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arXiv (422,153 recursos)
This is one of the most extensive subject based repositories in the world in the field of physics, mathematics, astronomy, computer sciences and quantitative biology. This is the principal site with almost 20 mirror versions around the globe. The site is supported by an extensive collection of information and background documentation. An RSS feed is available for anyone interested in keeping up-to-date with newly added materials.

Mostrando recursos 41 - 60 de 110

41. Sparse Estimators and the Oracle Property, or the Return of Hodges' Estimator - Leeb, Hannes; Poetscher, Benedikt M.
We point out some pitfalls related to the concept of an oracle property as used in Fan and Li (2001, 2002, 2004) which are reminiscent of the well-known pitfalls related to Hodges' estimator. The oracle property is often a consequence of sparsity of an estimator. We show that any estimator satisfying a sparsity property has maximal risk that converges to the supremum of the loss function; in particular, the maximal risk diverges to infinity whenever the loss function is unbounded. For ease of presentation the result is set in the framework of a linear regression model, but generalizes far beyond that setting. In a Monte Carlo study we...

42. Can One Estimate The Unconditional Distribution of Post-Model-Selection Estimators? - Leeb, Hannes; Poetscher, Benedikt M.
We consider the problem of estimating the unconditional distribution of a post-model-selection estimator. The notion of a post-model-selection estimator here refers to the combined procedure resulting from first selecting a model (e.g., by a model selection criterion like AIC or by a hypothesis testing procedure) and then estimating the parameters in the selected model (e.g., by least-squares or maximum likelihood), all based on the same data set. We show that it is impossible to estimate the unconditional distribution with reasonable accuracy even asymptotically. In particular, we show that no estimator for this distribution can be uniformly consistent (not even locally). This follows as a corollary to (local) minimax lower...

43. Theoretical Aspects of the SOM Algorithm - Cottrell, Marie; Fort, Jean-Claude; Pagès, Gilles
The SOM algorithm is very astonishing. On the one hand, it is very simple to write down and to simulate, its practical properties are clear and easy to observe. But, on the other hand, its theoretical properties still remain without proof in the general case, despite the great efforts of several authors. In this paper, we pass in review the last results and provide some conjectures for the future work.

44. Traitement Des Donnees Manquantes Au Moyen De L'Algorithme De Kohonen - Cottrell, Marie; Ibbou, Smail; Letrémy, Patrick
Nous montrons comment il est possible d'utiliser l'algorithme d'auto organisation de Kohonen pour traiter des donn\'ees avec valeurs manquantes et estimer ces derni\`eres. Apr\`es un rappel m\'ethodologique, nous illustrons notre propos \`a partir de trois applications \`a des donn\'ees r\'eelles. ----- We show how it is possible to use the Kohonen self-organizing algorithm to deal with data which contain missing values and to estimate them. After a methodological recall, we illustrate our purpose from three real databases applications.

45. Information-Based Asset Pricing - Brody, Dorje C.; Hughston, Lane P.; Macrina, Andrea
A new framework for asset price dynamics is introduced in which the concept of noisy information about future cash flows is used to derive the price processes. In this framework an asset is defined by its cash-flow structure. Each cash flow is modelled by a random variable that can be expressed as a function of a collection of independent random variables called market factors. With each such "X-factor" we associate a market information process, the values of which are accessible to market agents. Each information process is a sum of two terms; one contains true information about the value of the market factor; the other represents "noise". The...

46. On the Computational Complexity of MCMC-based Estimators in Large Samples - Belloni, Alexandre; Chernozhukov, Victor
In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the Laplace-Bernstein-Von Mises central limit theorem, which states that in large samples the posterior or quasi-posterior approaches a normal density. Using this observation, we establish polynomial bounds on the computational complexity of general Metropolis random walks methods in large samples. Our analysis covers cases, where the underlying log-likelihood or extremum criterion function is possibly non-concave, discontinuous, and of increasing dimension. However, the central limit theorem restricts the deviations from continuity and log-concavity of the log-likelihood or extremum...

47. Inference on Eigenvalues of Wishart Distribution Using Asymptotics with respect to the Dispersion of Population Eigenvalues - Sheena, Yo; Takemura, Akimichi
In this paper we derive some new and practical results on testing and interval estimation problems for the population eigenvalues of a Wishart matrix based on the asymptotic theory for block-wise infinite dispersion of the population eigenvalues. This new type of asymptotic theory has been developed by the present authors in Takemura and Sheena (2005) and Sheena and Takemura (2007a,b) and in these papers it was applied to point estimation problem of population covariance matrix in a decision theoretic framework. In this paper we apply it to some testing and interval estimation problems. We show that the approximation based on this type of asymptotics is generally much better...

48. Structural adaptation via $L_p$-norm oracle inequalities - Goldenhsluger, A.; Lepski, O.
In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the underlying function. The problem of structural adaptation is stated as the problem of selection from a given collection of estimators. We develop a general selection rule and establish for it global oracle inequalities under arbitrary $\rL_p$--losses. These results are applied for adaptive estimation in the additive multi--index model.

49. A universal procedure for aggregating estimators - Goldenshluger, A.
In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators ${\cal F}$ built on the basis of available observations. The goal is to construct a new estimator whose risk is as close as possible to that of the best estimator in the family. We propose a general aggregation scheme that is universal in the following sense: it applies for families of arbitrary estimators and a wide variety of models and global risk measures. The procedure is based on comparison of empirical estimates of certain linear functionals with estimates induced by the family ${\cal F}$. We derive...

50. Analytic crossing probabilities for certain barriers by Brownian motion - Kahale, Nabil
We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval [0,T] via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class of barriers on [0,T] by proving a Schwartz distribution version of the method of images. Analytic expressions for crossing probabilities and related densities are given for new explicit and semi-explicit barriers.

51. On bounds and algorithms for frequency synchronization for collaborative communication systems - Parker, Peter A.; Mitran, Patrick; Bliss, Daniel W.; Tarokh, Vahid
Cooperative diversity systems are wireless communication systems designed to exploit cooperation among users to mitigate the effects of multipath fading. In fairly general conditions, it has been shown that these systems can achieve the diversity order of an equivalent MISO channel and, if the node geometry permits, virtually the same outage probability can be achieved as that of the equivalent MISO channel for a wide range of applicable SNR. However, much of the prior analysis has been performed under the assumption of perfect timing and frequency offset synchronization. In this paper, we derive the estimation bounds and associated maximum likelihood estimators for frequency offset estimation in a cooperative communication...

52. Multiple pattern matching: A Markov chain approach - Lladser, Manuel; Betterton, M. D.; Knight, Rob
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches in genomewide searches, and for predicting whether a given function has evolved many times in different species or arose from a single common ancestor. In this manuscript, we review in an integrated and self-contained manner some basic concepts of automata theory, generating functions and transfer matrix methods that are relevant to pattern analysis in biological sequences. We formalize, in a general framework, the concept of Markov chain embedding to analyze patterns in random strings produced...

53. Density Estimation of Censored Data with Infinite-Order Kernels - Berg, Arthur; Politis, Dimitris N.
Higher-order accurate density estimation under random right censorship is achieved using kernel estimators from a family of infinite-order kernels. A compatible bandwidth selection procedure is also proposed that automatically adapts to level of smoothness of the underlying lifetime density. The combination of infinite-order kernels with the new bandwidth selection procedure produces a considerably improved estimate of the lifetime density and hazard function surpassing the performance of competing estimators. Infinite-order estimators are also utilized in a secondary manner as pilot estimators in the plug-in approach for bandwidth choice in second-order kernels. Simulations illustrate the improved accuracy of the proposed estimator against other nonparametric estimators of the density and hazard function.

54. On the Marginal Distributions of Stationary AR(1) Sequences - Satheesh, S; Sandhya, E
In this note we correct an omission in our paper (Satheesh and Sandhya, 2005) in defining semi-selfdecomposable laws and also show with examples that the marginal distributions of a stationary AR(1) process need not even be infinitely divisible.

55. Quantile and Probability Curves Without Crossing - Chernozhukov, Victor; Fernandez-Val, Ivan; Galichon, Alfred
The most common approach to estimating conditional quantile curves is to fit a curve, typically linear, pointwise for each quantile. Linear functional forms, coupled with pointwise fitting, are used for a number of reasons including parsimony of the resulting approximations and good computational properties. The resulting fits, however, may not respect a logical monotonicity requirement -- that the quantile curve be increasing as a function of probability. This paper studies the natural monotonization of these empirical curves induced by sampling from the estimated non-monotone model, and then taking the resulting conditional quantile curves that by construction are monotone in the probability. This construction of monotone quantile curves may be seen...

56. Improving Estimates of Monotone Functions by Rearrangement - Chernozhukov, Victor; Fernandez-Val, Ivan; Galichon, Alfred
Suppose that a target function is monotonic, namely, weakly increasing, and an original estimate of the target function is available, which is not weakly increasing. Many common estimation methods used in statistics produce such estimates. We show that these estimates can always be improved with no harm using rearrangement techniques: The rearrangement methods, univariate and multivariate, transform the original estimate to a monotonic estimate, and the resulting estimate is closer to the true curve in common metrics than the original estimate. We illustrate the results with a computational example and an empirical example dealing with age-height growth charts.

57. Recovery of edges from spectral data with noise -- a new perspective - Engelberg, Shlomo; Tadmor, Eitan
We consider the problem of detecting edges in piecewise smooth functions from their N-degree spectral content, which is assumed to be corrupted by noise. There are three scales involved: the "smoothness" scale of order 1/N, the noise scale of order $\eta$ and the O(1) scale of the jump discontinuities. We use concentration factors which are adjusted to the noise variance, $\eta$ >> 1/N, in order to detect the underlying O(1)-edges, which are separated from the noise scale, $\eta$ << 1.

58. Semiparametric efficiency in GMM models with auxiliary data - Chen, Xiaohong; Hong, Han; Tarozzi, Alessandro
We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. The auxiliary sample can be independent of the primary sample, or can be a subset of it. For both cases, we derive bounds when the probability of missing data given the proxy variables is unknown, or known, or belongs to a correctly specified parametric family. We find that the conditional probability is...

59. Support vector machine for functional data classification - Rossi, Fabrice; Villa, Nathalie
In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In fact most of the traditional data analysis tools for regression, classification and clustering have been adapted to functional inputs under the general name of functional Data Analysis (FDA). In this paper, we investigate the use of Support Vector Machines (SVMs) for functional data analysis and we focus on the problem of curves discrimination. SVMs are large margin classifier tools based on implicit non linear mappings of the considered data into high dimensional spaces thanks to...

60. Un r\'esultat de consistance pour des SVM fonctionnels par interpolation spline - Villa, Nathalie; Rossi, Fabrice
This Note proposes a new methodology for function classification with Support Vector Machine (SVM). Rather than relying on projection on a truncated Hilbert basis as in our previous work, we use an implicit spline interpolation that allows us to compute SVM on the derivatives of the studied functions. To that end, we propose a kernel defined directly on the discretizations of the observed functions. We show that this method is universally consistent.

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