170,903 research outputs found
VERYFICATION OF LOCATION PROBLEM IN ECONOMIC RESEARCH
In economic research very often the location problem in the single sample or estimation of the difference in two samples location is commonly tested by experimental economists. Usually the used tests are Wilcoxon test for single sample location or Wilcoxon – Mann – Whitney for two samples location problem. Unfortunately those tests have some disadvantages such as robustness against assumptions or week efficiency. In the paper, some less known procedures, which allow avoid those problems, will be presented. Considered methods will be illustrated on the example of the data analysis from real-estate market
mfEGRA: Multifidelity Efficient Global Reliability Analysis through Active Learning for Failure Boundary Location
This paper develops mfEGRA, a multifidelity active learning method using
data-driven adaptively refined surrogates for failure boundary location in
reliability analysis. This work addresses the issue of prohibitive cost of
reliability analysis using Monte Carlo sampling for expensive-to-evaluate
high-fidelity models by using cheaper-to-evaluate approximations of the
high-fidelity model. The method builds on the Efficient Global Reliability
Analysis (EGRA) method, which is a surrogate-based method that uses adaptive
sampling for refining Gaussian process surrogates for failure boundary location
using a single-fidelity model. Our method introduces a two-stage adaptive
sampling criterion that uses a multifidelity Gaussian process surrogate to
leverage multiple information sources with different fidelities. The method
combines expected feasibility criterion from EGRA with one-step lookahead
information gain to refine the surrogate around the failure boundary. The
computational savings from mfEGRA depends on the discrepancy between the
different models, and the relative cost of evaluating the different models as
compared to the high-fidelity model. We show that accurate estimation of
reliability using mfEGRA leads to computational savings of 46% for an
analytic multimodal test problem and 24% for a three-dimensional acoustic horn
problem, when compared to single-fidelity EGRA. We also show the effect of
using a priori drawn Monte Carlo samples in the implementation for the acoustic
horn problem, where mfEGRA leads to computational savings of 45% for the
three-dimensional case and 48% for a rarer event four-dimensional case as
compared to single-fidelity EGRA
Rank-based optimal tests of the adequacy of an elliptic VARMA model
We are deriving optimal rank-based tests for the adequacy of a vector
autoregressive-moving average (VARMA) model with elliptically contoured
innovation density. These tests are based on the ranks of pseudo-Mahalanobis
distances and on normed residuals computed from Tyler's [Ann. Statist. 15
(1987) 234-251] scatter matrix; they generalize the univariate signed rank
procedures proposed by Hallin and Puri [J. Multivariate Anal. 39 (1991) 1-29].
Two types of optimality properties are considered, both in the local and
asymptotic sense, a la Le Cam: (a) (fixed-score procedures) local asymptotic
minimaxity at selected radial densities, and (b) (estimated-score procedures)
local asymptotic minimaxity uniform over a class F of radial densities.
Contrary to their classical counterparts, based on cross-covariance matrices,
these tests remain valid under arbitrary elliptically symmetric innovation
densities, including those with infinite variance and heavy-tails. We show that
the AREs of our fixed-score procedures, with respect to traditional (Gaussian)
methods, are the same as for the tests of randomness proposed in Hallin and
Paindaveine [Bernoulli 8 (2002b) 787-815]. The multivariate serial extensions
of the classical Chernoff-Savage and Hodges-Lehmann results obtained there thus
also hold here; in particular, the van der Waerden versions of our tests are
uniformly more powerful than those based on cross-covariances. As for our
estimated-score procedures, they are fully adaptive, hence, uniformly optimal
over the class of innovation densities satisfying the required technical
assumptions.Comment: Published at http://dx.doi.org/10.1214/009053604000000724 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
High-dimensional change-point detection with sparse alternatives
We consider the problem of detecting a change in mean in a sequence of
Gaussian vectors. Under the alternative hypothesis, the change occurs only in
some subset of the components of the vector. We propose a test of the presence
of a change-point that is adaptive to the number of changing components. Under
the assumption that the vector dimension tends to infinity and the length of
the sequence grows slower than the dimension of the signal, we obtain the
detection boundary for this problem and prove its rate-optimality
Pointwise adaptive estimation for robust and quantile regression
A nonparametric procedure for robust regression estimation and for quantile
regression is proposed which is completely data-driven and adapts locally to
the regularity of the regression function. This is achieved by considering in
each point M-estimators over different local neighbourhoods and by a local
model selection procedure based on sequential testing. Non-asymptotic risk
bounds are obtained, which yield rate-optimality for large sample asymptotics
under weak conditions. Simulations for different univariate median regression
models show good finite sample properties, also in comparison to traditional
methods. The approach is extended to image denoising and applied to CT scans in
cancer research
Spatial aggregation of local likelihood estimates with applications to classification
This paper presents a new method for spatially adaptive local (constant)
likelihood estimation which applies to a broad class of nonparametric models,
including the Gaussian, Poisson and binary response models. The main idea of
the method is, given a sequence of local likelihood estimates (``weak''
estimates), to construct a new aggregated estimate whose pointwise risk is of
order of the smallest risk among all ``weak'' estimates. We also propose a new
approach toward selecting the parameters of the procedure by providing the
prescribed behavior of the resulting estimate in the simple parametric
situation. We establish a number of important theoretical results concerning
the optimality of the aggregated estimate. In particular, our ``oracle'' result
claims that its risk is, up to some logarithmic multiplier, equal to the
smallest risk for the given family of estimates. The performance of the
procedure is illustrated by application to the classification problem. A
numerical study demonstrates its reasonable performance in simulated and
real-life examples.Comment: Published in at http://dx.doi.org/10.1214/009053607000000271 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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