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Accelerated Monte Carlo estimation of exceedance probabilities under monotonicity constraints

Nicolas Bousquet (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

The problem of estimating the probability p = P ( g ( X ) ≤ 0 ) is considered when X represents a multivariate stochastic input of a monotonic function g . First, a heuristic method to bound p , originally proposed by de Rocquigny (2009), is formally described, involving a specialized design of numerical experiments. Then a statistical estimation of p is considered based on a sequential stochastic exploration of the input space. A maximum likelihood estimator of p build from successive dependent Bernoulli data is defined...

Adaptive tests of homogeneity for a Poisson process

M. Fromont, B. Laurent, P. Reynaud-Bouret (2011)

Annales de l'I.H.P. Probabilités et statistiques

We propose to test the homogeneity of a Poisson process observed on a finite interval. In this framework, we first provide lower bounds for the uniform separation rates in -norm over classical Besov bodies and weak Besov bodies. Surprisingly, the obtained lower bounds over weak Besov bodies coincide with the minimax estimation rates over such classes. Then we construct non-asymptotic and non-parametric testing procedures that are adaptive in the sense that they achieve, up to a possible logarithmic...

An algorithm for QMC integration using low-discrepancy lattice sets

Vojtěch Franěk (2008)

Commentationes Mathematicae Universitatis Carolinae

Many low-discrepancy sets are suitable for quasi-Monte Carlo integration. Skriganov showed that the intersections of suitable lattices with the unit cube have low discrepancy. We introduce an algorithm based on linear programming which scales any given lattice appropriately and computes its intersection with the unit cube. We compare the quality of numerical integration using these low-discrepancy lattice sets with approximations using other known (quasi-)Monte Carlo methods. The comparison is based...

An asymptotically unbiased moment estimator of a negative extreme value index

Frederico Caeiro, M. Ivette Gomes (2010)

Discussiones Mathematicae Probability and Statistics

In this paper we consider a new class of consistent semi-parametric estimators of a negative extreme value index, based on the set of the k largest observations. This class of estimators depends on a control or tuning parameter, which enables us to have access to an estimator with a null second-order component of asymptotic bias, and with a rather interesting mean squared error, as a function of k. We study the consistency and asymptotic normality of the proposed estimators. Their finite sample...

An empirical evaluation of small area estimators.

Álex Costa, Albert Satorra, Eva Ventura (2003)

SORT

This paper compares five small area estimators. We use Monte Carlo simulation in the context of both artificial and real populations. In addition to the direct and indirect estimators, we consider the optimal composite estimator with population weights, and two composite estimators with estimated weights: one that assumes homogeneity of within area variance and squared bias and one that uses area-specific estimates of variance and squared bias. In the study with real population, we found that among...

Analysis on the individual efficiency prediction in the composed error frontier model. A Monte Carlo study.

Rafaela Dios Palomares, Antonio Ramos Millán, José Angel Roldán-Casas (2002)

Qüestiió

This study seeks to analyse some important questions related to the Stochastic Frontier Model, such as the method proposed by Jondrow et al (1982) to separate the error term into its two components, and the measure of efficiency given by Timmer (1971). To this purpose, a Monte Carlo experiment has been carried out using the Half-Normal and Normal-Exponential specifications throughout the rank of the γ parameter. The estimation errors have been eliminated, so that the intrinsic variability of the...

Application of MCMC to change point detection

Jaromír Antoch, David Legát (2008)

Applications of Mathematics

A nonstandard approach to change point estimation is presented in this paper. Three models with random coefficients and Bayesian approach are used for modelling the year average temperatures measured in Prague Klementinum. The posterior distribution of the change point and other parameters are estimated from the random samples generated by the combination of the Metropolis-Hastings algorithm and the Gibbs sampler.

Approximate maximum likelihood estimation for a spatial point pattern.

Jorge Mateu, Francisco Montes (2000)

Qüestiió

Several authors have proposed stochastic and non-stochastic approximations to the maximum likelihood estimate for a spatial point pattern. This approximation is necessary because of the difficulty of evaluating the normalizing constant. However, it appears to be neither a general theory which provides grounds for preferring a particular method, nor any extensive empirical comparisons. In this paper, we review five general methods based on approximations to the maximum likelihood estimate which have...

Assessing influence in survival data with a cured fraction and covariates.

Edwin M. M. Ortega, Vicente G. Cancho, Victor Hugo Lachos (2008)

SORT

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to...

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