arXiv
(422,153 recursos)
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Mostrando recursos 81 - 100 de 110
81.
Small time Edgeworth-type expansions for weakly convergent
nonhomogeneous Markov chains - Konakov, Valentin; Mammen, Enno
We consider triangular arrays of Markov chains that converge weakly to a
diffusion process. Second order Edgeworth type expansions for transition
densities are proved. The paper differs from recent results in two respects. We
allow nonhomogeneous diffusion limits and we treat transition densities with
time lag converging to zero. Small time asymptotics are motivated by
statistical applications and by resulting approximations for the joint density
of diffusion values at an increasing grid of points.
82.
Sparsity oracle inequalities for the Lasso - Bunea, Florentina; Tsybakov, Alexandre; Wegkamp, Marten
This paper studies oracle properties of $\ell_1$-penalized least squares in
nonparametric regression setting with random design. We show that the penalized
least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in
terms of the number of non-zero components of the oracle vector. The results
are valid even when the dimension of the model is (much) larger than the sample
size and the regression matrix is not positive definite. They can be applied to
high-dimensional linear regression, to nonparametric adaptive regression
estimation and to the problem of aggregation of arbitrary estimators.
83.
Deconvolution with unknown error distribution - Johannes, J.
We consider the problem of estimating a density $f_{X}$ using a sample
$Y_{1},...,Y_{n}$ from $f_{Y}=f_{X}*f_{\epsilon}$, where $f_{\epsilon}$ is an
unknown density function. We assume that an additional sample
$\epsilon_{1},...,\epsilon_{m}$ from $f_{\epsilon}$ is given. Estimators of
$f_{X}$ and its derivatives are constructed using nonparametric estimators of
$f_{Y}$ and $f_{\epsilon}$ and applying a spectral cut-off in the Fourier
domain. In this paper the rate of convergence of the estimator is derived in
the case of a known and an unknown density $f_{\epsilon}$ assuming that $f_{X}$
belongs to a Sobolev space $H_{p}$ and that the Fourier transform of
$f_{\epsilon}$ descents polynomial, exponential or in some general form. It is
shown that the proposed...
84.
Orthogonal arrays from Hermitian varieties - Aguglia, A.; Giuzzi, L.
An orthogonal array OA(q^{2n-1},q^{2n-2}, q,2) is constructed from the action
of a subset of PGL(n+1,q^2) on some non--degenerate Hermitian varieties in
PG(n,q^2). It is also shown that the rows of this orthogonal array correspond
to some blocks of an affine design, which for q> 2 is a non--classical model of
the affine space AG(2n-1,q).
85.
Fast computation by block permanents of cumulative distribution
functions of order statistics from several populations - Glueck, Deborah H.; Karimpour-Fard, Anis; Mandel, Jan; Hunter, Larry; Muller, Keith E.
The joint cumulative distribution function for order statistics arising from
several different populations is given in terms of the distribution function of
the populations. The computational cost of the formula in the case of two
populations is still exponential in the worst case, but it is a dramatic
improvement compared to the general formula by Bapat and Beg. In the case when
only the joint distribution function of a subset of the order statistics of
fixed size is needed, the complexity is polynomial, for the case of two
populations.
86.
Efficient independent component analysis - Chen, Aiyou; Bickel, Peter J.
Independent component analysis (ICA) has been widely used for blind source
separation in many fields such as brain imaging analysis, signal processing and
telecommunication. Many statistical techniques based on M-estimates have been
proposed for estimating the mixing matrix. Recently several nonparametric
methods have been developed but in-depth analysis on asymptotic efficiency has
not been available. We analyze ICA using semiparametric theories and propose a
straightforward estimate based on the efficient score function by using
B-spline approximations. The estimate is asymptotically efficient under
moderate conditions and exhibits better performance than standard ICA methods
in a variety of simulations.
87.
Learning about a Categorical Latent Variable under Prior Near-Ignorance - Piatti, Alberto; Zaffalon, Marco; Trojani, Fabio; Hutter, Marcus
It is well known that complete prior ignorance is not compatible with
learning, at least in a coherent theory of (epistemic) uncertainty. What is
less widely known, is that there is a state similar to full ignorance, that
Walley calls near-ignorance, that permits learning to take place. In this paper
we provide new and substantial evidence that also near-ignorance cannot be
really regarded as a way out of the problem of starting statistical inference
in conditions of very weak beliefs. The key to this result is focusing on a
setting characterized by a variable of interest that is latent. We argue that
such a setting is by far...
88.
Network tomography based on 1-D projections - Chen, Aiyou; Cao, Jin
Network tomography has been regarded as one of the most promising
methodologies for performance evaluation and diagnosis of the massive and
decentralized Internet. This paper proposes a new estimation approach for
solving a class of inverse problems in network tomography, based on marginal
distributions of a sequence of one-dimensional linear projections of the
observed data. We give a general identifiability result for the proposed method
and study the design issue of these one dimensional projections in terms of
statistical efficiency. We show that for a simple Gaussian tomography model,
there is an optimal set of one-dimensional projections such that the estimator
obtained from these projections is asymptotically as efficient...
89.
Multiple solutions to the likelihood equations in the Behrens-Fisher
problem - Drton, Mathias
The Behrens-Fisher problem concerns testing the equality of the means of two
normal populations with possibly different variances. The null hypothesis in
this problem induces a statistical model for which the likelihood function may
have more than one local maximum. We show that such multimodality contradicts
the null hypothesis in the sense that if this hypothesis is true then the
probability of multimodality converges to zero when both sample sizes tend to
infinity. Additional results include a finite-sample bound on the probability
of multimodality under the null and asymptotics for the probability of
multimodality under the alternative.
90.
Total singular value decomposition. Robust SVD, regression and
location-scale - Rey, William
Singular Value Decomposition (SVD) is the basic body of many statistical
algorithms and few users question whether SVD is properly handling its job.
SVD aims at evaluating the decomposition that best approximates a data
matrix, given some rank restriction. However often we are interested in the
best components of the decomposition rather than in the best approximation .
This conflict of objectives leads us to introduce {\em Total SVD}, where the
word "Total" is taken as in "Total" least squares.
SVD is a least squares method and, therefore, is very sensitive to gross
errors in the data matrix. We make SVD robust by imposing a weight...
91.
The M-estimator in a multi-phase random nonlinear model - Ciuperca, Gabriela
We consider a multi-phase random regression model, discontinuous in each
change-point, with an arbitrary error $\epsilon$. In the case that the number
of jumps is known, the M-estimator for the locations of the jumps and for the
coefficient parameters are studied. These estimators are consistent and the
distribution for the estimators of the coefficients is Gaussian. The estimators
of the change-points converge, with the rate $n^{-1}$, to the smallest
minimizer of the independent compound Poisson processes.
92.
False discovery rate control with multivariate p-values - Chi, Zhiyi
In multiple testing, hypotheses can often be assessed by multivariate test
statistics. We study how to use such statistics to control false discovery rate
(FDR) with reasonable power and capacity to control the so-called positive FDR
(pFDR). We show that this can be done by using nested regions of multivariate
p-values derived from the test statistics. If the distributions of the test
statistics are known, then, by choosing the regions appropriately, the FDR can
be controlled while the power is maximized. Our focus, however, is how to
select nested regions when the distributions of the test statistics are only
partially known. Under certain conditions, the procedure based on...
93.
Central limit theorems in linear structural error-in-variables models
with explanatory variables in the domain of attraction of the normal law - Martsynyuk, Yuliya V.
Linear structural error-in-variables models with univariate observations are
revisited for studying modified least squares estimators of the slope and
intercept. New marginal central limit theorems (CLT's) are established for
these estimators, assuming the existence of four moments for the measurement
errors and that the explanatory variables are in the domain of attraction of
the normal law. The latter condition for the explanatory variables is used the
first time, and is so far the most general in this context. It is also optimal,
or nearly optimal, for our CLT's. Moreover, due to the obtained CLT's being in
Studentized and self-normalized forms to begin with, they are a priori nearly,
or...
94.
Adaptive Optimal Nonparametric Regression and Density Estimation Based
on Fourier-Legendre Expansion - Ostrovsky, E.; Zelikov, correspondent author; Y.
Motivated by finance and technical applications, the objective of this paper
is to consider adaptive estimation of regression and density distribution based
on Fourier-Legendre expansion, and construction of confidence intervals - also
adaptive. The estimators are asymptotically optimal and adaptive in the sense
that they can adapt to unknown smoothness.
95.
Additive Regression Model for Continuous Time Processes - Debbarh, Mohammed; Maillot, Bertrand
In the setting of additive regression model for continuous time process, we
establish the optimal uniform convergence rates and optimal asymptotic
quadratic error of additive regression. To build our estimate, we use the
marginal integration method.
96.
Some Uniform Limit Results in Additive Regression Model - Debbarh, Mohammed
We establish some uniform limit results in the setting of additive regression
model estimation. Our results allow to give an asymptotic 100% confidence bands
for these components. These results are stated in the framework of i.i.d random
vectors when the marginal integration estimation method is used.
97.
Bootstrapping confidence intervals for the change-point of time series - Huskova, Marie; Kirch, Claudia
We study an AMOC time series model with an abrupt change in the mean and
dependent errors that fulfill certain mixing conditions. We obtain confidence
intervals for the unknown change-point via bootstrapping methods.
Precisely we use a block bootstrap of the estimated centered error sequence.
Then we reconstruct a sequence with a change in the mean using the same
estimators as before. The difference between the change-point estimator of the
resampled sequence and the one for the original sequence can be use as an
approximation of the difference between the real change-point and its
estimator. This enables us to construct confidence intervals using the
empirical distribution of the...
98.
t-Wise Independence with Local Dependencies - Gradwohl, Ronen; Yehudayoff, Amir
In this note we prove a large deviation bound on the sum of random variables
with the following dependency structure: there is a dependency graph $G$ with a
bounded chromatic number, in which each vertex represents a random variable.
Variables that are represented by neighboring vertices may be arbitrarily
dependent, but collections of variables that form an independent set in $G$ are
$t$-wise independent.
99.
The Explicit Chaotic Representation of the powers of increments of Levy
Processes - Yip, Wing Yan; Stephens, David; Olhede, Sofia
An explicit formula for the chaotic representation of the powers of
increments, (X_{t+t_0}-X_{t_0})^n, of a Levy process is presented. There are
two different chaos expansions of a square integrable functional of a Levy
process: one with respect to the compensated Poisson random measure and the
other with respect to the orthogonal compensated powers of the jumps of the
Levy process. Computationally explicit formulae for both of these chaos
expansions of (X_{t+t_0}-X_{t_0})^n are given in this paper. Simulation results
verify that the representation is satisfactory. The CRP of a number of
financial derivatives can be found by expressing them in terms of
(X_{t+t_0}-X_{t_0})^n using Taylor's expansion.
100.
Concentration of the Spectral Measure for Large Random Matrices with
Stable Entries - Houdré, Christian; Xu, Hua
We derive concentration inequalities for functions of the empirical measure
of large random matrices with infinitely divisible entries and, in particular,
stable ones. We also give concentration results for some other functionals of
these random matrices, such as the largest eigenvalue or the largest singular
value.
81.
