38,456 research outputs found
Nonparametric Bayesian multiple testing for longitudinal performance stratification
This paper describes a framework for flexible multiple hypothesis testing of
autoregressive time series. The modeling approach is Bayesian, though a blend
of frequentist and Bayesian reasoning is used to evaluate procedures.
Nonparametric characterizations of both the null and alternative hypotheses
will be shown to be the key robustification step necessary to ensure reasonable
Type-I error performance. The methodology is applied to part of a large
database containing up to 50 years of corporate performance statistics on
24,157 publicly traded American companies, where the primary goal of the
analysis is to flag companies whose historical performance is significantly
different from that expected due to chance.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS252 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Confidence Corridors for Multivariate Generalized Quantile Regression
We focus on the construction of confidence corridors for multivariate
nonparametric generalized quantile regression functions. This construction is
based on asymptotic results for the maximal deviation between a suitable
nonparametric estimator and the true function of interest which follow after a
series of approximation steps including a Bahadur representation, a new strong
approximation theorem and exponential tail inequalities for Gaussian random
fields. As a byproduct we also obtain confidence corridors for the regression
function in the classical mean regression. In order to deal with the problem of
slowly decreasing error in coverage probability of the asymptotic confidence
corridors, which results in meager coverage for small sample sizes, a simple
bootstrap procedure is designed based on the leading term of the Bahadur
representation. The finite sample properties of both procedures are
investigated by means of a simulation study and it is demonstrated that the
bootstrap procedure considerably outperforms the asymptotic bands in terms of
coverage accuracy. Finally, the bootstrap confidence corridors are used to
study the efficacy of the National Supported Work Demonstration, which is a
randomized employment enhancement program launched in the 1970s. This article
has supplementary materials
On a Nonparametric Notion of Residual and its Applications
Let be a continuous random vector in , . In this paper, we define the notion of a
nonparametric residual of on that is always independent of the
predictor . We study its properties and show that the proposed
notion of residual matches with the usual residual (error) in a multivariate
normal regression model. Given a random vector in
, we use this notion of
residual to show that the conditional independence between and , given
, is equivalent to the mutual independence of the residuals (of
on and on ) and . This result is used
to develop a test for conditional independence. We propose a bootstrap scheme
to approximate the critical value of this test. We compare the proposed test,
which is easily implementable, with some of the existing procedures through a
simulation study.Comment: 19 pages, 2 figure
Heteroscedastic semiparametric transformation models: estimation and testing for validity
In this paper we consider a heteroscedastic transformation model, where the
transformation belongs to a parametric family of monotone transformations, the
regression and variance function are modelled nonparametrically and the error
is independent of the multidimensional covariates. In this model, we first
consider the estimation of the unknown components of the model, namely the
transformation parameter, regression and variance function and the distribution
of the error. We show the asymptotic normality of the proposed estimators.
Second, we propose tests for the validity of the model, and establish the
limiting distribution of the test statistics under the null hypothesis. A
bootstrap procedure is proposed to approximate the critical values of the
tests. Finally, we carry out a simulation study to verify the small sample
behavior of the proposed estimators and tests.Comment: 33 pages, 1 figur
Nonparametric checks for single-index models
In this paper we study goodness-of-fit testing of single-index models. The
large sample behavior of certain score-type test statistics is investigated. As
a by-product, we obtain asymptotically distribution-free maximin tests for a
large class of local alternatives. Furthermore, characteristic function based
goodness-of-fit tests are proposed which are omnibus and able to detect peak
alternatives. Simulation results indicate that the approximation through the
limit distribution is acceptable already for moderate sample sizes.
Applications to two real data sets are illustrated.Comment: Published at http://dx.doi.org/10.1214/009053605000000020 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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