95,137 research outputs found
Empirical likelihood based testing for regression
Consider a random vector and let . We are interested
in testing for some known function , some compact set
IR and some function set of real valued
functions. Specific examples of this general hypothesis include testing for a
parametric regression model, a generalized linear model, a partial linear
model, a single index model, but also the selection of explanatory variables
can be considered as a special case of this hypothesis. To test this null
hypothesis, we make use of the so-called marked empirical process introduced by
\citeD and studied by \citeSt for the particular case of parametric regression,
in combination with the modern technique of empirical likelihood theory in
order to obtain a powerful testing procedure. The asymptotic validity of the
proposed test is established, and its finite sample performance is compared
with other existing tests by means of a simulation study.Comment: Published in at http://dx.doi.org/10.1214/07-EJS152 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Optimal testing of equivalence hypotheses
In this paper we consider the construction of optimal tests of equivalence
hypotheses. Specifically, assume X_1,..., X_n are i.i.d. with distribution
P_{\theta}, with \theta \in R^k. Let g(\theta) be some real-valued parameter of
interest. The null hypothesis asserts g(\theta)\notin (a,b) versus the
alternative g(\theta)\in (a,b). For example, such hypotheses occur in
bioequivalence studies where one may wish to show two drugs, a brand name and a
proposed generic version, have the same therapeutic effect. Little optimal
theory is available for such testing problems, and it is the purpose of this
paper to provide an asymptotic optimality theory. Thus, we provide asymptotic
upper bounds for what is achievable, as well as asymptotically uniformly most
powerful test constructions that attain the bounds. The asymptotic theory is
based on Le Cam's notion of asymptotically normal experiments. In order to
approximate a general problem by a limiting normal problem, a UMP equivalence
test is obtained for testing the mean of a multivariate normal mean.Comment: Published at http://dx.doi.org/10.1214/009053605000000048 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Locally most powerful sequential tests of a simple hypothesis vs one-sided alternatives
Let be a discrete-time stochastic process with a distribution
, , where is an open subset of the real
line. We consider the problem of testing a simple hypothesis
versus a composite alternative ,
where is some fixed point. The main goal of this article is
to characterize the structure of locally most powerful sequential tests in this
problem.
For any sequential test with a (randomized) stopping rule
and a (randomized) decision rule let be the
type I error probability, the derivative, at
, of the power function, and an average
sample number of the test . Then we are concerned with the problem
of maximizing in the class of all sequential tests
such that where and are some
restrictions. It is supposed that is calculated under some
fixed (not necessarily coinciding with one of ) distribution of the
process .
The structure of optimal sequential tests is characterized.Comment: 30 page
Testing uniformity on high-dimensional spheres against monotone rotationally symmetric alternatives
We consider the problem of testing uniformity on high-dimensional unit
spheres. We are primarily interested in non-null issues. We show that
rotationally symmetric alternatives lead to two Local Asymptotic Normality
(LAN) structures. The first one is for fixed modal location and allows
to derive locally asymptotically most powerful tests under specified .
The second one, that addresses the Fisher-von Mises-Langevin (FvML) case,
relates to the unspecified- problem and shows that the high-dimensional
Rayleigh test is locally asymptotically most powerful invariant. Under mild
assumptions, we derive the asymptotic non-null distribution of this test, which
allows to extend away from the FvML case the asymptotic powers obtained there
from Le Cam's third lemma. Throughout, we allow the dimension to go to
infinity in an arbitrary way as a function of the sample size . Some of our
results also strengthen the local optimality properties of the Rayleigh test in
low dimensions. We perform a Monte Carlo study to illustrate our asymptotic
results. Finally, we treat an application related to testing for sphericity in
high dimensions
- …