Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 09 Dec 2022 16:39:04 GMT2022-12-09T16:39:04Z5051Histograms and Associated Point Processeshttp://hdl.handle.net/10316/7759Title: Histograms and Associated Point Processes
Authors: Jacob, Pierre; Oliveira, Paulo
Abstract: 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. This is quite natural in what regards applications, but presents some theoretical problems. In another direction, we drop the usual independence assumption on the sample, replacing it by an association assumption. Under this setting, we study the convergence of the histogram, in probability and almost surely which, under association, depends on conditions on the covariance structure. In the final section we prove that the finite dimensional distributions converge in distribution to a Gaussian centered vector with a specified covariance. The main tool of analysis is a decomposition of second order moment measures.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10316/77591999-01-01T00:00:00ZLocal 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/10316/137052010-01-01T00:00:00ZPenalized 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/10316/113422006-01-01T00:00:00ZPenalized 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/10316/113102007-01-01T00:00:00ZHistograms 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/10316/112281998-01-01T00:00:00Z