arXiv
(422,153 recursos)
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Mostrando recursos 61 - 80 de 110
61.
Multilayer Perceptron with Functional Inputs: an Inverse Regression
Approach - Ferré, Louis; Villa, Nathalie
Functional data analysis is a growing research field as more and more
practical applications involve functional data. In this paper, we focus on the
problem of regression and classification with functional predictors: the model
suggested combines an efficient dimension reduction procedure [functional
sliced inverse regression, first introduced by Ferr\'e & Yao (Statistics, 37,
2003, 475)], for which we give a regularized version, with the accuracy of a
neural network. Some consistency results are given and the method is
successfully confronted to real-life data.
62.
Forward stagewise regression and the monotone lasso - Hastie, Trevor; Taylor, Jonathan; Tibshirani, Robert; Walther, Guenther
We consider the least angle regression and forward stagewise algorithms for
solving penalized least squares regression problems. In Efron, Hastie,
Johnstone & Tibshirani (2004) it is proved that the least angle regression
algorithm, with a small modification, solves the lasso regression problem. Here
we give an analogous result for incremental forward stagewise regression,
showing that it solves a version of the lasso problem that enforces
monotonicity. One consequence of this is as follows: while lasso makes optimal
progress in terms of reducing the residual sum-of-squares per unit increase in
$L_1$-norm of the coefficient $\beta$, forward stage-wise is optimal per unit
$L_1$ arc-length traveled along the coefficient path. We also...
63.
Needlet algorithms for estimation in inverse problems - Kerkyacharian, Gérard; Petrushev, Pencho; Picard, Dominique; Willer, Thomas
We provide a new algorithm for the treatment of inverse problems which
combines the traditional SVD inversion with an appropriate thresholding
technique in a well chosen new basis. Our goal is to devise an inversion
procedure which has the advantages of localization and multiscale analysis of
wavelet representations without losing the stability and computability of the
SVD decompositions. To this end we utilize the construction of localized frames
(termed "needlets") built upon the SVD bases. We consider two different
situations: the "wavelet" scenario, where the needlets are assumed to behave
similarly to true wavelets, and the "Jacobi-type" scenario, where we assume
that the properties of the frame truly depend...
64.
The Dagum family of isotropic correlation functions - Berg, Christian; Mateu, Jorge; Porcu, Emilio
A function $\rho: [0, \infty) \to (0,1]$ is a completely monotonic function
if and only if $\rho(||\xx||^2)$ is positive definite on $\RR^d$ for all $d$,
and thus it represents the correlation function of a weakly stationary and
isotropic Gaussian random field. Radial positive definite functions are also of
importance as they represent the characteristic function of spherically
symmetric probability distributions.In this paper we analyse the function $$
\rho(\b,\gamma)(x)=1-(\frac{x^\b}{1+x^\b})^\gamma,\quad x\ge 0, \qquad \beta,
\gamma >0 $$ called the Dagum function (\cite{Porcu}), and show those ranges
for which this function is completely monotonic, that is positive definite on
any $d$-dimensional Euclidean space. Important relations arise with other
families of completely monotonic and...
65.
Change point estimation for the telegraph process observed at discrete
times - De Gregorio, Alessandro; Iacus, Stefano M.
The telegraph process models a random motion with finite velocity and it is
usually proposed as an alternative to diffusion models. The process describes
the position of a particle moving on the real line, alternatively with constant
velocity $+ v$ or $-v$. The changes of direction are governed by an homogeneous
Poisson process with rate $\lambda >0.$ In this paper, we consider a change
point estimation problem for the rate of the underlying Poisson process by
means of least squares method. The consistency and the rate of convergence for
the change point estimator are obtained and its asymptotic distribution is
derived. Applications to real data are also presented.
66.
Inflated Beta Distributions - Ospina, Raydonal; Ferrari, Silvia L. P.
This paper considers the issue of modeling fractional data observed in the
interval [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are
proposed. The beta distribution is used to describe the continuous component of
the model since its density can have quite diferent shapes depending on the
values of the two parameters that index the distribution. Properties of the
proposed distributions are examined. Also, maximum likelihood and method of
moments estimation is discussed. Finally, practical applications that employ
real data are presented.
67.
Statistical minimax approach of the Hausdorff moment problem - Ngoc, Thanh Mai Pham
The purpose of this paper is to study the problem of estimating a compactly
supported density of probability from noisy observations of its moments. In
fact, we provide a statistical approach to the famous Hausdorff classical
moment problem. We prove an upper bound and a lower bound on the rate of
convergence of the mean squared error showing that the considered estimator
attains minimax rate over the corresponding smoothness classes.
68.
Diffusion covariation and co-jumps in bidimensional asset price
processes with stochastic volatility and infinite activity Levy jumps - Gobbi, Fabio; Mancini, Cecilia
In this paper we consider two processes driven by diffusions and jumps. The
jump components are Levy processes and they can both have finite activity and
infinite activity. Given discrete observations we estimate the covariation
between the two diffusion parts and the co-jumps. The detection of the co-jumps
allows to gain insight in the dependence structure of the jump components and
has important applications in finance. Our estimators are based on a threshold
principle allowing to isolate the jumps. This work follows Gobbi and Mancini
(2006) where the asymptotic normality for the estimator of the covariation,
with convergence speed given by the squared root of h, was obtained...
69.
Causal inference in longitudinal studies with history-restricted
marginal structural models - Neugebauer, Romain; van der Laan, Mark J.; Joffe, Marshall M.; Tager, Ira B.
A new class of Marginal Structural Models (MSMs), History-Restricted MSMs
(HRMSMs), was recently introduced for longitudinal data for the purpose of
defining causal parameters which may often be better suited for public health
research or at least more practicable than MSMs \citejoffe,feldman. HRMSMs
allow investigators to analyze the causal effect of a treatment on an outcome
based on a fixed, shorter and user-specified history of exposure compared to
MSMs. By default, the latter represent the treatment causal effect of interest
based on a treatment history defined by the treatments assigned between the
study's start and outcome collection. We lay out in this article the formal
statistical framework behind HRMSMs....
70.
Titre : Estimating High dimensional faithful Gaussian graphical Models :
uPC-algorithm - Malouche, Dhafer; Sevestre-Ghalila, Sylvie
When the number of variables $p$ is larger than the sample size $n$ of a
dataset generated from a Gaussian Graphical Model, the maximum likelihood
estimation of the precision matrix does not exist. To circumvent this
difficulty, in \cite{WiBu}, the authors assume a \textit{faithful} property on
the models and propose a procedure based on conditioning on only one variable.
The aim of this paper is to devise a new PC-algorithm (\textit{partial
correlation}), uPC-algorithm, for estimating a high dimension undirected graph
associated to a \textit{faithful} Gaussian Graphical Model. First, we define
the \textit{separability order} of a graph as the maximum cardinality among all
its minimal separators. We construct a sequence...
71.
Universality results for largest eigenvalues of some sample covariance
matrix ensembles - Peche, Sandrine
For sample covariance matrices with iid entries with sub-Gaussian tails, when
both the number of samples and the number of variables become large and the
ratio approaches to one, it is a well-known result of A. Soshnikov that the
limiting distribution of the largest eigenvalue is same as the of Gaussian
samples. In this paper, we extend this result to two cases. The first case is
when the ratio approaches to an arbitrary finite value. The second case is when
the ratio becomes infinity or arbitrarily small.
72.
Recursive Parameter Estimation: Convergence - Sharia, Teo
We consider estimation procedures which are recursive in the sense that each
successive estimator is obtained from the previous one by a simple adjustment.
We propose a wide class of recursive estimation procedures for the general
statistical model and study convergence.
73.
Rate of Convergence in Recursive Parameter Estimation procedures - Sharia, Teo
We consider estimation procedures which are recursive in the sense that each
successive estimator is obtained from the previous one by a simple adjustment.
We study rate of convergence of recursive estimation procedures for the general
statistical model.
74.
Recursive Parameter Estimation: Asymptotic expansion - Sharia, Teo
We consider estimation procedures which are recursive in the sense that each
successive estimator is obtained from the previous one by a simple adjustment.
The model considered in the paper is very general as we do not impose any
preliminary restrictions on the probabilistic nature of the observation process
and cover a wide class of nonlinear recursive procedures. In this paper we
study asymptotic behaviour of the recursive estimators. The results of the
paper can be used to determine the form of a recursive procedure which is
expected to have the same asymptotic properties as the corresponding
non-recursive one defined as a solution of the corresponding estimating
equation.
75.
Semimartingale Stochastic Approximation Procedures and Recursive
Estimation - Lazrieva, N.; Sharia, T.; Toronjadze, T.
The semimartingale stochastic approximation procedure, namely, the
Robbins-Monro type SDE is introduced which naturally includes both generalized
stochastic approximation algorithms with martingale noises and recursive
parameter estimation procedures for statistical models associated with
semimartingales. General results concerning the asymptotic behaviour of the
solution are presented. In particular, the conditions ensuring the convergence,
rate of convergence and asymptotic expansion are established. The results
concerning the Polyak weighted averaging procedure are also presented.
76.
Linear Prediction of Long-Memory Processes: Asymptotic Results on
Mean-squared Errors - Godet, Fanny
We present two approaches for linear prediction of long-memory time series.
The first approach consists in truncating the Wiener-Kolmogorov predictor by
restricting the observations to the last $k$ terms, which are the only
available values in practice. We derive the asymptotic behaviour of the
mean-squared error as $k$ tends to $ + \infty$. By contrast, the second
approach is non-parametric. An AR($k$) model is fitted to the long-memory time
series and we study the error that arises in this misspecified model.
77.
Dimensional reduction for particle filters of systems with time-scale
separation - Givon, Dror; Stinis, Panagiotis; Weare, Jonathan
We present a particle filter construction for a system that exhibits
time-scale separation. The separation of time-scales allows two simplifications
that we exploit: i) The use of the averaging principle for the dimensional
reduction of the system needed to solve for each particle and ii) the
factorization of the transition probability which allows the
Rao-Blackwellization of the filtering step. Both simplifications can be
implemented using the coarse projective integration framework. The resulting
particle filter is faster and has smaller variance than the particle filter
based on the original system. The convergence of the new particle filter to the
analytical filter for the original system is proved and some numerical...
78.
A Bayesian approach to the estimation of maps between riemannian
manifolds - Butler, Leo T.; Levit, Boris
Let \Theta be a smooth compact oriented manifold without boundary, embedded
in a euclidean space and let \gamma be a smooth map \Theta into a riemannian
manifold \Lambda. An unknown state \theta \in \Theta is observed via
X=\theta+\epsilon \xi where \epsilon>0 is a small parameter and \xi is a white
Gaussian noise. For a given smooth prior on \Theta and smooth estimator g of
the map \gamma we derive a second-order asymptotic expansion for the related
Bayesian risk. The calculation involves the geometry of the underlying spaces
\Theta and \Lambda, in particular, the integration-by-parts formula. Using this
result, a second-order minimax estimator of \gamma is found based on...
79.
Sample eigenvalue based detection of high dimensional signals in white
noise using relatively few samples - Rao, N. Raj; Edelman, Alan
We present a mathematically justifiable, computationally simple, sample
eigenvalue based procedure for estimating the number of high-dimensional
signals in white noise using relatively few samples. The main motivation for
considering a sample eigenvalue based scheme is the computational simplicity
and the robustness to eigenvector modelling errors which are can adversely
impact the performance of estimators that exploit information in the sample
eigenvectors.
There is, however, a price we pay by discarding the information in the sample
eigenvectors; we highlight a fundamental asymptotic limit of sample eigenvalue
based detection of weak/closely spaced high-dimensional signals from a limited
sample size. This motivates our heuristic definition of the effective number of
identifiable signals...
80.
Asymptotics for Duration-Driven Long Range Dependent Processes - Hsieh, Meng-Chen; Hurvich, Clifford M.; Soulier, Philippe
We consider processes with second order long range dependence resulting from
heavy tailed durations. We refer to this phenomenon as duration-driven long
range dependence (DDLRD), as opposed to the more widely studied linear long
range dependence based on fractional differencing of an $iid$ process. We
consider in detail two specific processes having DDLRD, originally presented in
Taqqu and Levy (1986), and Parke (1999). For these processes, we obtain the
limiting distribution of suitably standardized discrete Fourier transforms
(DFTs) and sample autocovariances. At low frequencies, the standardized DFTs
converge to a stable law, as do the standardized sample autocovariances at
fixed lags. Finite collections of standardized sample autocovariances at a
fixed...
61.
