Semiparametric linear regression with censored data and stochastic regressors

We propose three new estimation procedures in the linear regression model with randomly-right censored data when the distribution function of the error term is unspecified, regressors are stochastic and the distribution function of the censoring variable is not necessarily the same for all observations ("unequal censoring"). The proposed procedures are derived combining techniques which produce accurate estimates with "equal censoring" with kernel-conditionalı Kaplan-Meier estimates. The performance of six estimation procedures (the three proposed methods and three alternative ones) is compared by means of some Monte Carlo experiments

Action Principles for Transgression and Chern-Simons AdS Gravities

Chern-Simons gravities are theories with a lagrangian given by a Chern-Simons form constructed from a space-time gauge group. In previous investigations we showed that, for some special field configurations that are solutions of the field equations, the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, automatically yields the boundary terms required to regularize the theory, giving finite conserved charges and black hole thermodynamics. Further work by other researchers showed that one of the action functionals considered in the above mentioned work yields a well defined action principle in the metric (zero torsion) case and for asymptotically Anti de Sitter (AdS) space-times. In the present work we consider several action functionals for Chern-Simons AdS gravity constructed from Transgression forms, and show the action principles to be well defined and the Noether charges and Euclidean action to be finite for field configurations satisfying only that the gauge field curvature (field strength) for the AdS gauge group is asymptotically finite. For that purpose we consider an asymptotic expansion of the vielbein and spin connection that may be regarded as a perturbation of an AdS space-time, but allowing a non zero torsion. Our results are of potential interest for Lovelock gravity theories, as it has been shown that the boundary terms dictated by the transgressions for Chern-Simons gravities are also suitable to regularize Lovelock theories.Comment: The review sections of the present paper may have some overlap with the work of the same author arXiv:1010.5110 (which has not been published in a journal). Version 2: Subsection 6.1 clarifying action principle added, references adde

Alternative approach to the regularization of odd dimensional AdS gravity

In this paper I present an action principle for odd dimensional AdS gravity which consists of introducing another manifold with the same boundary and a very specific boundary term. This new action allows and alternative approach to the regularization of the theory, yielding a finite euclidean action and finite conserved charges. The choice of the boundary term is justified on the grounds that an enhanced 'almost off-shell' local AdS/Conformal symmetry arises for that very special choice. One may say that the boundary term is dictated by a guiding symmetry principle. Two sets of boundary conditions are considered, which yield regularization procedures analogous to (but different from) the standard 'background substraction' and 'counterterms' regularization methods. The Noether charges are constructed in general. As an application it is shown that for Schwarszchild-AdS black holes the charge associated to the time-like Killing vector is finite and is indeed the mass. The Euclidean action for Schwarzschild-AdS black holes is computed, and it turns out to be finite, and to yield the right thermodynamics. The previous paragraph may be interpreted in the sense that the boundary term dictated by the symmetry principle is the one that correctly regularizes the action.Comment: References added, typos corrected.Content changes: Title (Alternative by Unified), Abstract, Introduction and Sections changed emphasizing and discussing differences with standard Counterterms and Background Subtraction regularization frameworks. Deeper and more detailed discussion of the enhanced symmetry of the proposed action and the required fall-off condition

Local calibrations for minimizers of the Mumford-Shah functional with a triple junction

We prove that, if u is a function satisfying all Euler conditions for the Mumford-Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions on the boundary of U. The proof is obtained by using the calibration method.Comment: 28 pages, 4 figure

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed- En aquest document de treball es proposa un procediment iteratiu per minimitzar la suma de quadrats dels errors que evita la naturalesa no lineal de l¿estimació del paràmetre del model mitjana mòbil de primer ordre i proporciona una expressió de l¿estimador en forma tancada. A continuació es discuteixen les propietats asimptòtiques del mètode i es demostra la consistència de l¿estimador per mínims quadrats lineals per a valors del paràmetre dins l¿interval obert (¡1; 1) : També es duen a terme diversos experiments de Monte Carlo per tal de comparar les propietats mostrals de ¿estimador per mínims quadrats lineals amb el seu homòleg no lineal pel cas condicional i pel no condicional. Finalment, es discuteixen alguns exemple

Two-stage index computation for bandits with switching penalties I : switching costs

This paper addresses the multi-armed bandit problem with switching costs. Asawa and Teneketzis (1996) introduced an index that partly characterizes optimal policies, attaching to each bandit state a "continuation index" (its Gittins index) and a "switching index". They proposed to jointly compute both as the Gittins index of a bandit having 2n states — when the original bandit has n states — which results in an eight-fold increase in O(n^3) arithmetic operations relative to those to compute the continuation index alone. This paper presents a more efficient, decoupled computation method, which in a first stage computes the continuation index and then, in a second stage, computes the switching index an order of magnitude faster in at most n^2+O(n) arithmetic operations. The paper exploits the fact that the Asawa and Teneketzis index is the Whittle, or marginal productivity, index of a classic bandit with switching costs in its restless reformulation, by deploying work-reward analysis and PCL-indexability methods introduced by the author. A computational study demonstrates the dramatic runtime savings achieved by the new algorithm, the near-optimality of the index policy, and its substantial gains against the benchmark Gittins index policy across a wide range of instances