Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sat, 19 Oct 2019 17:23:48 GMT2019-10-19T17:23:48Z50221Large deviations for the empirical mean of associated random variableshttp://hdl.handle.net/10316/4590Title: Large deviations for the empirical mean of associated random variables
Authors: Henriques, Carla; Oliveira, Paulo Eduardo
Abstract: We find conditions under which the sequence of empirical means of associated random variables, , satisfies the large deviation principle.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/45902008-01-01T00:00:00ZConvergence rates for the estimation of two-dimensional distribution functions under association and estimation of the covariance of the limit empirical processhttp://hdl.handle.net/10316/8982Title: Convergence rates for the estimation of two-dimensional distribution functions under association and estimation of the covariance of the limit empirical process
Authors: Henriques, Carla; Oliveira, Paulo Eduardo
Abstract: Let Xn, n=1, be an associated and strictly stationary sequence of random variables, having marginal distribution function F. The limit in distribution of the empirical process, when it exists, is a centred Gaussian process with covariance function depending on terms of the form ?k(s, t)=P(X1 s, Xk+1 t)-F(s)F(t). We prove the almost sure consistency for the histogram to estimate each ?k and also to estimate the covariance function of the limit empirical process, identifying, for both, uniform almost sure convergence rates. The convergence rates depend on a suitable version of an exponential inequality. The rates obtained, assuming the covariances to decrease geometrically, are of order n-1/3log2/3nfor the estimator of ?k and of order n-1/3log5/3nfor the estimator of the covariance function.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/89822006-01-01T00:00:00ZCovariance of the limit empirical process under association: consistency and rates for the histogramhttp://hdl.handle.net/10316/11430Title: Covariance of the limit empirical process under association: consistency and rates for the histogram
Authors: Henriques, Carla; Oliveira, Paulo Eduardo
Abstract: The empirical process induced by a sequence of associated random variables
has for limit in distribution a centered Gaussian process with covariance function
defined by an infinite sum of terms of the form .k(s, t) = P(X1 . s,Xk+1 . t).
F(s)F(t). We study the estimation of such series using the histogram estimator.
Under a convenient decrease rate on the covariance structure of the variables we
prove the strong consistency with rates, pointwise and uniformly, of the estimator
of the covariance of the limit empirical process. We also study the estimation of the
eigenvalues of the integral operator defined by this limit covariance function. The
knowledge of these eigenvalues is relevant for the characterization of tail probabilities
of some functionals of the empirical process. We approximate the eigenvalues
by those of the integral operator defined by the estimator of the limit covariances
and prove, under the same assumptions as for the estimation of this covariance, the
strong consistency of such estimators, with rates.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/114302003-01-01T00:00:00ZExponential rates for kernal density estimation under associationhttp://hdl.handle.net/10316/11445Title: Exponential rates for kernal density estimation under association
Authors: Henriques, Carla; Oliveira, Paulo Eduardo
Abstract: The estimation of density based on positive dependent samples has been studied recently
with consistency and asymptotic normality results being obtained. In what concerns the
characterization on decrease rates the results have been scarce. The article proves an exponential
decrease rate for the kernel estimator of the density with an uniform version, over compact sets.
The conditions assumed impose convenient decrease rates on the covariance structure of the sample.
Some examples supposing exponential but also polynomial decrease rates on the covariances that
fulfill our assumptions are presented in the last section.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10316/114452002-01-01T00:00:00ZBivariante distribution function estimation for associated variableshttp://hdl.handle.net/10316/11474Title: Bivariante distribution function estimation for associated variables
Authors: Azevedo, Cecília; Oliveira, Paulo Eduardo
Abstract: The estimation of distribution functions of pairs of associated variables is addressed based on
a kernel estimator. This problem is motivated by the need to approximate covariance functions
appearing as the limiting covariances of the empirical process sequence. Results characterizing
the asymptotics and convergence rates of the estimator are obtained. From these we derive
the optimal bandwidth convergence rate, which is of order n-1 . Finally, we give conditions
for the asymptotic normality of the finite dimensional distributions, characterizing their limit
covariance matrix. Besides some usual conditions on the kernel function, the conditions typically
impose a convenient decrease rate on the covariances Cov(X1 , X n ).
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10316/114742000-01-01T00:00:00ZAlmost optimal convergence rates for kernel density estimation under associationhttp://hdl.handle.net/10316/11422Title: Almost optimal convergence rates for kernel density estimation under association
Authors: Henriques, Carla; Oliveira, Paulo Eduardo
Abstract: Exponential inequalities for associated variables are derived under an
assumption milder than the absolute continuity of joint distributions of the sample
variables. This inequality is used to prove convergence rates for the kernel estimator
for the density which are just slightly slower than the optimal rates known form
independent samples.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10316/114222004-01-01T00:00:00ZMean square error for histograms when estimating Radon-Nikodym derivativeshttp://hdl.handle.net/10316/11227Title: Mean square error for histograms when estimating Radon-Nikodym derivatives
Authors: Oliveira, Paulo Eduardo
Abstract: The use of histograms for estimation of Radon-Nikodym derivatives is addressed. Some
results concerning the convergence have been established with no reference about the behaviour
of the error. In this paper we study the mean square convergence rate of this error. The
optimization of the partitions thus obtained recovers the n -2/3 rate known for some problems
that are included in this more general framework.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/10316/112271998-01-01T00:00:00ZCovariance estimator for associated random variableshttp://hdl.handle.net/10316/11562Title: Covariance estimator for associated random variables
Authors: Henriques, Carla; Oliveira, Paulo Eduardo
Abstract: Considering an associated and strictly stationary sequence of random variables we introduce an histogram estimator for the covariances between indicator functions of those random
variables. We find conditions on the covariance structure of the original random variables for
the almost sure convergence of the estimator and for the convergence in distribution of the
finite dimensional distributions. Finally we characterize the usual error criteria finding their
convergence rates under assumptions on the convergence rate of the covariances
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10316/115621999-01-01T00:00:00ZConvergence rates for the strong law of large numbers under associationhttp://hdl.handle.net/10316/11262Title: Convergence rates for the strong law of large numbers under association
Authors: Henriques, Carla; Oliveira, Paulo Eduardo
Abstract: We prove convergence rates for the Strong Laws of Large Numbers
(SLLN) for associated variables which are arbitrarily close to the optimal rates for
independent variables. A rst approach is based on exponential inequalities, a usual
tool for this kind of problems. Following the optimization e orts of several authors,
we improve the rates derived from exponential inequalities to log2 n
n1=2 . A more recent
approach tries to use maximal inequalities together with moment inequalities. We
prove a new maximal order inequality of order 4 for associated variables, using a
telescoping argument. This inequality is then used to prove a SLLN convergence
rate arbitrarily close to log1=4 n
n1=2 .
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10316/112622008-01-01T00:00:00ZHistograms and associated point processeshttp://hdl.handle.net/10316/11228Title: Histograms and associated point processes
Authors: Jacob, Pierre; Oliveira, Paulo Eduardo
Abstract: Non parametric inference for point processes is approached using histograms, which provide a
nice tool for the analysis of on-line data. The construction of histograms depend on a sequence of
partitions, which we take to be non embedded. This is quite natural in what regards applications,
but presents some theoretical problems. On another direction, we drop the usual independence
assumption on the sample, replacing it by an association hypothesis. Under this setting, we
study the convergence of the histogram, in probability and almost surely, finding conditions on
the covariance structure, which is well known to be the determinant factor under association, to
ensure the convergence. On the final section we look at the similar question regarding the finite
dimensional distributions, proving a convergence in distribution to a gaussian centered vector
with a covariance we can describe. The main tool of analysis will be a decomposition of second
order moment measures.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/10316/112281998-01-01T00:00:00ZA central limit theorem for associated variableshttp://hdl.handle.net/10316/11226Title: A central limit theorem for associated variables
Authors: Oliveira, Paulo Eduardo
Abstract: Using a coupling technique we prove a Central Limit Theorem for associated random variables supposing only the existence of moments of second order, and assumptions that imply
some sort of weak stationarity. Supposing the existence of absolute moments of order 3 and
without any stationarity condition, we derive a convergence rate, based on a convenient version
of the classical Berry-Esséen inequality.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/10316/112261998-01-01T00:00:00ZPenalized smoothing of sparse tableshttp://hdl.handle.net/10316/11310Title: Penalized smoothing of sparse tables
Authors: Jacob, Pierre; Oliveira, Paulo Eduardo
Abstract: In models using categorical data one may use some adjacency relations
to justify the use of smoothing to improve upon simple histogram approximations of
the probabilities. This is particularly convenient when in presence of a sparse number
of observations. Moreover, in many models, the prior knowledge of a marginal
distribution is available. We propose two families of polynomial smoothers that
incorporate this marginal information into the estimates. Besides, one of the family,
the penalized polynomial smoothers, corrects the well known drawback of the
polynomial smoothers of producing negative approximations. A simulation study
show a good performance of the proposed estimators with respect to usual error
criteria. Our estimators, and particularly the penalized family, perform especially
well for sparse situations.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10316/113102007-01-01T00:00:00ZLocal smoothing with given marginalshttp://hdl.handle.net/10316/13705Title: Local smoothing with given marginals
Authors: Jacob, Pierre; Oliveira, Paulo Eduardo
Abstract: In models using categorical data one may use adjacency relations to
justify smoothing to improve upon simple histogram approximations of the probabilities.
This is particularly convenient for sparsely observed or rather peaked
distributions. Moreover, in a few models, prior knowledge of a marginal distribution
is available. We adapt local polynomial estimators to include this partial
information about the underlying distribution and give explicit representations for
the proposed estimators. An application to a set of anthropological data is included.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/137052010-01-01T00:00:00ZOptimal convergence rates for the Strong Law of Large Numbers under Associationhttp://hdl.handle.net/10316/13702Title: Optimal convergence rates for the Strong Law of Large Numbers under Association
Authors: Oliveira, Paulo Eduardo
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10316/137022010-01-01T00:00:00ZPenalized smoothing of discrete distributions with sparse observationshttp://hdl.handle.net/10316/11342Title: Penalized smoothing of discrete distributions with sparse observations
Authors: Jacob, Pierre; Oliveira, Paulo Eduardo
Abstract: It happens quite often that we are faced with a sparse number of observations
over a finite number of cells and we are interested in the estimation of
the cell probabilities. The simple histogram produces approximations with the zero
value for too many cells. Some polynomial smoothers have been proposed to circumvent
this problem which show good properties in the analysis of such sparse
situations but have the drawback of producing negative values. We propose a penalized
polynomial smoothing for this problem. The estimators that are proposed
in this paper are always positive and a simulation study show a very good behaviour
with respect to the natural error criterias: mean squared sum of errors, sparse sup
and the sup-norm. Our estimator perform specially well for sparse observations.
Nevertheless, when the number of observations increases the proposed estimators
still show good performance
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10316/113422006-01-01T00:00:00ZNonparametric density and regression estimation for functional datahttp://hdl.handle.net/10316/11391Title: Nonparametric density and regression estimation for functional data
Authors: Oliveira, Paulo Eduardo
Abstract: We consider kernel estimation of density and regression based on functional
data. We prove the strong convergence and the asymptotic normality of the
centered estimators. We include results both for independent and mixing data, as
the mathematical treatment and conditions for convergence are different.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/113912005-01-01T00:00:00ZAn exponential inequality for associated variableshttp://hdl.handle.net/10316/4625Title: An exponential inequality for associated variables
Authors: Oliveira, Paulo Eduardo
Abstract: We prove an exponential inequality for positively associated and strictly stationary random variables replacing an uniform boundedness assumption by the existence of Laplace transforms. The proof uses a truncation technique together with a block decomposition of the sums to allow an approximation to independence. We show that for geometrically decreasing covariances our conditions are fulfilled, identifying a convergence rate for the strong law of large numbers.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10316/46252005-01-01T00:00:00ZDensity estimation for associated sampling: a point process influenced approachhttp://hdl.handle.net/10316/11461Title: Density estimation for associated sampling: a point process influenced approach
Authors: Oliveira, Paulo Eduardo
Abstract: Let Xn, n E¸ IN, be a sequence of associated variables with common density function. We
study the kernel estimation of this density, based on the given sequence of variables. Sufficient
conditions are given for the consistency and asymptotic normality of the kernel estimator. The
assumptions made require that the distribution of pairs (Xi,Xj) decompose as the sum of an
absolutely continuous measure with another measure concentrated on the diagonal of IR ~ IR
satisfying a further absolute continuity with respect to the Lebesgue measure on this diagonal.
For the convergence in probability we find the usual convergence rate on the bandwidth, whereas
for the almost sure convergence we need to require that the bandwidth does not decrease to fast
and that the kernel is of bounded variation. This assumption on the kernel is also required for
the asymptotic normality, together with a slightly strengthened version of the usual decrease
rate on the bandwidth. The assumption of bounded variation on the kernel is needed as a
consequence of the dependence structure we are dealing with, as association is only preserved
by monotone transformations.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10316/114612001-01-01T00:00:00ZOn proportional reversed failure rate classhttp://hdl.handle.net/10316/30343Title: On proportional reversed failure rate class
Authors: Oliveira, Paulo Eduardo; Torrado, Nuria
Abstract: Motivated by the recent use of the proportional reversed failure rate in economics (rates of increase and elasticity, see Veres-Ferrer and Pavia (Stat Pap 55:275–284, 2014) and in reliability (stochastic comparisons among systems, see Khaledi et al. (J Stat Plan Inference 141:276–286, 2011), in this work, we investigate characterizations and closure properties of the decreasing proportional reversed failure rate (DPRFR) classes for continuous, nonnegative random variables. Among others, we prove that DPRFR distributions are closed under convolutions. In addition, we relate this class of distributions with the class of monotone failure rate, proportional failure rate and likelihood ratio distributions.
Sun, 01 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10316/303432015-11-01T00:00:00ZStrong laws for associated random variableshttp://hdl.handle.net/10316/43681Title: Strong laws for associated random variables
Authors: Çağın, Tonguç; Oliveira, Paulo Eduardo
Abstract: We study the almost sure convergence and rates of weighted sums of associated random variables under the classical assumption of existence of Laplace transforms. This assumption implies the existence of every moment, so we address the same problem assuming a suitable decrease rate on tail joint probabilities which only implies the existence of finitely many moments, proving the analogous characterizations of convergence and rates. Still relaxing further the assumptions on moment existence, we also prove a Marcinkiewicz-Zygmund for associated variables without means, complementing existing results for this dependence structure.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10316/436812017-01-01T00:00:00ZA moderate deviation for associated random variableshttp://hdl.handle.net/10316/36684Title: A moderate deviation for associated random variables
Authors: Çaǧın, Tonguç; Oliveira, Paulo Eduardo; Torrado, Nuria
Abstract: Moderate deviations are an important topic in many theoretical or applied statistical areas.
We prove two versions of a moderate deviation for associated and strictly stationary
random variables with finite moments of order q > 2. The first one uses an assumption
depending on the rate of a Gaussian approximation, while the second one discusses more
natural assumptions to obtain the approximation rate. The control of the dependence
structure relies on the decay rate of the covariances, for which we assume a relatively mild
polynomial decay rate. The proof combines a coupling argument together with a suitable
use of Berry–Esséen bounds.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/366842016-01-01T00:00:00ZHistogram estimation of Radon-Nikodym derivatives for strong mixing datahttp://hdl.handle.net/10316/11552Title: Histogram estimation of Radon-Nikodym derivatives for strong mixing data
Authors: Bensaïd, Nadia; Oliveira, Paulo Eduardo
Abstract: Nonparametric inference for point processes is discussed by way histograms, which provide a
nice tool for the analysis of on-line data. The construction of histograms depends on a sequence
of partitions, which we take to be nonembedded to allow partitions with sets of equal measure.
This presents some theoretical problems, which are addressed with an assumption on the decomposition
of second order moments. In another direction, we drop the usual independence
assumption on the sample, replacing it by a strong mixing assumption. Under this setting, we
study the convergence of the histogram in probability, which depends on approximation conditions
between the distributions of random pairs and the product of their marginal distributions,
and almost completely, which is based on the decomposition of the second order moments. This
last convergence is stated on two versions according to the assumption of Laplace transforms
or the Cramer moment conditions. These are somewhat stronger, bet enable us to recover the
usual condition on the decrease rate of sets on each partition. In the final section we prove that
the finite dimensional distributions converge in distribution to a gaussian centered vector with
a specified covariance
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10316/115521999-01-01T00:00:00Z