has high power in a large class of models with conditional
moment inequalities. Some existing tests have nontrivial power against
n^{-1/2}-local alternatives in a certain class of these models whereas my
method only allows for nontrivial testing against (n/\log n)^{-1/2}-local
alternatives in this class. There exist, however, other classes of models with
conditional moment inequalities where the mentioned tests have much lower power
in comparison with the test developed in this paper
On the existence of most-preferred alternatives in complete lattices
If a preference ordering on a complete lattice is quasisupermodular, or just satisfies a rather weak analog of the condition, then it admits a maximizer on every subcomplete sublattice if and only if it admits a maximizer on every subcomplete subchainlattice optimization; quasisupermodularity
Testing for Changes in Kendall's Tau
For a bivariate time series we want to detect
whether the correlation between and stays constant for all . We propose a nonparametric change-point test statistic based on
Kendall's tau and derive its asymptotic distribution under the null hypothesis
of no change by means a new U-statistic invariance principle for dependent
processes. The asymptotic distribution depends on the long run variance of
Kendall's tau, for which we propose an estimator and show its consistency.
Furthermore, assuming a single change-point, we show that the location of the
change-point is consistently estimated. Kendall's tau possesses a high
efficiency at the normal distribution, as compared to the normal maximum
likelihood estimator, Pearson's moment correlation coefficient. Contrary to
Pearson's correlation coefficient, it has excellent robustness properties and
shows no loss in efficiency at heavy-tailed distributions. We assume the data
to be stationary and P-near epoch dependent on an
absolutely regular process. The P-near epoch dependence condition constitutes a
generalization of the usually considered -near epoch dependence, , that does not require the existence of any moments. It is therefore very
well suited for our objective to efficiently detect changes in correlation for
arbitrarily heavy-tailed data
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